literature review on cash management pdf

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• Published: 15 March 2023

A multidimensional review of the cash management problem

• Francisco Salas-Molina   ORCID: orcid.org/0000-0002-1168-7931 1 ,
• Juan A. Rodríguez-Aguilar 2 &
• Montserrat Guillen 3  

Financial Innovation volume  9 , Article number:  67 ( 2023 ) Cite this article

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In this paper, we summarize and analyze the relevant research on the cash management problem appearing in the literature. First, we identify the main dimensions of the cash management problem. Next, we review the most relevant contributions in this field and present a multidimensional analysis of these contributions, according to the dimensions of the problem. From this analysis, several open research questions are highlighted.

Introduction

Cash managers must make daily decisions about the number of transactions between cash holdings and any other type of available investment asset. On the one hand, a certain amount of cash must be kept for operational and precautionary purposes. On the other hand, idle cash balances may be invested in short-term assets such as interest-bearing accounts or treasury bills for profit. Since Baumol ( 1952 ), several cash management models have been proposed to address the cash management problem(CMP).

Keynes ( 1936 ) initially identified three motives for holding cash: the transaction motive, the precautionary motive and the speculative motive. Other authors have added other motives for holding cash, such as the agency motive (Jensen 1986 ) or tax motive (Foley et al. 2007 ). More recently, other authors have highlighted other determinants of corporate cash policies (e.g., Gao et al. ( 2013 ) and Pinkowitz et al. ( 2016 )). As a result, the first objective of this study is to review the literature related to CMP from an economic and financial perspective, derived from the analysis of the main motives for holding cash.

While most cash management literature stems from the seminal paper by Baumol ( 1952 ), many cash management works approach CMP from a decision-making perspective. Our second objective is to review the literature related to CMP from a decision-making perspective, considering models proposed by different researchers to deal with cash when the ultimate goal is to elicit a cash management policy, namely, a temporal sequence of transactions between accounts.

To the best of our knowledge, only three surveys on cash management have been published since the 1950s. Gregory ( 1976 ) covered the beginning of the cash management literature including the important works by Baumol ( 1952 ) and Miller and Orr ( 1966 ). Ten years later, Srinivasan and Kim ( 1986 ) extended the analysis to models not considered by Gregory ( 1976 ). Finally, da Costa Moraes et al. ( 2015 ) reviewed several stochastic models since the 1980s. However, there is a lack of taxonomy for classifying models and identifying open research questions in cash management.

Within the context of CMP, from a decision-making perspective, we propose a taxonomy based on the main dimensions of the cash management problem: (i) the model deployed, (ii) the type of cash flow process considered, (iii) the particular cost functions used, (iv) the objectives pursued by cash managers, (v) the method used to set the model and solve the problem, and (vi) the number of accounts considered. These six dimensions provide a sound framework to classify the cash management models proposed in the literature. Here, we focus on the most relevant models in terms of number of citations. For a comprehensive review, we refer interested readers to Gregory ( 1976 ), da Costa Moraes et al. ( 2015 ) and Srinivasan and Kim ( 1986 ).

Our taxonomy helps researchers use a common framework to establish cash management areas. In addition, our multidimensional analysis enhances the understanding of the cash management problem, making it easier to identify open research questions. Note that the multidimensional framework described in this paper is not limited to the six dimensions mentioned above. Researchers may extend the number of dimensions, thereby enriching the analysis of the cash management problem.

The remainder of this paper is organized as follows. In " Motives for holding cash and related literature " in section, we consider the main motives for holding cash and review the literature related to CMP from an economic and financial perspective. In " A multidimensional taxonomy of the cash management problem " in section, we introduce and motivate the six dimensions of the CMP that define our taxonomy proposal. In " A review of the main contributions to the cash management problem " in section, we review the most relevant contributions to CMP from a decision-making perspective. Next, " A multidimensional analysis of the cash management problem " in section, we perform a comparative analysis of alternative cash management models that are directly linked to " Open research questions in cash management " in section, which identifies several open research questions in cash management. Finally, " Concluding remarks " in section concludes the paper.

Motives for holding cash and related literature

In this section, we consider the main motives for holding cash and review the literature related to CMP from an economics and finance perspective. We first consider the three motives for holding cash, initially identified by Keynes ( 1936 ), as follows:

The transaction motive, which is the need for cash for the current transaction of personal and business exchanges.

The precautionary motive, which is the desire for security as the future cash equivalent of a certain proportion of total resources acts as a financial reserve.

The speculative motive or the object of securing profit from knowing better than the market what the future will bring forth. The goal is to take advantage of future investment opportunities.

Later, Jensen ( 1986 ) argued that managers tend to accumulate cash rather than increase payouts to shareholders because of agency motives. Cash holdings may act as a buffer to cover eventual bad management decisions. One possible reason for this behavior is information asymmetry. Information is distributed asymmetrically throughout the organization; thus, managers usually have an advantage over shareholders in handling specific events because of information asymmetry (Eisenhardt 1989 ; Dierkens 1991 ). In addition, managers have an incentive to make the company bigger when compensation is linked to the size of the company, even when the company has poor investment opportunities. The motive for holding cash stems from the financial implications of agency theory (Jensen and Meckling 1976 ; Fama 1980 ; Fama and Jensen 1983 ; Eisenhardt 1989 ). In this theory, the firm is viewed as a set of contracts among the factors of production, in which each one is motivated by self-interest (Fama 1980 ). Consequently, the relationship between corporate managers (including cash managers) and owners presents friction due to conflicts of interest. The concept of agency costs defined by Jensen and Meckling ( 1976 ) is derived from an agency relationship in which managers and owners present divergences that result in monitoring costs, bonding costs to avoid certain actions, and other residual losses. One of these divergences relates to cash holdings. For example, consider that cash outflows to shareholders in the form of dividends reduce resources under managers’ control.

Kaplan and Zingales ( 1997 ) investigated the relationship between sensitivity of investment to cash flow and financing constraints, expressed as the differential cost between internal and external finance. They found that even though investment is sensitive to cash flow for the vast majority of firms analyzed, investment-cash flow sensitivities do not increase monotonically with the degree of financing constraints. Most of the firms analyzed could increase their investment if they choose to do so, thus providing further evidence of the agency motive for holding cash. Contrary to what was thought before, the authors concluded that higher sensitivities cannot be interpreted as evidence that firms are more financially constrained.

Leland ( 1998 ) argued that the key insight by Jensen and Meckling ( 1976 ) is that the firm’s choice of risk may depend on capital structure, hence challenging the Modigliani and Miller ( 1958 , 1963 ) assumption that investment decisions are independent of capital structure. Consequently, Leland ( 1998 ) proposed integrating both approaches to derive the optimal capital structure of a firm. The model reflects the interaction of different cash flow policies, namely, financing decisions and investment risk strategies. When investment policies are chosen, agency costs appear as a critical element in the model.

Further evidence of the agency motive for holding cash can be found in Dittmar et al. ( 2003 ), Pinkowitz et al. ( 2006 ), Dittmar and Mahrt-Smith ( 2007 ) and Harford et al. ( 2008 ). More recently, but still within the context of agency theory, Tran ( 2020 ) emphasized how external factors, such as the economic cycle, including the eventual financial crisis, affect cash holdings. The author found that the 2008 global financial crisis decreased the controlling effect of shareholder rights on corporate cash holdings, regardless of any control agency mechanism. Following a similar line of research, Tekin ( 2020 ) and Tekin et al. ( 2021 ) examined whether an agency cost explanation is valid for cash holdings during and after the financial crisis. During a financial crisis, agency costs tend to be higher than usual and the agency motive for holding cash is greater. The authors assessed the role of governance in cash management in 26 Asian developing countries and found that firms with poor governance increased their cash levels after the financial crisis. They concluded that cash holdings had a substitution effect on governance due to changes in managers’ risk aversion perceptions.

Cash management relates to financial constraints. The impact of financial restrictions on optimal cash holdings in the context of a financial crisis was considered by Tekin and Polat ( 2020 ), who compared firms in a highly regulated market with firms in a relatively unregulated market in the United Kingdom. The authors found that less-regulated firms had a faster adjustment of cash over the period 2002-2017. However, these firms decreased their cash adjustment speed more than highly regulated firms did during the financial crisis. Using a sample of firms from 26 developing Asian economies from 1991 to 2016, Tekin ( 2022 ) recently showed that financially constrained firms increased their cash levels more than financially unconstrained firms after the 2008 global financial crisis. In summary, exogenous shocks such as financial crises represent an important external factor in cash management.

Conversely, Foley et al. ( 2007 ) identify the tax motive for holding cash. More precisely, they found that the U.S. corporations, that would incur tax consequences associated with repatriating foreign earnings, hold higher levels of cash. Bates et al. ( 2009 ) showed that the average cash-to-assets ratio for U.S. industrial firms doubled from 1980 to 2006. They argue that the precautionary motive for cash holdings plays an important role in explaining the increase in cash ratios. From an analysis of the literature, Bates et al. ( 2009 ) summarized two additional motives for holding cash:

The agency motive, which is the need for cash derived from conflicts of interest among managers and owners.

The tax motive, which is the desire to avoid tax consequences associated with repatriation of foreign earnings.

Gao et al. ( 2013 ) analyzed a sample of public and private U.S. firms during the period 1995-2011 to conclude that public firms hold more cash than private firms. By examining the drivers of cash policies for each group, the authors attribute this difference to the much higher agency costs in public firms. Using a similar period (1998–2011), Pinkowitz et al. ( 2016 ) showed that U.S. firms held more cash on average than similar foreign firms. However, they argued that country characteristics had negligible explanatory power for the differences in cash holdings between U.S. firms and their foreign twins. Graham and Leary ( 2018 ) included the historic perspective in the analysis by studying average and aggregate cash holdings of companies in the U.S. from 1920 to 2014. Corporate cash holdings doubled in the first 25 years of the sample before returning to 1920 levels by 1970. Since then, the average and aggregate patterns have diverged.

Interest rates and environmental and health motives have recently been included in cash holding analyses. Gao et al. ( 2021 ) highlighted a non-monotonic relation between corporate cash and both real and nominal interest rates in both aggregate and firm-level data. The authors argue that these results imply that interest rates are unlikely to be the cause of the recent increase in corporate cash. Tan et al. ( 2021 ) compared cash holdings before and after the Environmental Inspection Program in China during the period 2014-2018 for manufacturing firms included and non-included in the program. The results suggest that this environmental program enhanced cash management efficiency because firms included in the program accumulated less cash. Finally, Alvarez and Argente ( 2022 ) focused on the impact of COVID-19 in household’s cash management behavior, considering the choice of means of payment and the average size and frequency of cash withdrawals. The authors used data on ATM (automated teller machine) cash disbursements in Argentina, Chile, and the U.S. to show that the intensity of the virus increased transaction costs.

A multidimensional taxonomy of the cash management problem

Cash flow management concerns the efficient use of a company’s cash and short-term investments (Gregory 1976 ). Cash is then viewed as a stock, a buffer, such as an inventory of wheat or bolts. Holding cash has a cost because of it being idle but, at the same time, transferring idle money to alternative investments is also costly. How much money should companies keep to operate efficiently? Identifying an appropriate answer to this question is the main goal of CMP. However, several aspects and dimensions must be considered to establish the boundaries of the problem. Hereafter, we focus on the main dimensions of the cash management problem, defining a cash management problem taxonomy to classify past research and identify open research questions.

Cash management models

In an attempt to solve CMP, several cash management models have been proposed to control cash balances based on a set of levels or bounds. CMP was first proposed from an inventory control perspective by Baumol ( 1952 ) in a deterministic manner. Later, Miller and Orr ( 1966 ) followed a stochastic approach, assuming that cash balance changes are random. Many other models have been developed based on these two seminal works. Most previous models assume a set of bounds to control cash balances; however, alternative configurations are also suitable.

Cash flow process

Cash flow statistical characterization is also a key issue in understanding cash management. Separation between inflows and outflows, or receipts and disbursements, is the basic breakdown, but a more detailed separation can be helpful when trying to extract patterns from data. In this sense, Stone and Miller ( 1981 , 1987 ) suggest the utility of problem structuring, or breaking down a problem into different subproblems, to appropriately handle cash flow forecasting as a key task in cash management. In addition, common assumptions on the statistical properties of cash flows include (i) normality, meaning that its values are centered around the average following a Gaussian distribution; (ii) independence, meaning that its values are not correlated with each other; and (iii) stationarity, meaning that its mean and variance are constant with time. However, little empirical evidence on the statistical properties of cash flow has been provided, with the exception of Mullins and Homonoff ( 1976 ), Emery ( 1981 ), Pindado and Vico ( 1996 ).

Costs in cash management

The main objective of managing cash is to keep the amount of available cash as low as possible while still keeping the company operating efficiently. Additionally, companies may place idle cash in short-term investments (Ross et al. 2002 ). Thus, the cash management problem can be viewed as a trade-off between holding and transaction costs. On the one hand, holding costs are usually opportunity costs due to idle cash that can be allocated to alternative investments. Holding too much cash is inefficient but holding too little may result in high shortage costs. On the other hand, transaction costs are associated with the movement of cash from/into a cash account into/from any other short-term available asset, such as treasury bills and other marketable securities. In summary, if a company tries to keep balances too low, holding costs will be reduced, but undesirable situations of shortage will force the sale of available marketable securities, thereby increasing transaction costs. By contrast, if the balance is too high, low trading costs will be incurred due to unexpected cash flow, but the company will carry high holding costs because no interest is earned on cash. Therefore, the company must optimize its target cash balance.

Desired objectives

In cash management literature, the focus is typically placed on a single objective, namely, cost. Except for Zopounidis ( 1999 ), Salas-Molina et al. ( 2018 ), cash management and multi-criteria decision-making are not usually linked concepts in financial literature. However, risk management is an important task in decision-making, and since different cash strategies entail different degrees of risk, a quantitative approach to measure risk is required. Furthermore, due to the different degrees of risk that firms are willing to accept, risk preferences are also an important issue for decision-makers.

Solving the cash management problem

Cash management poses a general optimization problem, namely, determining a policy that optimizes objective functions. However, several different techniques have been used to solve this optimization problem, ranging from mathematical programming, such as dynamic programming (Eppen and Fama 1968 ; Penttinen 1991 ) and control theory methods Sethi and Thompson ( 1970 ), to approximate techniques such as genetic algorithms (Gormley and Meade 2007 ; da Costa Moraes and Nagano 2014 ). An important question regarding alternative solvers is the optimality of solutions, which is a desired objective, but must be balanced with computational and deployment costs.

Managing multiple bank accounts

In cash management literature, cash management systems with multiple bank accounts have received little attention from the research community, with the exception of Baccarin ( 2009 ). However, cash management systems with multiple bank accounts are a rule, rather than an exception, in most firms.

Once the six main dimensions of the CMP are established, namely, models, cash flow, costs, objectives, solvers and number of accounts, we are in a position to review the most relevant cash management models proposed in the literature.

A review of the main contributions to the cash management problem

Although the advancement of a specific research topic is gradual rather than sharp, the history of CMP is long enough to distinguish at least two main periods: the classical period up to 2000 and the modern period from 2000 onwards. Since the initial inventory approach to CMP by Baumol ( 1952 ), the classical period is characterized by the common two-assets framework, linear cost functions, and the minimization of cost as the single goal of cash managers. However, a multidimensional approach to CMP emerges with Baccarin ( 2009 ), who considered cash management systems with multiple bank accounts and non-linear cost functions. We argue that this change in perspective and implied complexity gives rise to a new period in the study of CMP. In the following sections, we present a review of the most relevant works on CMP from Baumol ( 1952 ) to Baccarin ( 2009 ) and consider the most recent contributions. We respect the authors’ notations and clarify issues regarding notation when necessary for comparison purposes.

Baumol ( 1952 )

The inventory control approach to the cash management problem was introduced by Baumol ( 1952 ). The author expected that inventory theory and monetary theory would learn from one another. However, several important assumptions were made to, using the exact Baumol’s words, abstract from precautionary and speculative demands. The most important was that transactions were perfectly foreseen and occurred in a steady stream. Baumol assumed that an outflow of T dollars occurred for a given period in a steady stream. To offset these outflows, inflows can be obtained by borrowing or withdrawing from an investment at a cost of i dollars per dollar per period. An additional assumption is made by considering that these withdrawals are performed in many C dollars, evenly spaced in time, with a fixed cost of b dollars (see Fig. 1 ).

The Baumol model

Under these constraints, cash managers make T / C withdrawals for a given period, and the total cost is given by

where the first part of the equation is the number of transactions multiplied by the unitary fixed cost of each transaction and the second part is the average cash balance multiplied by the cost of holding this balance. Then, the goal for cash managers is to choose C such that Eq. ( 1 ) is minimized. Setting the derivative of the total cost with respect to C to zero, we obtain the value of C that minimizes ( 1 ) as follows:

The steady stream of payments and absence of receipts during the relevant period make this model impractical in many real applications. It was “only a suggestive oversimplification,” in the author’s own words. However, the first step in the inventory control approach to the cash management problem was performed. Interestingly, Baumol also envisioned the inherent task of forecasting cash flow by stating that with sufficient foresight, if receipts can meet payments, savings in the use of cash can be achieved.

Summarizing, Baumol ( 1952 ) initiated the inventory approach to the cash management problem proposing a deterministic model with uniform cash flows, with the objective of minimizing fixed transaction and holding costs for a single bank account using analytical methods.

Tobin ( 1956 )

Tobin argued that cash requirements depend inversely on the interest rate for a given volume of transactions, governed by the lack of synchronization of receipts and disbursements. The higher the lack of synchronization, the higher the need for transaction balances. However, there is no need to hold a cash balance. Instead, cash managers have the opportunity to maintain balances in assets with higher yields, such as bonds or marketable securities. When cash is needed, these assets could be shifted to cash again for payments. Consequently, it is likely that the amount of cash held for transaction purposes is inversely related to the interest rates of such alternative assets.

Given an interest rate r , the problem is to find the relationship between what is held in cash and what is held in alternative assets to maximize interest earnings, net of transaction costs. At the beginning of each period \(t=0\) , an amount Y is held by the cash manager that is uniformly disbursed until the end of period \(t=1\) when no cash is available, as shown in Fig. 2 . Thus, the total transaction balance is \(T(t)=Y(1-t)\) with \(0 \ge t \ge 1\) . However, this total T ( t ) can be divided between cash C ( t ) and bonds B ( t ) such that \(T(t)=C(t)+B(t)\) , where B ( t ) yields interest r per time period. Three different questions are then faced by Tobin: (i) given r and a fixed number n of transactions, determine the optimal timing and amounts to be held in cash and bonds; (ii) given r but a variable number n of transactions, determine the optimal \(n^*\) ; and (iii) how does \(n^*\) depends on r ?

The Tobin model

Considering transaction x between bonds and cash, the transaction cost is given by \(a + b \cdot x\) , with \(a,b >0\) . Then, for the general case, Tobin proves that the average number of bonds is given by

where \(n \ge 2\) and \(r \ge 2b\) . In order to determine the optimal number of transactions, the next profit function is maximized:

that is a decreasing function of n . Then, the optimal number of transactions \(n^*\) is greater than two when \(1/12 Y r (1 - 2b/r)^2 \ge a\) holds true. Finally, the relationship between the optimal number of transactions \(n^*\) and interest rate is given by Eq. ( 3 ). Since \(B_n\) is an increasing function of n , and \(n^*\) directly varies with r , the optimal proportion of bonds also directly varies with r ; consequently, the proportion of cash inversely varies with  r for sufficiently high rates.

Smith ( 1986 ) proposed a Dynamic Baumol-Tobin Model of Money Demand . However, this Baumol-Tobin model is more closely related to the Constantinides and Richard ( 1978 ) model than with the initial proposals by Baumol ( 1952 ) and Tobin ( 1956 ). More recently, Mierzejewski ( 2011 ) followed Tobin’s approach, according to which companies hold cash as a behavior towards risk, to propose a theoretical model of equilibrium in cash-balance markets, which is beyond the scope of this thesis.

Summarizing the above, the Tobin ( 1956 ) model is also a deterministic model dealing with a uniform cash flow such as the Baumol ( 1952 ) but incorporating the interest rate as a key parameter. In addition, Tobin considered not only fixed costs, but also variable transaction costs between two alternative assets, namely, bonds and cash. The goal was to minimize costs, and an analytical solution was provided.

Miller and Orr ( 1966 )

Miller and Orr introduced the stochastic cash balance problem by relying on the fact that the cash balance does not fluctuate steadily but rather irregularly for many companies, resulting in an impractical application of the Baumol model. Miller and Orr developed a simple model following an opposite approach to Baumol by considering stochastic cash flows. From a predictability point of view, Miller and Orr shifted from the perfect knowledge of cash flows in Baumol model to cash flows generated by a stationary random walk, from a deterministic approach to completely stochastic cash flows. They considered cash flows to be characterized as a sequence of independent and symmetric Bernoulli trials. They supposed that the cash balance will either increase or decrease by m dollars with probability \(p=1/2\) . The main features of this approach are independence, stationarity, zero-drift, and the absence of regular swings in cash flows. Moreover, they ignored shortages and variable transaction costs.

In their first attempt to deal with the corporate cash management problem, they assumed that companies seek to minimize the long-term average costs of managing the cash balance under a simple policy. This policy sets a lower bound, zero, and an upper bound, h , where cash balance is allowed to wander between the lower and upper levels. We say that the Miller and Orr ( 1966 ) is a Bound Based Model (BBM). Apart from the cash balance, the model also assumes the existence of a second asset of any kind, such as interest bearing assets or marketable securities grouped in a portfolio of investments that are easily transformed into cash at the company’s convenience. The policy implies that, when the upper bound reaches a withdrawal transfer, the balance is restored to a target level of z . Similarly, when the cash balance reaches zero, a positive transfer will be made to restore the balance to z , as shown in Fig. 3 .

The Miler-Orr model

Although Miller and Orr set the lower limit to zero in their work, in practice, a real cash manager should set the lower limit above zero for precautionary motives. This lower limit represents a safety cash buffer, and its selection depends on the level of risk the company is willing to accept. This model variation can be found in (Ross et al. 2002 ), which sets a lower limit l and an upper bound h . When h is reached, a withdrawal transfer is performed to restore the balance to the target level of z . Similarly, when the cash balance reaches l , a positive transfer is made to restore the balance to z . Formally, the transfer occurring at time t , \(x_t\) , is elicited by comparing the current cash balance, \(b_{t-1}\) , with the lower and upper bounds:

To obtain the limits, once the cash manager sets the lower limit l , the optimal values of the policy parameters h and z are derived from the expected cost per day over any planning horizon of T days, given by

where E ( c ) is the expected cost per day, E ( N ) is the expected number of transfers during the planning period T , \(\gamma\) is the cost per transfer, E ( M ) is the average daily cash balance, and v is the daily interest rate earned on the portfolio as the opportunity cost of idle cash. By letting \(Z=h-z\) , the problem can be stated in terms of the variance of the net cash flow as:

where the first part of the equation is the transfer cost term, and the second part is the holding cost term. The average cash balance is \((h+z)/3\) . Hence, the optimal parameters are given by

or in terms of the original parameters

The equivalent equations for the case of a lower bound ( l ) distinct from zero can easily be derived, as presented in Ross et al. ( 2002 ), to obtain

The major implication and main novelty of this model in comparison to the Baumol model is the presence of the observable variance of the net daily cash flow. As in the case of the Baumol model, the greater the transfer cost ( \(\gamma\) ), the higher the target cash balance ( z ), and the greater the daily interest rate ( v ), the lower the target cash balance ( z ). However, the greater the uncertainty of the net daily cash flow, measured by \(\sigma ^2\) , the higher the target cash balance ( z ), and the higher the difference between the lower bound ( l ) and the higher bound ( h ). This represents the first step towards a more practical approach to the corporate cash management problem because common sense shows that the greater the uncertainty, the greater the chance that the balance will drop below the lower bound.

Several extensions of the model have been considered to incorporate systematic drift in the cash balance and to allow for more than one portfolio asset with different transfers and holding costs. Despite the assumption of the totally stochastic mechanism of cash flow, the authors pointed out the presence of both stochastic and deterministic, or at least highly predictable, elements in cash flow, such as payroll disbursements or dividend payments. However, they argued that the gains from exploiting any cash flow patterns are by no means sufficiently large to offset the added costs of model development and implementation.

In summary, Miller and Orr ( 1966 ) was the first stochastic cash management model proposed in the literature. They introduced the concept of bounds or control limits, which are directly linked to the statistical properties of cash flows and are assumed to be random walks. Only fixed transaction costs were considered, and analytical solutions were provided for a single objective and cash account.

Eppen and Fama ( 1969 )

A variation of the Miller and Orr ( 1966 ) model was introduced by Eppen and Fama ( 1969 ) following a dynamic programming approach. However, it was a previous publication (Eppen and Fama 1968 ) which provided a complete analysis of the effect of variations in transfer, holding, and penalty costs on the optimal policies. The Eppen-Fama model is a generalization of the stochastic Miller-Orr model, in which transfer costs contain both fixed and variable components. They showed that if transfer costs have a fixed cost as well as a cost, proportional to the amount transferred, the optimal strategy is in the form of two limits ( u ,  d ) and two return points ( U ,  D ), one for each limit. In this model, when the cash balance reaches the upper bound ( d ), it is immediately restored to the upper return point ( D ), and when it reaches the lower bound ( u ), it is restored to the lower return point ( U ), as shown in Fig.  4 .

Eppen-Fama model representation with two return points

Following the Markovian approach, they assumed that the probability mass function of the transitions between different possible states is known and stationary. This assumption implies the process of discretization of the cash balance. At any point in time, the cash balance can be in one of N possible states, \(i=1,2,...N\) , each representing a discrete level of cash balance. The lowest level occurs in state 1 and the highest in state N , and each successive level differs by some constant R , for example 1000 €.

For the general case, two cost functions are defined. First, the transfer cost ( \(t_{i}^{k}\) ) caused by moving the cash balance from state i to state k :

where \(K_u\) and \(c_u\) are the fixed and variable components of a positive cash movement, respectively, and \(K_d\) and \(c_d\) are the fixed and variable components of a negative cash movement, respectively. Second, the holding or penalty cost ( L ( k )) associated with starting a period in state k can be defined as follows:

where \(c_p\) is the marginal penalty cost per period per R unit of cash, \(c_h\) is the marginal holding cost per period per R unit of cash, say 1000 €, and M is the minimum cash balance that must be maintained because of any condition required by banks. In the absence of this restriction, M is usually set to zero as the minimum cash balance required to be held in the bank account.

Recall that Miller and Orr ( 1966 ) suggests the use of two or three bounds. To account for fixed and variable transaction costs, Eppen and Fama ( 1968 ) proposed the use of four bounds. From an experimental perspective, the authors pointed out that higher dispersion in the probability distribution caused the outer bounds u and d and the return points U and D to be further away from zero. Therefore, in practical applications, it is highly recommended to carefully estimate the probability distribution, particularly in extremes. Moreover, when both the probability distribution and cost function are symmetric about zero, the optimal policies are symmetrical.

In summary, several interesting contributions on the practical side of the corporate cash balance problem were made by Eppen and Fama under the assumption of cash flow following a random walk. They considered both fixed and variable transaction costs, resulting in a policy based on four bounds aimed at minimizing costs. They proposed linear programming as a solver in Eppen and Fama ( 1968 ) and dynamic programming in Eppen and Fama ( 1969 ) for a single cash bank account.

Daellenbach ( 1971 )

Daellenbach proposes an improvement to the Eppen and Fama ( 1969 ) model, claiming that his model is a generalization of the Eppen-Fama model to situations where bank account overdrafts are not possible, and using two different sources of short-term funds, namely, marketable securities and short-term loans. Furthermore, in contrast to previous models, the probability distribution of cash flows is not necessarily stationary and the length of the review period may vary from period to period. Again, a decision about the adjustment of the cash balance must be made; however, in this model, an allocation decision about either marketable securities or borrowing transactions is also necessary. A dynamic programming approach was proposed for labeling periods in the planning horizon as \(n=N\) for the first period and \(n=1\) for the last period. Three state variables were then considered to describe the cash balance situation:

\(B_n\) or the cash balance at the beginning of period n carried forward from \(n+1\) .

\(Z_n\) or the borrowing balance at the beginning of period n carried forward from \(n+1\) .

\(S_n\) or the marketable securities balance at the beginning of period n carried forward from \(n+1\) .

If \(X_n\) and \(Y_n\) denote transactions in the form of borrowings or marketable securities, respectively, and \(R_n\) is the sum of uncontrollable cash transactions in period n with the probability density function \(f_n(r_n)\) , the following balance equation is used to link period \(n-1\) to period n :

subject to:

meaning that, (i) the initial cash balance before any adjustment has to be non-negative; (ii) the outstanding borrowing balance cannot be below zero; and (iii) marketable securities cannot be sold short.

According to the previous equations, the state variable set for the cash position at the beginning of period n , prior to any cash balance adjustment, is denoted by \(\Omega _n=(B_n,Z_n,S_n)\) , the decision variables are \((X_n,Y_n)\) , the total cost is the sum of (i) fixed and variable transaction costs for borrowing, (ii) fixed and variable transaction costs for marketable securities, (iii) interest cost on borrowings, (iv) returns on marketable securities (note that this is a negative cost or a benefit), and (v) penalty costs for cash shortages. These costs can be summarized as follows:

where \(H_1(X_n)\) is the borrowing cost function computed as

where \(b_{1}^{-}, b_{1}^{+}\) is the variable borrowing transaction costs for cash increases (+) and decreases (-), \(H_2(Y_n)\) is the marketable securities cost function computed as

where \(b_{2}^{-}, b_{2}^{+}\) are variable marketable security transaction costs for cash increases (+) and decreases (-), respectively; \(c_{1n}\) is the interest cost on ending loan balances; \(c_{2n}\) is the return on ending marketable securities holdings; \(L_n(B_n)\) is the expected cost of cash shortage incurred at the end of period n computed as:

where \(c_{3n}\) is the penalty for negative ending cash balances in period n .

Considering alternative funding sources, such as borrowings and marketable securities, introduces additional considerations on priorities based on feasible permutations of the cost coefficients as follows:

Case 1. If \(-b_{2}^{-}+c_2 \le -b_{1}^{-}+c_1 \le b_{1}^{+}+c_1 \le b_{2}^{+}+c_2\) , then borrowing transactions are preferred over marketable securities.

Case 2. If \(-b_{1}^{-}+c_1 \le -b_{2}^{-}+c_2 \le b_{2}^{+}+c_2 \le b_{1}^{+}+c_1\) , then marketable security transactions are preferred over borrowing.

Case 3. If \(-b_{2}^{-}+c_2 \le -b_{1}^{-}+c_1 \le b_{2}^{+}+c_2 \le b_{1}^{+}+c_1\) , then borrowing transactions are preferred over marketable securities for cash withdrawals, and marketable securities are preferred over borrowing for cash procurements.

Case 4. If \(-b_{1}^{-}+c_1 \le -b_{2}^{-}+c_2 \le b_{1}^{+}+c_1 \le b_{2}^{+}+c_2\) , then marketable securities are preferred over borrowing transactions for cash withdrawals, and borrowings are preferred over marketable securities for cash procurements.

Case 5. If \(-b_{2}^{-}+c_2 \le b_{2}^{+}+c_2 \le -b_{1}^{-}+c_1 \le b_{1}^{+}+c_1\) , then borrowing transactions are preferred over marketable securities for cash withdrawals, and marketable securities are preferred over borrowings for cash procurements.

As a result, the Daellenbach model can be regarded as an extension of the Eppen and Fama ( 1968 , 1969 ) model, but with four return points: \(\{U_{1n},D_{1n}\}\) denote the use of borrowings as the source of funds, and \(\{U_{2n},D_{2n}\}\) denote the use of marketable securities as the source of funds. The optimal policy gives preference to the source of funds dictated by the previous five cases based on the cost coefficients. If either constraint ( 19 ) or ( 20 ) prevents the completion of the transaction, then use the return point relevant to the other source of funds.

Subsequently, Daellenbach ( 1974 ) pointed out an important issue by posing the following general question: Are cash management models worthwhile? The objective was to determine the upper bounds of potential savings that could be realized by applying cash management models. In this study, a variant of the model in Daellenbach ( 1971 ) is proposed to consider fixed and variable transaction costs. In addition, a deterministic shortage cost function that charges negative cash balances at the end of the day is defined instead of the previous stochastic one. The main criticism of cash management models is based on the assumption of perfectly predictable cash flows. Any cost estimate based on perfect predictions will provide optimistic lower bounds for the actual cost incurred, which corresponds to determining what the optimal policy would have been given the actual cash flow. Using random normal simulations, the author estimated the upper bounds obtained by this variant of his cash management model on the performance of a hypothetical cash manager. The author concluded that the benefits of cash management optimization models were, in most cases, highly uncertain and offered a very small economic return.

In summary, Daellenbach ( 1971 ) used dynamic programming to provide a solution to the CMP as a set of control bounds but considered two available sources of funds, namely, marketable securities and short-term loans. In addition, the usual assumption on stationary cash flow was relaxed and fixed and variable transaction costs were considered as objectives to minimize.

Stone ( 1972 )

The use of forecasts and smoothing in control-limit models for cash management was proposed by Stone ( 1972 ). In this work, Stone first reviewed the assumptions of the Baumol ( 1952 ) and Miller and Orr ( 1966 ) models and pointed out a series of limitations of these models in real-world cash management situations. Stone argued that cash flows are neither completely certain, uniform, and continuous (as they are in the Baumol model) nor completely unpredictable (as they are in the Miller-Orr model). Most firms can forecast their cash flows. This is the first time that the concept of forecasting cash flows has been a key input to any cash management model. The author focused on the generally attempted tasks performed by cash managers. They usually:

Look ahead when buying and selling securities to incorporate data from their cash forecasts.

Smoothen cash flows by coordinating security maturities with predicted cash needs.

Buy the highest yielding securities subject to portfolio and liquidity constraints.

Maintain cash balances sufficient to meet banking requirements.

From these tasks, Stone derived the idea of including both forecasts and maturing securities in his model. The operation of this control-limit model is based on the ability to buy and sell securities of different maturities to reduce transaction costs by smoothing cash flows and thereby reducing the number of transactions. It is assumed that the current cash balance, \(CB_0\) , is known, and that a forecast of the net cash flow, \(E(C_t)\) , that will occur on each day t over the next k days is available. The expected level of cash balances k days from now is the sum of the current level of cash balances and the sum of k daily net cash flow. This can be expressed as

Alternatively, if the sum of net cash flows over the next k days is lumped into a single figure, the last equation can be rewritten as:

Next, a number of simple rules are proposed to be followed by cash managers to return to the desired target balance TB , based on two sets of control limits as shown in Fig. 5 . One set is defined by \(h_1\) and \(h_0\) as the upper and lower control limits for initiating considerations of a transactions. The other set is defined by \(h_1-\delta _1\) and \(h_0+\delta _0\) as the upper and lower limits, respectively, and determine if a transaction will actually be made.

Structure of the Stone model with two sets of limits

The set of rules followed by cash managers to operate the model are summarized as follows.

If the current cash balance \(CB_0\) is inside the control limits defined by \(h_1\) and \(h_0\) , no action is taken.

If the control limits \(h_1\) and \(h_0\) are exceeded, the forecasts over the next k days is considered to decide whether a transaction should be made.

If the expected cash balance in the next k days, \(E(CB_k)\) , exceed the control limits defined by \(h_1-\delta _1\) and \(h_0+\delta _0\) , a transaction is made to return the expected cash balance to the target level TB in k days.

No action is taken otherwise.

The innovation introduced by the Stone model is that when a transaction is made, the model returns the expected level of balance to the target level in k days rather than immediately returning the current balance to the target. Furthermore, the actual cash balance is the target plus the net cumulative forecast error. As \(K_t\) is the number of transactions to be made, these rules can be represented mathematically as follows:

Since the cash policy is fixed for a period of k-days, the use of forecasts forces the cash manager to monitor errors for k days after a transaction has occurred. However, the impact of the predictive accuracy of the forecasts on the policy performance was not evaluated. It is expected that a better prediction will lead to better policies, as hypothesized in Gormley and Meade ( 2007 ), and consequently, an evaluation of the impact of predictive accuracy is a mandatory step. Furthermore, efforts to improve predictive accuracy have associated costs that must be compared to the savings obtained to decide if further efforts are worthy. The impact of cash flow forecasts is an ongoing issue in cash management, which we address in Question 1, as we consider it a crucial challenge.

For the selection of the model parameters, no particular procedure was specified by Stone, although some suggestions were made, namely, not to treat them as fixed parameters, but rather adjust them as necessary. Simulation and the practitioner’s judgment were suggested as the best approaches to parameterization. The involvement of cash managers in the process of parameter selection was considered an advantage of this method. An alternative approach to deal with cash flow uncertainty was followed by Hinderer and Waldmann ( 2001 ) who developed a rigorous mathematical framework to include varying environmental factors in the cash manager decision-making process.

In summary, Stone was the first to formally develop a cash management model using forecasts as a key input. Consequently, they assume that cash flows are predictable to some extent. Several studies on daily cash flow prediction (Stone and Wood 1977 ; Stone and Miller 1981 ; Miller and Stone 1985 ; Stone and Miller 1987 ) represent an important contribution to cash management literature. However, the lack of a formal procedure to determine the set of parameters (bounds) of the look-ahead procedure, rather than the mere suggestion of using simulations, has become a serious limitation. No cost function was considered by Stone.

Constantinides and Richard ( 1978 )

Although Neave ( 1970 ) showed that the Eppen and Fama ( 1969 ) model was not optimal, Constantinides and Richard ( 1978 ) proved the existence of optimal simple policies for discounted costs when net cash flow followed a Wiener process. They studied the case of fixed and variable transaction costs and linear holding and penalty costs and used impulse control techniques to find sufficient conditions for an optimal policy defined by parameters \(d \le D \le U \le u\) . Similar to other bound-based models, control actions are only taken whenever the cash level either rises above u or falls below d money units.

Instead of the discrete time framework considered in Eppen and Fama ( 1968 ), Eppen and Fama ( 1969 ), Girgis ( 1968 ), Neave ( 1970 ), Constantinides and Richard assumed that decisions are made continuously over time. Moreover, they assumed that demand over any length of time is generated by a Wiener process, meaning that it is normally distributed with both the mean and standard deviation proportional to the length of time considered. However, they followed the impulse control approach of Bensoussan and Lions ( 1975 ) which was later extended by Richard ( 1977 ). This control technique is based on control actions taken at stochastic stopping times.

The problem formulation was similar to that used in previous studies on cash management. The cash balance at time t is defined as \(x=x(t)\) and it is charged with a holding/penalty cost \(C(x)={\text {max}} \{hx,-px\}\) , with \(h,p>0\) . The transaction cost of changing the cash level from \(x_0\) to \(x_1\) is

with \(k^+, k^-, K^+, K^- >0\) , such that a zero-control action incurs a fixed cost.

In addition, the cumulative demand for cash in interval [ t ,  s ], denoted by D ( t ,  s ), is independent and normally distributed with mean \(E[D(t,s)]=\mu (s-t)\) and variance \({\text {var}}[D(t,s)]=\sigma ^2(s-t)\) , where \(\mu\) and \(\sigma ^2\) are constants. Thus, the cumulative demand is given by

Where, w is a Wiener process in \(\mathbb {R}\) with zero drift and a diffusion coefficient of one. However, the use of diffusion processes to represent the cash holding evolution is not new (Miller and Orr 1966 ).

In this framework, cash managers continuously observe cash levels and perform control actions when necessary. At any stopping time \(\tau _i\) , the applied control \(\phi _i\) , is a random variable that is independent of the future state of the system. An impulse control policy v is represented as a sequence of stopping times and controls, \(v=[\tau _1,\phi _1; \tau _2,\phi _2; \ldots ]\) . If \(x(\tau _i^-)\) denotes the cash level at the stopping time \(\tau _i\) before the control action \(\phi _i\) is applied, and \(x(\tau _i)\) denotes the cash level after the control action, then the state equations of the cash level when policy v is applied are given by

when \(0 \le t < \tau _i\) , with \(x(0^-)=x_0\) , and:

when \(\tau _i \le t < \tau _{i+1}^-\) , with \(i \ge 1\) . Given a policy v and an initial cash balance \(x(0^-)=x_0\) , the expected total cost from time zero to infinity, discounted to time zero, is

where \(\beta\) denotes the discount rate. The final goal is to choose policy \(v^*\) such that \(J_{x_0}(v^*) \le J_{x_0}(v)\) , \(\forall v \in \Omega\) , where \(\Omega\) is the class of all impulse control policies.

Let \(V(x)=J_{x}(v)\) be the expected total cost from time t to infinity discounted to time t and conditional on the cash level \(x(t^-)=x\) . Note also that \(V(x)\ge 0\) since all costs are non-negative. There are only two possible alternatives for cash managers: taking no control action or making the most convenient transaction in terms of future costs. By applying dynamic programming and assuming that the subsequent decisions are also optimal, V ( x ) must satisfy

From this, the following theorem is derived.

Suppose that \(h>\beta k^-\) and \(p>\beta k^+\) hold true, then , an optimal policy exists for the cash management problem. This policy is simple and is given by

Note that the previous theorem implies that, if \(h<\beta k^-\) , it will never be optimal to reduce the cash level as long as \(K^->0\) . Similarly, if \(p<\beta k^+\) , it will never be optimal to increase the cash level, as long as \(K^+>0\) . If both conditions, \(h<\beta k^-\) and \(p<\beta k^+\) hold, the optimal policy prescribes no intervention. In the special case of \(h<\beta k^-\) and \(p>\beta k^+\) , it is optimal to increase the cash level, but not optimal to decrease the cash level. They then deal with an inventory problem in which the control action \(\xi (x)\) is constrained to be non-negative.

This model was later extended to the case of quadratic holding-penalty costs in Baccarin ( 2002 ) and to a multidimensional cash management system and general cost functions in Baccarin ( 2009 ), when cash balances fluctuate as a diffusion process. Premachandra ( 2004 ) also used a diffusion process to propose a more generalized version of the Miller-Orr model which relaxes most of its restrictive assumptions. The Wiener process is also a diffusion process (Itô 1974 ).

In summary, in addition to considering continuous cash flows, the most important contribution of the Constantinides and Richard ( 1978 ) model is Theorem 1 , which provides the necessary conditions to avoid the triviality of the cash policy. Furthermore, it represents the origin of several recent studies (Baccarin 2002 ; Premachandra 2004 ; Baccarin 2009 ) on cash management. However, the strong assumption of modeling cash flows as a diffusion process represents a serious limitation when dealing with empirical non-Gaussian cash flows.

Penttinen ( 1991 )

Penttinen presented myopic and stationary solutions for linear costs using a logistic distribution as the probability density function of random cash demand. Myopic one-period solutions have been suggested to avoid computational difficulties in multi-period applications with a large number of discrete states. In contrast to Constantinides and Richard ( 1978 ), Penttinen chose a discrete time framework because common planning and control practices in most organizations are typically performed in discrete intervals.

His main goal was to analyze the amount of suboptimality in myopic solutions. Thus, the problem formulation considers a stochastic cash balance in which demand \(\delta\) is a random variable. The amount of cash at the beginning of each period n is denoted by x and the cash balance after a control action is taken is denoted by y ( x ). The author considers the transaction costs \(a_n(y-x)\) as

where \(K_n,Q_n,k_n,q_n \ge 0\) . In addition, the retained and penalty costs \(m_n(y)\) charge the cash level y at the beginning of each period according to

Finally, the holding and shortage costs \(l_n(z)\) charge the cash level z at the end of each period. Here, the amount of cash remaining is given by \(z = y - \delta\) and the optimal balance at this point is zero because any positive balance is subject to a holding cost and any negative balance to a shortage cost:

The expected holding and shortage costs are given by the following loss function:

which is the convolution of \(l_n(y-\delta )\) with the probability density function \(\phi _n(\delta )\) . Then, the optimal discounted value of future costs at the beginning of period n is:

where \(\alpha\) is a discount factor, and \(*\) denotes convolution. Note that, when \(\alpha =0\) , the dynamic model is called a myopic model. The optimal policy of this general convex model is given by

where \(t \le T \le U \le u\) defines a transaction rule in the form of a simple policy \(y_n(x)\) such that

Penttinen introduced logistic distribution to ease calculations. In this case, the optimal myopic policy is given by

The reorder point t and disposal point u are derived numerically from T and U from Eqs. ( 42 ) and ( 43 ). To this end, an iterative procedure is presented to compute solutions that are expected to achieve rapid convergence. Different empirical results show the proportionality of policy parameters t , T , U , and u with the shortage cost ratio; thus, the higher the shortage cost, the higher the reorder and disposal points.

In contrast, stationary solutions are based on the assumption that each period possesses the same cost functions, and that cash demand is independent and identically distributed. Then, Penttinen presented additional empirical results on the amount of suboptimality between myopic and stationary solutions in the case of no fixed costs. His results show that the stationary model leads to slightly more cautious ordering policies.

In summary, it is important to highlight the assumption of the logistic distribution within the commonly used family of Gaussian cash flows to better represent empirical cash flows. Penttinen also assumed fixed and linear transaction costs to derive, by dynamic programming, two kinds of optimal policies, namely, myopic (minimizing short-term costs) and stationary (minimizing long-term costs). He considered both a single objective and single bank account in this proposal.

Gormley and Meade ( 2007 )

Gormley and Meade claimed the utility of cash flow forecasts in the management of corporate cash balances and proposed a Dynamic Simple Policy (DSP) to demonstrate that savings can be obtained using cash flow forecasts. They suggested the use of an autoregressive model as a key input for their model. However, gains in the forecast accuracy over the naive model are scant. Gormley and Meade expected that savings from using a non-naive forecasting model would increase if there were more systematic variations in cash flow and, consequently, higher forecast accuracy. If this hypothesis is correct, then the savings produced by a better forecasting model are expected to be significantly higher than those obtained by the naive forecasting model.

In their approach to the corporate cash management problem, Gormley and Meade used an inventory control stochastic model in which cash balances were allowed to move freely between two limits, as shown in Fig. 6 : the lower ( D ) and the upper balance limit ( V ). When the cash balance reaches any of these limits, a cash transfer returns to the corresponding rebalance level ( d ,  v ), as shown in Fig. 6 . Thus, the management of the cash balance over a period T is determined by a set of policy parameters or limits for the instant  t that can be extended \(\tau\) days ahead: \(D_{t+\tau }\) is the lower balance limit at time \(t+\tau\) , \(V_{t+\tau }\) is the upper balance limit at time \(t+\tau\) , \(d_{t+\tau }\) is the lower rebalance level at time \(t+\tau\) , and \(v_{t+\tau }\) is the upper rebalance level at time \(t+\tau\) .

The Dynamic Simple Policy of Gormley-Meade

The transfers for any prediction horizon are determined by

where \(\tilde{O}_{t+\tau -1}\) is the predicted opening balance at time \(t+\tau -1\) , \(\hat{w}_{t+\tau |t}\) is the predicted cash flow for \(t+\tau\) using a model that has been trained up to time t . In this model, \(D_{t+\tau } \le d_{t+\tau } \le v_{t+\tau } \le V_{t+\tau }\) and the following continuity function holds:

The expected cost over horizon T is given by the following objective function:

where the transfer cost function \(\Gamma\) is defined as

The notation used by the expected and transfer cost functions is as follows: h is the holding cost per money unit of a positive cash balance at the end of the day; u is the shortage cost per money unit of a negative cash balance at the end of the day; \(\gamma _{0}^{+}\) is the fixed cost of transfer into account; \(\gamma _{0}^{-}\) is the fixed cost of transfer from account; \(\gamma _{1}^{+}\) is the variable cost of transfer into account; \(\gamma _{1}^{-}\) is the variable cost of transfer from account; \(I_{\tilde{O}_{t+\tau }>0}\) is a boolean variable that equals one if \(\tilde{O}_{t+\tau }>0\) is true, zero otherwise; \(I_{\tilde{O}_{t+\tau }<0}\) is a boolean variable that equals one if \(\tilde{O}_{t+\tau }<0\) is true, zero otherwise.

The authors used genetic algorithms to solve the CMP, that is, to estimate the parameters \(\{D_{t+\tau }, d_{t+\tau }, v_{t+\tau }, V_{t+\tau }\}\) from \(\tau =1, \ldots , T\) . Moreover, because the model accepts forecasts as its main input, a cash flow autoregressive forecasting model was developed. To this end, a Box-Cox transformation (Box and Cox 1964 ) was used to achieve the normality of the real cash flow dataset used in this study.

In summary, Gormley and Meade ( 2007 ) proposed a cash management model that uses forecasts as a key input. Surprisingly, they did not refer to the work by Stone ( 1972 ) on the use of forecasts in cash management. They proposed evolutionary algorithms to derive cash policies within the usual context of fixed and linear transaction costs and a single objective. This solving procedure was recently followed in da Costa Moraes and Nagano ( 2014 ).

Chen and Simchi-Levi ( 2009 )

The concept of K-convexity was first used by Neave ( 1970 ) to show that the Eppen and Fama ( 1969 ) model may not be optimal. When fixed costs exist for both inflows and outflows, Chen and Simchi-Levi ( 2009 ) used the concept of (K,Q)-convexity by Ye and Duenyas ( 2007 ) to characterize the optimal policy in the stochastic cash balance problem. Their approach was closely related to inventory control, in that they used common inventory terminology rather than that usually employed in cash management research. For example, they speak about order and return rather than increase or decrease in cash transactions.

They considered a general cost function with holding and transaction costs. A transaction decision must be made at the beginning of each period. Let x be the cash balance at the beginning of period n before a decision is made and let y be the cash balance after a transaction is made. Transaction cost is computed as follows:

where \(K\ge 0\) , \(Q\ge 0\) , and \(k+q\ge 0\) , assuming that \(k\ge q\) ; that is, the positive variable transaction cost is greater than or equal to the negative variable transaction cost.

In contrast, the holding cost in time period n is described as a general cost function \(l_n(z)\) , which depends on the inventory level at the end of day z which, in turn, depends on the stochastic cash flow \(\xi _n\) . Therefore, the expected holding or penalty cost in period n is given by

In this study, the stochastic cash balance problem is formulated as a dynamic program, where \(C_n(x)\) is the cost-to-go function at the beginning of a period when there are n periods left in the planning horizon, and the initial inventory level is x :

where \(\gamma \in (0,1]\) denotes the discount factor.

They built a process to obtain the optimal policy based on the concept of ( K ,  Q )-convexity (Ye and Duenyas 2007 ) of the recursive function \(C_n(x)\) . A real value function is called ( K ,  Q )-convex for \(K,Q \ge 0\) . If for any \(x_0\) , \(x_1\) with \(x_0 \le x_1\) and \(\lambda \in [0,1]\) , the following condition holds:

We refer the interested reader to Chen and Simchi-Levi ( 2009 ) for further details on the properties of ( K ,  Q )-convex functions and for proof that the cost-to-go function \(C_n(x)\) is a ( K ,  Q )-convex function. However, several additional definitions are required to derive the optimal policy.

where \(t_n \le t'_n \le T_n\) and \(u'_n \le U_n \le u_n\) . Based on the previous definitions and assuming \(K>Q \ge 0\) , it is optimal to set the cash level \(y_n(x)\) after a decision is made according to

In summary, Chen and Simchi-Levi ( 2009 ) followed a sequential decision-making approach using dynamic programming to minimize the total expected costs over the planning horizon. They proposed a model based on bounds, without assuming any particular density function for cash flows, but rather a general one. However, no practical application has been provided to illustrate the model using a real case.

Baccarin ( 2009 )

To the best of our knowledge, quadratic holdings and penalty costs have been considered for the first time in Baccarin ( 2002 ). Furthermore, a general multidimensional approach to the cash management problem was first introduced by Baccarin ( 2009 ) using generalized cost functions and providing theoretical results for two bank accounts. Baccarin considered cash management systems with multiple bank accounts, in which cash balances fluctuate as a homogeneous diffusion process in \(\mathbb {R}^n\) . They formulated the model as an impulse control problem with unbounded cost functions and linear costs.

The optimization problem considers an n -dimensional Wiener cash flow process \(W_t\) that determines the dynamics of cash balances x ( t ) in the absence of any control action using the following Ito stochastic differential equation:

where \(b(x), \sigma (x) \in W^{1,\infty } (\mathbb {R}^n)\) . Then, an impulse control strategy within a continuous time framework is a sequence of control actions \(\xi _i\) at time \(t_i\) to form policy \(V=\{\xi _1,t_1; \ldots \xi _i,t_i; \ldots \}\) with \(t_i \le t_{i+1}\) . Subsequently, given policy V , the controlled process y ( t ) is defined as follows:

where \(\alpha _t = {\text {max}}\{n|t_n \le t\}\) . Holding costs are given by function f ( y ) and transaction costs by function \(C(\xi )\) , which is assumed to be lower semicontinuous and unbounded from above when \(|\xi |\rightarrow \infty\) . These holding and transaction cost functions satisfy the following inequalities:

As a result, each control policy V has an associated cost

where \(\gamma >0\) is the discount rate and \(\chi _{t_i < \infty } = 1\) if \(t_i<\infty\) , and zero otherwise. The problem is then to minimize \(J_x(V)\) over the set A of admissible controls V . The optimal control is obtained by dividing \(\mathbb {R}^n\) into two complementary regions: a continuation set, where the system evolves freely, and an intervention set, where the system is controlled in an optimal manner.

In summary, Baccarin ( 2009 ) provided a sound theoretical framework for cash management systems with multiple bank accounts within a continuous time framework with general cost functions and a single objective, namely, cost. Cash flows are assumed to follow a Wiener process, and the numerical solution to the optimization problem can be obtained by the finite element method, as described in Cortey-Dumont ( 1985 ), Boulbrachene ( 1998 ), which considers a discrete approximation of the continuous framework described above.

Recent contributions: the operation’s research perspective

In this section, we refer to several recent cash management works (after 2000) that deserve a mention because of some interesting characteristics. In this sense, Hinderer and Waldmann ( 2001 ) formally introduced the concept of environmental uncertainty in CMP by providing a rigorous mathematical framework and exploring different cases of cash flow processes. Premachandra ( 2004 ) used a diffusion process as in Baccarin ( 2009 ) to propose a generalized version of the Miller and Orr ( 1966 ) model. Baccarin ( 2002 ) also considered quadratic holding costs for the first time in the cash management literature. Bensoussan et al. ( 2009 ) extended the model by Sethi and Thompson ( 1970 ) by applying a stochastic maximum principle to obtain the optimal cash management policy.

Melo and Bilich ( 2013 ) proposed an Expectancy Balance Model to minimize combined holding and shortage costs in an attempt to deal with uncertainty. This model considers the existence of both deterministic flows, which are known in advance, and stochastic flows, grouped into intervals of occurrence. Recently, da Costa Moraes and Nagano ( 2014 ) proposed the use of genetic algorithms, as in Gormley and Meade ( 2007 ) and particle swarm optimization to solve the CMP using the Miller and Orr ( 1966 ) model. They provide numerical examples using Gaussian cash flows for both solvers within the structure of a single bank account and two alternative investment accounts.

Salas-Molina et al. ( 2018 ) proposed a multi-objective approach to the CMP by considering not only the cost but also the risk of alternative policies using the Miller and Orr ( 1966 ) model and compromise programming (Zeleny 1982 ; Yu 1985 ; Ballestero and Romero 1998 ). They proposed the use of the standard deviation (and upper semi-deviation) of daily costs as a measure of risk. The third goal (stability) was proposed in Salas-Molina et al. ( 2020 ). In Salas-Molina et al. ( 2017 ), the authors showed that forecasting accuracy is highly correlated to cost savings in cash management when using forecasts and the Gormley and Meade ( 2007 ) model. The authors used different cash flow forecasters based on time-series features. A similar approach, based on machine learning was proposed by Moubariki et al. ( 2019 ) and Salas-Molina ( 2019 ), developed a machine-learning approach to fit cash management models to specific datasets.

Herrera-Cáceres and Ibeas ( 2016 ) proposed a model predictive control approach in which a given cash balance function is used as a reference trajectory to be followed by means of the appropriate control actions. In this proposal, cash managers aim to minimize deviations from a reference trajectory instead of minimizing any cost function. In contrast, Schroeder and Kacem ( 2019 ), Schroeder and Kacem ( 2020 ) described online algorithms to deal with interrelated demands for cash flows without making any assumptions about the probability distribution of cash flows. Finally, a formal approach to managing cash with multiple accounts based on the graph theory was proposed by Salas-Molina et al. ( 2021 ).

A multidimensional analysis of the cash management problem

In the following section, we summarize the main cash management models presented in the literature according to the six dimensions introduced in Section 3, as shown in Tables  1 and  2 .

Models. The use of Bound-Based Models (BBM), whose policies are determined by a set of level or bounds, is a common pattern. From the initial inventory approach to the CMP by Baumol ( 1952 ), most models have attempted to derive optimal policies within the framework of some simple policy, typically employing constant cash balance bounds. A slight departure of this framework was considered by Stone ( 1972 ) and Gormley and Meade ( 2007 ) to introduce forecasts as key inputs to a BBM model. A more practical approach was followed by Archer ( 1966 ) to focus on the statistical exploration of data to deal with the lack of synchronization of inflows and outflows. Recently, Baccarin ( 2009 ), Bensoussan et al. ( 2009 ) and Schroeder and Kacem ( 2020 ) proposed models without relying on bounds.

Cash flow process. A wide variety of cash flow processes have been considered in the literature, ranging from the uniform and perfectly known cash flow in Baumol ( 1952 ) and Tobin ( 1956 ), to purely stochastic behavior in Miller and Orr ( 1966 ), Eppen and Fama ( 1969 ), Constantinides and Richard ( 1978 ), Premachandra ( 2004 ), Baccarin ( 2009 ), da Costa Moraes and Nagano ( 2014 ), which usually implies a Gaussian distribution. The selection of any cash flow process implies the assumption of either a continuous time framework (Constantinides and Richard 1978 ; Baccarin 2009 ) or a discrete time framework (Stone 1972 ; Penttinen 1991 ; Gormley and Meade 2007 ). Data sets are hardly used with the exception of Salas-Molina et al. ( 2018 ).

Cost functions. The linear cost assumption is also a common pattern with the exception of Baccarin ( 2002 , 2009 ), that considered more general cost functions. However, there also exist differences in the linear approach. While Baumol ( 1952 ) and Miller and Orr ( 1966 ) considered only fixed costs, Tobin ( 1956 ) and the subsequent works included fixed and variable costs in their models.

Objectives. It is also important to note that all models focus on a single objective, namely, cost, neglecting risk analysis. However, the works by Stone ( 1972 ), Hinderer and Waldmann ( 2001 ), Gormley and Meade ( 2007 ) are remarkable initial attempts to include uncertainty in the analysis of the best policies. The use of forecasts seems to be a sound strategy to reduce uncertainty in the CMP as shown in Salas-Molina et al. ( 2017 ). To handle the inherent uncertainty of cash flows, Salas-Molina et al. ( 2018 ) introduce the concept of risk analysis in a multi-objective approach to the CMP. Finally, Salas-Molina et al. ( 2020 ) extended the multi-objective approach to three different goals: cost, risk, and stability.

Solvers. There are also differences in the techniques used for solving the CMP. However, three solving techniques stand out: analytic solutions as in Baumol ( 1952 ), Tobin ( 1956 ), Miller and Orr ( 1966 ), Constantinides and Richard ( 1978 ), Hinderer and Waldmann ( 2001 ), Schroeder and Kacem ( 2020 ); dynamic programming as in Eppen and Fama ( 1969 ), Daellenbach ( 1971 ), Penttinen ( 1991 ), Chen and Simchi-Levi ( 2009 ); and approximate techniques as in Archer ( 1966 ), Stone ( 1972 ), Gormley and Meade ( 2007 ), da Costa Moraes and Nagano ( 2014 ).

Bank accounts. Although cash management systems with multiple bank accounts are the rule rather than the exception in practice, almost all previous models derive policies for a single bank account and provide no method to extend their results to multiple bank accounts. Only Baccarin ( 2009 ) approached the CMP from a multidimensional perspective to deal with multiple bank accounts. More recently, Salas-Molina et al. ( 2020 ) considered multiple bank accounts in the CMP and Salas-Molina et al. ( 2021 ) proposed a formal analysis of cash management models with multiple bank accounts based on graph theory.

Open research questions in cash management

From the previous review, it can be concluded that all relevant issues regarding cash management have been covered by the aforementioned cash management models. However, our taxonomy allows for the identification of open research questions in cash management, as we discuss next. From Table 1 , we can infer that bound-based models seem to be a common pattern in cash management. However, recent proposals have questioned the use of bounds (Baccarin 2009 ; Herrera-Cáceres and Ibeas 2016 ) and probability distribution assumptions to derive optimal policies (Schroeder and Kacem 2019 , 2020 ). Indeed, the ultimate goal of cash managers is not to find the best set of bounds but the best policy disregarding the required steps to achieve it. The utility of forecasts in cash management have been demonstrated in Gormley and Meade ( 2007 ) and Salas-Molina et al. ( 2017 ). These results must encourage cash managers to rely on time-series forecasting or machine learning techniques to reduce uncertainty in the near future.

In addition to its critical importance for real-world institutions, empirical cash flows are not common in cash management literature, with the exception of Emery ( 1981 ), Gormley and Meade ( 2007 ) and Salas-Molina et al. ( 2017 ), Salas-Molina et al. ( 2018 ). Common assumptions imply Gaussian, independent, and stationary cash flows in the form of a random walk or a diffusion process (Miller and Orr 1966 ; Constantinides and Richard 1978 ; Baccarin 2009 ). However, real-world cash flows may not accommodate such strong assumptions. As a result, the particular statistical properties of cash flows and their ability to predict them are research questions worth addressing.

The assumption of linear cost functions is not as restrictive in cash management as it may appear at first glance. However, considering piece-wise linear cost functions as in Katehakis et al. ( 2016 ) or even non-linear cost functions as in Baccarin ( 2002 , 2009 ) may allow a better representation of real-world cash management problems. A closely related topic is the selection of risk measures when considering not only cost but also the risk of alternative policies as an additional objective in cash management, as suggested by Salas-Molina et al. ( 2018 ). The authors used the standard deviation of daily costs as a measure of risk; however, alternative measures of risk can also be explored (Artzner et al. 1999 ; Szegö 2002 ; Rockafellar and Uryasev 2002 ). Indeed, a comprehensive risk analysis of cash management represents an appealing research area in cash management.

Obtaining a policy that optimizes some objective functions is not straightforward. Beyond the discussion about the required assumptions to apply one technique or another, a rather unexplored issue is the optimality of the solutions provided by each method. While dynamic or linear programming ensure optimality, evolutionary algorithms, or particle swarm optimization they return only approximate solutions. However, there is a lack of supporting technology in the form of software applications for cash management that deserves the attention of the research community. The computing times, robustness of the solutions provided, and deployment costs of alternative methods are also worth exploring. From Table 2 , we observe that only Baccarin ( 2009 ) and Salas-Molina et al. ( 2020 ) approached the cash management problem considering multiple bank accounts. Since the presence of several accounts is very common in practice, cash management models that can handle multiple bank accounts and transactions between them constitute an interesting topic.

It is important to highlight that open research questions do not arise by exploring only one dimension at a time. On the contrary, chances are that new research opportunities derive from a combination of values that received little attention of the research community. As an example, consider an unconstrained model using forecasts obtained from empirical cash flows that aim to minimize a multi-objective cost-risk function with piecewise linear cost functions through linear programming within a cash management system with multiple bank accounts.

The existence of multiple dimensions in CMP implies that the selection of cash management models, cost functions, solvers, and many other factors is a complex task. It seems clear that no cash management model is best for any decision-making context. As a result, the design of methodologies to select the appropriate models to solve CMP is an additional open research question. The set of all relevant operating conditions that are important in the decision-making context can be expressed as a set of parameters (Hernández-Orallo et al. 2013 ) that can ultimately be used to select models according to the preferences of practitioners. Multiple criteria decision-making techniques can help deal with multidimensional problems in finance. An example of the application of these techniques to the context of evaluating clustering algorithms in financial risk analysis can be found in Kou et al. ( 2014 ). More recently, Kou et al. ( 2021a ) proposed the use of a hybrid multicriteria decision-making process in which different models were used to rank available alternatives.

Except for Salas-Molina et al. ( 2017 ) and Salas-Molina et al. ( 2018 ), the use of datasets and the application of forecasting models in cash management are scarce. We argue that time-series prediction models and other machine learning techniques may enhance decision-making in finance. We refer interested readers to recent reference books by Dixon et al. ( 2020 ) and Consoli et al. ( 2021 ), reviews by West and Bhattacharya ( 2016 ) and Henrique et al. ( 2019 ), and applications by Moubariki et al. ( 2019 ), Li et al. ( 2021 ), Kou et al. ( 2021b ) and Manthoulis et al. ( 2021 ).

Finally, we must also point out that the integration of external factors, such as the impact of a financial crisis, in cash management models is also an interesting future line of research. In Section 2, we review the related literature on CMP from economic and financial perspectives. In Section 4, we review the most relevant contributions to CMP from the decision-making perspective. By combining these two approaches, we expect that cash management decision-making models can be enhanced with additional relevant factors. We consider this integration to remain an important open research question in cash management.

Concluding remarks

In this study, we review the research literature relevant to the cash management problem since the first contribution by Baumol ( 1952 ) to the most recent contributions. We use this review to identify several research opportunities in cash management. We propose a new taxonomy based on the main dimensions of the cash management problem: (i)the model deployed, (ii)the type of cash flow process considered, (iii)the particular cost functions used, (iv)the objectives pursued by cash managers, (v)the method used to set the model and solve the problem, and (vi)the number of accounts considered. We use these six important dimensions as a framework to classify the most relevant contributions in cash management. Linking the dimensions with the reviews, we performed a multidimensional analysis of these contributions, which ultimately allowed us to highlight several open research questions in cash management. As a result, topics such as risk analysis in cash management, the utility of forecasts, and the possibility of handling multiple accounts have been identified as new research opportunities. Researchers may extend the number of dimensions, suggest new instances for each dimension, or even link unexplored instances to enrich the analysis of the cash management problem.

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Abbreviations

Cash management problem

Automated teller machine

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Acknowledgements

We wish to express our thanks to Universitat Politècnica de València, the Spanish Ministry of Science, CSIC and ICREA Academia for their support.

Research supported by projects:

\(\bullet\) Crowd4SDG (H2020-872944);

\(\bullet\) CI-SUSTAIN (PID 2019-104156GB-I00);

\(\bullet\) TAILOR (H2020-952215);

\(\bullet\) TED2021-131295B-C31;

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\(\bullet\) VALAWAI (funded by the European Commission under Grant 101070930);

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Cash management strategies and firm financial performance

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Cash(liquidity) management is at the heart of a firm’s financial management. It is a silver lining between the bankruptcy and the success story of a company. Therefore, this study intends to contribute some insights into cash management practices and how firms can use them to achieve sound financial performance. This study provides a comprehensive literature review on existing theories and cash management practices that are useful in decision making. After the analysis of the available literature, the study highlights important theories including trade-off theory (TOT), transaction model, precautionary measures, financial hierarchy, and cash flow theory. Furthermore, management practices such as stochastic cash management model, speeding up cash collections, centralization & decentralization of management, asset portfolio diversification, and cash disbursement are discussed. The study suggests that a sound financial performance can be achieved through a hybrid approach and through ...

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A bibliometric analysis of cash holdings literature: current status, development, and agenda for future research

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• Volume 72 , pages 707–744, ( 2022 )

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• Saleh F. A. Khatib   ORCID: orcid.org/0000-0001-7652-4191 1 ,
• Dewi Fariha Abdullah   ORCID: orcid.org/0000-0002-7799-6972 1 ,
• Ernie Hendrawaty   ORCID: orcid.org/0000-0001-8798-9947 2 &
• Ahmed A. Elamer   ORCID: orcid.org/0000-0002-9241-9081 3 , 4  

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Despite the growing interest in exploring the cash holding aspects among scholars, systematic reviews and comprehensive evaluation in this area has been limited. Also, there is only a fragmented understanding about how the cash holdings concept is formed among researchers and experts. We fill this gap in the literature by identifying and evaluating the research development of cash holdings topic. Using 874 articles from the Scopus database that were published between 1947 and early 2020, bibliometric and content analyses were employed to assess the patterns of global cash holdings research. We find that previous studies have substantially enriched our knowledge of the antecedents and consequences of cash holdings. Yet, there are still several opportunities to make significant contributions in this area. The contribution of this research is to provide a comprehensive evaluation of the development of cash holdings research (using a sizeable archival database). It identifies the current joint development and potential opportunities for future work directions on cash holdings association with payout policy, corporate social responsibility, and corporate governance. Our results are likely to be of interest to academics, practitioners, and educators in related business and finance fields.

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1 Introduction

Cash holding constitutes a significant aspect at the heart of corporates’ financial policy. Indeed, holding cash is the most popular way for companies to maintain enough liquidity (Almeida et al. 2014 ). In the past two decades, corporates around the globe have substantially increased their cash holdings as it enables companies to respond to unpredictable cash flow changes, hedge risk, daily financing operations, and financing long-term investments (Opler 1999 ). Opler ( 1999 ) conducted the earliest pioneering empirical study on the causal factors of cash holdings, inspiring the emergence of the scholar interest to this topic. Thus Far, previous studies have substantially enriched our knowledge of the antecedents of cash holdings. However, despite the growing interest in cash holdings topics, there remains a paucity of research on evaluating and describing scientific publications from an international viewpoint (Da Cruz et al. 2019 ).

The cash management activities of corporations remained an interesting topic among scholars. The cash holding literature has traditionally concentrated on the presence of the target cash holding and its determinants. Companies are more likely to maintain cash for several motives. It allows corporates to avoid losses of underinvestment because of funds scarcity and to diminish transaction costs (Opler 1999 ). Considering financial instruments, cash holding can be used to finance the firm's operational activities during financial difficulties (Campello et al. 2011 ). It also helps in reducing the costs of external financing (Almeida et al. 2004 ), and it serves to pay the obligations of debts during economic distress (Acharya et al. 2007 ), it also enables corporates to accept profitable investments opportunities (Ferreira and Vilela 2004 ). Moreover, companies are said to bypass valuable investment opportunities, particularly when facing financing constraints, therefore, cash can be utilized to cover future shortfalls (Bates et al. 2009 ). These findings were further supported by Almeida et al. ( 2004 ), who argue that firms with more financial constraints are more likely to incorporate savings from incremental cash flows to protect their futures. Consequently, hedging for downturns, such firms would keep a substantial amount of cash.

However, holding cash is not costless, and it has been argued that holding a significant amount of cash leads to lower return on investments (Dittmar et al. 2003 ), because excessive cash is said to be misused by executives (Jensen 1986 ). Executives might invest in projects with negative net present value due to the conflicts of interest emerge from the ownership separation of corporate. Such investments lead to the agency problem of high cash and reduce the value of their shares (Denis 2001 ; Jensen 1986 ). Additionally, holding excessive cash comes with other costs (transaction costs) like flotation fees and taxation affecting the valuation of reserved cash (Faulkender and Wang 2006 ).

In the cash holdings literature, a stream of researchers focused on the antecedents of cash holding (Akben-Selcuk and Sener 2020 ; Opler 1999 ). These research studies further support the individuality of organizational policies and practices of companies' cash holdings that differ across countries because of the differences in the business environments (Tahir and Alifiah 2015 ). Also, several essential motives were introduced that contribute to our understanding of the antecedents and outcomes of cash holding such as agency motives, transaction motive, and precautionary motive.

The agency motives for holding cash posit that due to the differences of interest between owners and executives, when executives might not act in the best interests of stockholders, they may use the company's excess cash for their wealth maximization instead of serving the owner (Jensen 1986 ). Hence, entrenched executives are more likely to hold more cash to maximize their personal benefits. Lee and Lee ( 2009 ) provide empirical evidence on the association between managerial entrenchment and cash holdings to be positively significant.

Transaction motive indicates that a company firm needs liquid resources to finance its daily operation and in case of scarcity of cash at a time when needed, a company might have to liquidate assets to meet its obligation, sometimes it will have to pay transaction costs. These costs can be avoided by keeping more liquid assets (Drobetz and Grüninger 2007 ; O’ Brien and Folta 2009 ). The precautionary motive emerges from the asymmetric information impact on external funds raising. In the future of a firm, there are unexpected additional expenses like price fluctuations, rising costs, and availability of raw materials, or any other unpredicted situations. In such scenarios, cash holding helps to cover the companies to meet these needs (Kawase et al. 2015 ; Ozkan and Ozkan 2004 ; Xu et al. 2019 ). However, it should be noted that previous studies have substantially enriched our knowledge about cash holdings. Yet, a little is known about the outcomes of cash holding (Jebran et al. 2019 ). Also, a limited number of researches have focused on evaluating and describing scientific publications from an international viewpoint (Da Cruz et al. 2019 ), Pointing to a need for comprehensive research to evaluate and review cash holdings topics from a broad sample of studies.

The limited number of researches have focused on evaluating and describing scientific publications from an international viewpoint (Aliyev et al. 2019 ; Block et al. 2020 ; Block and Fisch 2020 ; Da Cruz et al. 2019 ), while other review studies have devoted a significant focus on the determinants of cash holdings (He 2018 ; Tahir and Alifiah 2015 ; Weidemann 2018 ). Similarly, Amess et al. ( 2015 ) concentrate on the determinant of cash holding and its association with corporate governance. Also, Akhtar et al. ( 2010 ) have limited their review work to the association between corporate governance and cash holding. Furthermore, a systematic analysis study conducted by Da Cruz et al. ( 2019 ) to explore the development of cash holding studies by using several databases for data mining. However, their study was limited to articles published in the journal with impact factor one or above excluding a large number of articles from the analysis (Table 1 summarizes the key differences between these review studies and the current study). Although there is extensive work on cash holdings explorings the association with other aspects of corporations, core debates on cash holdings remain to be addressed (Da Cruz et al. 2019 ). We believe that this field has reached the level of maturity which necessitates an in-depth and comprehensive evaluation of the cash holding researches. We also argue that previous review studies are better to be integrated with research that includes a comprehensive overview to map the existing knowledge on cash holding topic (Castriotta et al. 2019 ). Such work helps to consolidate the achievements of the field and craft a research agenda for years to come.

By using a large number of articles, this research addresses several questions related to cash holdings: (i) What is the current publication trend of cash holdings research? (ii) What is the leading articles, countries, authors, and journals in term of the publication or 'citations' number? (iii) Which topics involving cash holding are the most recent or common among scholars? (iv) what is the intellectual development of the field? and (v) What themes involving cash holding needs more attention from researchers?

This study has used the Scopus database for data mining. Many similar studies in various fields including management have been conducted using this database only (Drago and Aliberti 2019 ; Md Khudzari et al. 2018 ; Moreira et al. 2019 ; Yahaya et al. 2020 ; Zheng and Kouwenberg 2019 ). It should be noted that Scopus data covers a wide range of subjects, and it is the most significant citation/abstract database (Md Khudzari et al. 2018 ). Following Da Cruz et al. ( 2019 ) the central theme in this research was all journal papers that cover the following terms in the title and abstract “Cash*Holding*”. Data collection was conducted in May 2020 and the query search string has resulted in 874 documents published from 1947 to 2020. This large number of sample literature enables us to map the development and contribution of the cash holdings studies and identifying challenges and avenues for future studies on this topic.

This paper contributes to the existing literature about cash holdings by presenting a comprehensive review of the existing studies. This study provides a review of the research landscape in the area of cash holdings and presents interesting insights and directions for future research. This paper also contributes to the theoretical development of cash holdings research because it helps researchers discover possible opportunities and determine the key research themes in cash holdings literature (Shi and Li 2019 ). Our study departs from previous reviews studies by being the first to provide a combination of systematic literature review and bibliometric analysis on cash holdings, offering a complementary approach to the more traditional literature review. Such criteria are based on a previous systematic literature review (Kumar and Ranjani 2019 ; Moreira et al. 2019 ; Baker et al. 2020 ), and it has been proven to be useful to academicians in identifying the current research structure of the subject and will inform them about the evolution of the various themes in this area (Kumar et al. 2020 ). This paper contributes to existing debates about determinants of cash holdings and suggest that country-level aspects exert a significant role determining the level of cash holdings. Also, it has been found highlighting that agency, trade-off, and theories are the dominating theoretical aspect in this area, yet, the interplay of cash holding theories is not well understood (Weidemann 2018 ).

The remainder of the paper is structured as follows. Section  2 explains the methodology employed in this research including the analysis methods and the searching strategy. Section  4 discusses the findings of the study. Section  5 summarizes several topics related to cash holdings that have been attracting researchers’ interests. Section 6 Conclusion of the research.

2 Methodology

Bibliometric analysis can be defined as the structured process of describing all documents that have been published in a specific field of science in terms of the number, connection, productivity, quality, citations, and evaluating the intellectual development of the scientific field. Ronda-Pupo ( 2017 ) suggested that the research activities of a scientific field can be an excellent tool to understand its structure. However, Block and Fisch ( 2020 ) suggested that providing only a list of references (leading research, authors, institutions, etc.) followed by a brief description does not qualify the research to be a bibliographic study, a bibliographic study should also focus on evaluating the structure of a particular research field (Block and Fisch 2020 ). Therefore, we followed the instructions provided by the novel work of Block and Fisch ( 2020 ) to conduct an impactful bibliometric study that evaluates the development of research on cash holdings. This process would help us understand the development of a scientific field.

Unlike review papers that mainly focus on discussing the latest progress, future directions, and challenges of a specific topic, the focus of this study is two folds. First, this study employed a bibliometric type of analysis to evaluate the research development on cash holding as it is an effective method to address the research trends on a particular topic by exploring existing documents (Md Khudzari et al. 2018 ; Shi and Li 2019 ). Second, following the systematic review method of Moreira et al. ( 2019 ) to conduct a rigorous bibliometric and content analysis of several themes that emerge from keywords and citations clusters. To identify the intellectual structure of the research on board diversity, citation and co-citation analysis were performed using VoSviewer. The co-citation network was formed using VosViewer to present the thematic flow of knowledge and the formation of clusters. Lead papers from the clusters were identified using weighted citation measure and then were used to perform cluster analysis. These methods enable us to provide a comprehensive evaluation of the development of cash holding research from an international perspective.

To map the literature, we employed VOSviewer as it is a powerful software tool to construct a visualized map based on the link to the objects of interest. This software has been widely used in bibliometric research investigation (Behrend and Eulerich 2019 [auditing]; Castriotta et al. 2019 [emerging organization structure]; Zheng and Kouwenberg 2019 [corporate governance]; Yahaya et al. 2020 [Innovation]). VOSviewer maps were created in this study for keywords of authors, document citations, and authors' network as they are the key concern of this study. The methods used in the analytical structure of this study are presented in Fig.  1 . It also shows the organization of this study, calculation, indicator, and the tool used.

Analytic structure of this paper. Note; TSA thematic structure analysis, SNA social network analysis, AJG academic journal guide, V vissualization view, KF keyword frequency, CoA co-authorship, CoC co-citation count, TLC total local citation, TSC total Scopus citation, TP total publications

2.1 Defining searching terms

Block and Fisch ( 2020 ) suggested that it is important for bibliometric studies to have a clear, transparent, reproducible searching process, this section is, therefore, presenting the process of data mining in a clear manner. Data collection was conducted in May 2020 from the Scopus database. Many similar studies in various fields including management have been conducted using Scopus database only (see, Md Khudzari et al. 2018 ; Drago and Aliberti 2019 ; Zheng and Kouwenberg 2019 ; Yahaya et al. 2020 ). It should be noted that Scopus data covers a wide range of subjects, and it is the most significant citation and abstract database and it is the most commonly used search databases (Amrutha and Geetha 2020 ; Md Khudzari et al. 2018 ). The advantage of this database is that it allows researcher to import a bibliography database for all the final results including citation matrix, publisher, affiliation, references, etc. in a single excel (.CSV) file. After reviewing the similar publication, definitions, and categories of cash holding, we developed a central theme search string. Given that cash holding is a broad topic, unlike Da Cruz et al. ( 2019 ), we limited our search by using the primary theme keyword. The central theme in this research was all journal papers that include 'Cash* Holding*' terms in the titles, keywords, and abstracts.

2.2 Search delimiting criteria

The query string has resulted in 874 documents published from 1947 to 2020 in the Scopus database after limiting the search for a journal article that is published in the English language. In the descriptive analysis (country/territory, affiliations, authors, sources, and years), all articles were utilized. For the keywords analysis, following the method of Md Khudzari et al. ( 2018 ) and Yahaya et al. ( 2020 ), 145 articles were excluded from the keyword analysis due to the lack of the keywords. This approach leaves us with 729 articles (1594 keywords) to map the development of the cash holdings studies and identifying challenges and avenues for future studies on this topic (see, Fig.  2 ). For the content analysis, this study follows the method of Moreira et al. ( 2019 ) to identify the themes of content analysis. Four themes were subject to the content evaluation in cash holding primary output. Two of them emerged from the cluster analysis (corporate governance and determinants of cash holdings) and the other two emerged from the keyword analysis, namely payout policy and corporate social responsibility. This is depicted in Table 5 later.

Workflow diagram for conducting bibliometric research

3 Descriptive analysis

A descriptive analysis of 874 articles was carried out to know the basic ongoing trend of publication on this topic. To achieve the first research question, we have first analyzed the publication trend, which is seen in terms of total publication by year, country, region, journal, and institution.

3.1 Growth of the publication

874 documents had been published in Scopus indexing journals related to cash holdings. The oldest document dates to 1947, and there were no publications recorded until 1975. Eleven articles have been published before 2000. The number of annual publications remained below 100 articles in total until 2010. At first glance, it is clear that a keen interest in the cash holdings topic started in 2010–2011 (see, Fig.  3 ). One possible explanation is that both developed and emerging economies have significantly affected by the international economic crisis in 2007. This downturn has triggered scholars to explore more the financial behaviour of corporations around the globe, including cash holding. Indeed, literature has stressed that the economic downturn has affected the cash holding practices of corporations (Jebran et al. 2019 ). Also, Tran ( 2020 ) found evidence that during the economic downturn time, executives were more likely to expropriate stockholders through the firm's liquidity policy. Hence, it is expected to see more work on cash holdings in the recent future evaluating the Covid-19 impact on the different aspects of cash holding. In 2010, there was a sharp increase in publications and it was almost doubled in 2011. Later, the accumulative number of documents has rapidly increased as a result of the steady growth in the number of annual articles. However, it should be noted that the majority of these publications are not free and readers have to pay for access. Out of 874, only 85 documents were open-access publication. It has been suggested that an open-access research paper more likely receives more citations than other journal articles.

The cumulative and annual numbers of publications on cash holding

3.2 Journals outlets

The findings indicate that only four publisher agencies owned the top 10 most productive journals (Table 2 ). Five of them were from Elsevier, including the four most productive journals. Wiley-Blackwell published two journals. The rest were published by Springer Nature, Cambridge University Press, and Oxford University Press. Furthermore, the most productive one was the Journal of Corporate Finance with 58 articles covering 6.6% of the total publications, followed by the Journal of Banking and Finance (32, 3.7%). Journal of Financial Economics (31, 3.5%) published the most cited paper among the top ten with 982 citations by Opler ( 1999 ). The rest of the journals were counted for less than 2.5% of total publications each. Moreover, based on the CiteScore in 2019, the number of journals with CiteScore 5 and above are three. Interestingly, although the rank of Journal of Finance is the 9th with 15 documents, the CiteScore and total citation were the highest in the list (8.30). The Journal of Financial Economics is the second-highest CiteScore (7.67). Indeed, the Journal of Financial Economics publishes four of the most cited articles.

4 Bibliometric analysis

4.1 leading countries and institutions.

This study shows that more than 50% of the total publications on the cash holdings topic were contributed by the USA and China which indicates that these countries are key players in the development of this topic (Table 3 ). The USA led the list with 329 publications, covering 38% of the total global publications. National Bureau of Economic Research is the most productive institution in the USA with total publications of 14 documents. It should be noted that it is also the most productive institution on cash holdings research. Among the 14 countries, two countries only seemed to have more than two-thirds of a single-country publication, namely Japan (81%), and Malaysia (85%). This indicates a strong collaboration between countries. The country with the least SCP was Hong Kong (16%); out of 24, about 20 documents were affiliated to different countries. Furthermore, the investigation revealed that few studies taking place in the African region, Latin America, and the Middle East countries while the main body of literature mostly and repeatedly collected data from developed countries.

4.2 Leading authors

We find that the ten most productive authors in cash holdings are affiliated with seven countries (Table 4 ). The total number of documents of these authors were counted for 48 documents. It indicates a high collaboration between them. Additionally, Chen, N. from Taiwan, is the most productive author with a total of 7 documents since 2007, 28 citations, and four h-index. Similarly, Lozano, M.B. from Spain got the same number of publications (7) and only nine citations by the end of 2019. The 3rd and 4th top authors are Drobetz W. from Germany and Ozkan N. from the U.K. with six articles each. Interestingly, Pinkowitz, L. is the least productive author within the top ten. Yet, he has the highest citation record.

4.3 Journal influence and quality analysis

To evaluate the journal influence in cash holdings research, we applied two methods. We assess leading journals in the area of cash holdings using analyzed the average citation per article (ACA) as an indicator. Then, we evaluate the Academic Journal Guide (AJG) rating of the journals. This analysis would help to differentiate between the quality and productivity of journal publications. As the number of citations is an indicator of the journal influence while the number of publications is an indicator of journal productivity. Following Kumar and Ranjani ( 2019 ), we calculated the ACA of the leading journals based on the total citations from Scopus database. As it is shown in Table  5 , although the Journal of Finance has 15 publish documents on cash holdings, it has the highest ACA within the list, followed by the Journal of Financial Economics. This interesting finding indicates that a large number of publications do not always guarantee more citations as the case with the Journal of Finance.

For journal quality analysis, the Academic Journal Guide 2018 was also utilized to evaluate the quality of the studies. It provides a quality ranks of the journals in management and business and categorizes them into the given groups 4*, 4, 3, 2, and 1. One is the lowest quality while 4* is the highest. AJG rates are an important tool for researchers' promotions in business schools and commonly utilized by scholars (Kumar and Ranjani 2019 ). The results indicate that a vast majority of cash holdings research has been published in none ranked journal (212 articles). Interestingly, out of 874 documents, only 73 (4.2%) articles have been published in Grade 4* journals. As it is shown in Fig.  4 , researchers were interested in Grade 2 journals, followed by Grade 3 and 4 with 219, 193, 96 articles respectively.

Map of documents citations 50 articles (minimum of 60 citations)

4.4 Citation analysis

We used citation analysis to identify the most popular articles within the cash holding community. It has been suggested that citation analysis counts the number of times other articles cite a particular article to identify the popularity and impact of the article in the scientific field (Kumar et al. 2020 ). Based on the based on ‘total times cited count’ provided by the Scopus database, we have analyzed the citation of 874 studies. The findings of the documents’ citations suggest the most cited articles were published in five different journals (Table 6 ). The first one was conducted by Opler ( 1999 ) with 982 citations as it is considered to be among the first studies to examine the determinants of cash holdings, followed by Bates et al. ( 2009 ) with 652 citations. However, among the most cited papers on cash holding topic, four articles were published by the Journal of Financial Economics and three published by the Journal of Finance. Interestingly, the AJG assessment shows that eight of the top ten leading studies are from the 4% of cash holding documents that are published in Grade 4* journals discussed in the previous section.

4.5 Citation trend

We analyze the references of our sample literature (874 documents) and this analysis results in 31,018 unique references that were cited by the sample literature. Out of 31,018, 3225 articles were locally cited two times or more. The locally cited document refers to the number of citations for an article within our sample of literature. Following Kumar and Ranjani ( 2019 ), we used this analysis as another means of evaluating the most influential studies within the cash holdings community. As shown in Table 7 , we found that there are eight research articles with more than 50 local citations. Opler ( 1999 ) is the highest in the list with 163 local citations and 48 links indicating that this study has been mentioned 163 times in the reference lists of our sample literature. Dittmar and Mahrt-Smith ( 2007 ) who studied the association between cash holdings and governance structure, were cited by about 15% of the cash holdings literature. Additionally, Dittmar et al. ( 2003 ) conducted a study investigating the correlation between investor protection and cash holding in 45 countries which was slightly less cited in the sample literature (89 times). The results indicated that about five percent of the cash holding studies have cited Faulkender and Wang ( 2006 ), Harford ( 1999 ), Han and Qiu ( 2007 ), Myers and Majluf ( 1984 ), and Almeida et al. ( 2004 ). However, this investigation provides use with the first glance on the thematic trend of cash holdings research. After reviewing these studies, we conclude that the thematic series following in cash holdings research is not wide and concentrated on corporate governance, financial policy, and the determinants of cash holdings.

4.6 Co-citation analysis

Co-citation also helps to structure literature and the thematic clusters and gaps in the scientific area (Block and Fisch 2020 ). It refers to the occurrence of two references in the reference list of a single document. Co-citation analysis helps identify the content and subject area by evaluating the more frequently cited reference together. The occurrence of two publications more than one time on the reference list of an article can be an indicator of the similarity in empirical discipline, methodology, theory, and topic. We used the link strength between two documents provided by VoSviewer to measure the connection between pair references. As suggested by Van Eck and Waltman ( 2013 ) this measure for each pair of linked items and indicates the strength of their connection. The co-citation investigation found that there exist 201 pairs of documents that are co-cited with each other at least 10 times. Among these 201 connections, the strongest co-citation connection exists between Dittmar and Mahrt-Smith ( 2007 ) and Opler ( 1999 ); the link strength between these articles is 78. Table 8 presents the pairs of authors with the highest number of link strength. As indicated in the table, the second strongest co-citation connection exists between Dittmar and Mahrt-Smith ( 2007 ) and Dittmar and Mahrt-Smith ( 2007 ), followed by Faulkender and Wang ( 2006 ) and Dittmar and Mahrt-Smith ( 2007 ). It should be noted that the highest connection list is concentrated among Opler ( 1999 ), Dittmar and Mahrt-Smith ( 2007 ), Dittmar et al. ( 2003 ), Faulkender and Wang ( 2006 ), Harford ( 1999 ), Han and Qiu ( 2007 ), Myers and Majluf ( 1984 ), and Ozkan et al. ( 2004 ). This finding confirms our discussion in the earlier section where the body literature of cash holdings is focusing on the determinant of cash holdings, corporate governance, and financial policy of corporations.

4.6.1 Co-citation network and data clustering

To address the intellectual development of the field, the co-citation network analysis was applied. From the co-citation network, several clusters were identified to conduct the content analysis. To study the intellectual structure of the topic ‘cash holdings’, we start by using VosViewer for the co-citation network analysis. Co-citation analysis in VosViewer gave us a.TEXT file, which we used in Excel to read the co-citation network. The initial findings result in 3225 references that are at least twice co-cited with one another. Among them, 65 articles occurred together more than 20 times. To visualize the co-citation map, VosViewer formed a random cluster map that was too complex to understand. Therefore, we follow Kumar and Ranjani ( 2019 ), who identified the leading 10 papers from each cluster. Similarly, we used the weighted citation count provided by VosViewer to ensure high-quality papers in cluster analysis.

As shown in Fig.  5 , the analysis results in three clusters with a high correlation between them. Among the three clusters, the red group is the largest that is led by Dittmar and Mahrt-Smith ( 2007 ). Followed by the green cluster with Bates et al. ( 2009 ) as the most dominant study. Finally, the blue cluster is dominated by Opler ( 1999 ), the most cited author in cash holdings literature. It should be noted that despite that the fact that these clusters address different aspects of cash holdings, they are highly interrelated and complement each other. Furthermore, following Moreira et al. ( 2019 ), we pooled these clusters based on the topic covered by each study with reference to the cited articles over 3 per cluster. As a result, two main themes related to cash holdings emerged: corporate governance, the determinant of cash holdings. These themes were then grouped and analyzed in terms of the association with cash holdings, followed by a summary of each article. The literature about cash holdings is still unclear about its determinants and the impact of corporate governance. This is depicted in Table 7 and 8 later.

Academic Journal Guide (AJG) 2018 rating of 874 articles

4.6.1.1 Group 1: corporate governance and cash holdings

The corporate governance mechanisms quality is the central influencing factor of corporate financial policies, including cash holding (Abdelfattah et al. 2020 ; Abdou et al. 2020 ; AlHares et al. 2020 2020a ; Alnabsha et al. 2018 ; Alshbili et al. 2019 ; Alshbili and Elamer 2020 ; Hazaea, Zhu, et al. , b ; Khatib et al. 2020 ). Corporate governance practices are expected to ensure that executives act in the best interest of stockholders (Asante-Darko et al. 2018 ; Bufarwa et al. 2020 ; El-Dyasty and Elamer 2020 ; Elamer et al. 2018 , 2020 , 2019 ; Elamer and Benyazid 2018 ; Elmagrhi et al. 2018 ; Hazaea et al. 2020a ). Jensen ( 1986 ) stressed that executives are reluctant to disburse the extra cash among stockholders to secure their benefits by investing it in unprofitable projects, which might destroy corporates' valuation. As a result of the ownership separation, the self-interested executive more likely to exploit the firm assets to maximize their personal wealth at the expense of stockholders' interest (Jensen and Meckling 1976 ). This detrimental effect of extensive cash saving on corporate performance is canceled in well-governed companies (Dittmar and Mahrt-Smith 2007 ; Luo and Hachiya 2005 ). Table 9 provides a summary of all studies in cluster one.

Corporate governance appears to be the most explored topic in relation to cash holding as evident by the number of keyword occurrences (96 times). Studies on this association can be categorized into several groups: first, studies that concentrated on board of director characteristics (Asante-Darko et al. 2018 ; Atif et al. 2019 ; Boubaker et al. 2015 ; Roy 2018 ; Thanatawee 2019 ). The overall evidence of the cash holding pattern of corporate governance negative (Harford et al. 2008 ; Roy 2018 ). The agency literature suggests that management can be prevented from holding excessive cash by the high quality of governance mechanisms like better law enforcement and higher investor protection (Da Cruz et al. 2019 ). Similarly, Dittmar and Mahrt-Smith ( 2007 ) reported that poor-governed companies dissipate cash quickly and in ways that significantly reduce operating performance. However, the findings of prior studies are still inconclusive. For instance, Dogru and Sirakay-Turk ( 2018 ) contend that cash holding is more considerable in well-governed corporates than in poorly governed ones. While Akben-Selcuk et al . (2020) argue that the structure of boardroom does not exert a significant influence on the level of cash holdings. Apart from the mixed findings, some mechanisms have been overlooked in the literature such as board diversity (Khatib et al. 2021 ). The existing research on board diversity and cash holding has concentrated on gender diversity as an indicator of board diversity, neglecting other indicators like ethnic, educational, experience, age, tenure, and others (see, Atif et al. 2019 ; Cambrea et al. 2019 ). Atif et al. ( 2019 ) reported a significant negative association between more gender diverse boardroom and cash holdings. Whereas, more diversity in terms of educated tend to keep extra cash (Wang et al. 2017 ).

The second school concentrated on the association between ownership structure and cash holdings. Amess et al. ( 2015 ) suggest that any governance mechanisms that able to mitigate the agency conflicts, including ownership structure, results in reducing the cash holding in firms. It is well documented in the literature that the ownership structure has a significant impact on cash holding. Among different ownership structures, managerial ownership has received large attention among cash holding scholars (Chen and Chuang 2009 ; Drobetz and Grüninger 2007 ; Lee and Lee 2009 ; Ozkan and Ozkan 2004 ; Thanatawee 2019 ; Yu et al. 2015 ). Supporting the incentive-alignment hypothesis, Thanatawee ( 2019 ) found that the level of cash holding is lower as the managerial ownership increase indicating that executives do not keep extra cash for personal benefits. While Yu et al. ( 2015 ) suggest that a higher level of firm cash holding is associated with a higher percentage of managerial ownership supporting the argument that board monitoring and managerial incentives are substitutes for each other. Others reported a non-linear association between cash holding and managerial ownership, indicating an incentive alignment effect and an opposing effect related to increased risk aversion (Drobetz and Grüninger 2007 ; Ozkan and Ozkan 2004 ). Additionally, using institutional ownership as the primary governance indicator, Nguyen and Rahman ( 2020 ) reported a negative relationship between cash holdings and corporate governance. A similar finding was documented by Loncan ( 2018 ) after focusing on foreign institutional ownership, suggesting that this effect is potentially transmitted to cash by reducing the agency problems and alleviate the financial constraint. Moreover, scant attention has been given to other ownership attributes like ownership concentration and directors ownership (see, Ferreira and Vilela 2004 ; Taufil Mohd et al. 2015 ).

Third, we found that there is a limited but recent interest among scholars in evaluating the impact of chief executive officer (CEO) characteristics on cash holding (average publication per year 2017.42). Chief Executive Officer (CEO) characteristics are known to affect corporate financial policies (Intintoli and Kahle 2016 ). Orens and Reheul ( 2013 ) argue that it is essential for shareholders to account for the demographics of current or future CEOs and to know their associated preferences concerning cash policy. However, they limited their study to the age and experience of the CEO and found a significant influence on the cash holding of small-medium enterprises. Furthermore, Liu et al. ( 2014 ) suggested a positive relation between CEOs deferred compensation (in debt) and firm cash holdings. Zeng and Wang ( 2015 ) examine the CEO’s gender effect on cash holding and found that the female CEOs are related to a higher level of corporates cash saving. While Yung et al. ( 2015 ) suggested that CEOs overconfidence do not have a significant impact on cash holdings. However, despite the growing number of studies on the impact of corporate governance, ownership structure, and CEO characteristics on cash holdings, the findings of prior research result in mixed conclusion and some attributes have received a little attention from research such as ownership concentration, board diversity, and CEO demographic characteristics (Feng et al. 2020 ; Hassan et al. 2020; Khatib et al. 2020 ; Malagila et al. 2020; Roberts et al. 2020 ). Thus, we believe that research on this area remains a fertile ground for future research.

4.6.1.2 Group 2: The determinants of cash holdings

The finance literature has paid more attention to the determinants of firm cash holding (Jebran et al. 2019 ). Understanding the factors behind holding cash in corporations, offers a critical insight into the complexity of cash management and finance decisions (Tahir and Alifiah 2015 ). After the pioneering empirical study of Opler ( 1999 ) who conducted the earliest research on the determinants of cash holdings inspiring the emergence of the scholar interest in this topic, the determinants of cash holdings witnessed a gradual increase in the number of studies. Table 10 provides a summary of all studies on the determinants of cash holdings resulting from the cluster analysis (cluster 2). The literature has suggested that public firms have high level of cash holding than private one due to the agency costs and conflict (Gao et al. 2013 ). This is in line with Ferreira and Vilela ( 2004 ) who found that concentrated ownership and investor protection are important factors affecting the level of cash in corporations. Also, several additional factors have been proven in the literature to be significant in determining the level of cash holdings, such as credit risk, which has been found to exert a positive impact on cash level (Acharya et al. 2012 ; Opler 1999 ). Similar relation was reported with dividend payments, cash conversion cycles, investment opportunity, and firm size (Bigelli and Sánchez-Vidal 2012 ; Ferreira and Vilela 2004 ; García-Teruel and Martínez-Solano 2008 ; Opler 1999 ). In contrast, there is an adverse relationship between bank debt, leverage, asset’s liquidity, the interest rates in the economy, concentrated ownership, investor protection, capital markets development, and cash holdings (Ferreira and Vilela 2004 ; García-Teruel and Martínez-Solano 2008 ). It should be noted that these studies have mainly focused on the firm-level determinants, while country-level aspects have been less investigated.

There is a growing body of literature highlighting the firm-level aspects as important cash holding determinants such as risk (Acharya et al. 2012 ; Bates et al. 2009 ; Bigelli and Sánchez-Vidal 2012 ; Opler 1999 ), growth opportunity (García-Teruel and Martínez-Solano 2008 ; Opler 1999 ), bank debt (García-Teruel and Martínez-Solano 2008 ; Ozkan and Ozkan 2004 ), R&D expenditures (Bates et al. 2009 ; Brown and Petersen 2011 ; Dittmar et al. 2003 ), and size (Bigelli and Sánchez-Vidal 2012 ; Ozkan and Ozkan 2004 ). Furthermore, studies have examined the determinants of cash holdings in different levels of investor protection markets (Ferreira and Vilela 2004 ), and industries (Bates et al. 2009 ). However, it should be noted that the literature about the determinants of cash holdings still unclear in some contexts. For example, Opler ( 1999 ) suggested that there is an inverse relationship between firm size and the level of cash holdings in the USA, while Ozkan and Ozkan ( 2004 ) used a large sample from the UK and found this association to be insignificant.

5 Keywords analysis

The keywords co-occurrence is an insightful technique to investigate scientific constructs according to the presumption that keywords provide a coherent explanation to the content of the documents (Comerio and Strozzi 2019 ). The connection between two keywords presented by a numerical value which shows the relationship between both of them, and the higher this value, the stronger the link (link strength). The link strength between two keywords represents the number of times where these keywords occurred appeared in the same article. The total number of these links refers to the aggregate number these two keywords occur together. In VOSviewer, five were set as the minimum occurrences of a keyword to be presented, which means that keywords will appear on the bibliometric map once two keywords occur together in a document more than five times.

The keywords co-occurrence analysis conducted in this study involved 1594 keywords from 729 articles. Because of a lack of keywords in 78 journals, the other 145 documents were omitted from the analysis of the keywords. Also, synonymic keywords were analyzed before inserting the data into VOSviewer. For instance, “the number of cash holdings,” “cash holding (ch)”, “cash holding balances”, “cash holdings”, and “cash-holding levels” were re-labelled as “cash holdings” and counted as one keyword. The same re-labelling process was conducted for all other keywords.

However, a large number of these keywords have been used once. About 1248 (78.3%) were used one time, 176 keywords (11%) were used two times, and 51 (3.2%) was used three times. The number of total keywords decreased to 1199 by re-labelling them. The keywords were inserted in VOSviewer to map the literature with a minimum of 5 occurrences, and only 99 keywords met the thesaurus.

It has been suggested that the keywords co-occurrence analyses are representative enough to make general claims about the articles' content (Comerio and Strozzi 2019 ). Scholars usually employ co-occurrence analyses as it is an effective method to address the research trends on a particular topic by exploring existing documents (Md Khudzari et al. 2018 ; Shi and Li 2019 ), including the field of economics and finance (Castriotta et al. 2019 ). Following Baker et al. ( 2020 ) and Md Khudzari et al. ( 2018 ), we conduct keyword co-occurrence to evaluate the prevalent themes within cash holding. The result from the keywords co-occurrence map (Fig.  6 ) shows that cash holding research is mainly focused on corporate governance (96 occurrences, 66 links strength). It indicates that most of the researches on cash holdings concentrated on examining the association between corporate governance mechanisms and cash holding. One possible explanation for this is that the financial policy of corporates is significantly affected by the corporate governance quality and the agency conflicts among agents and principles (Lee and Lee 2009 ).

The bibliometric map of author keywords co-occurrence. To open this map in VOSviewer, use the following URL: https://bit.ly/2XLu2eD

Additionally, given that cash holding is considered as one approaches a firm would follow to structure its capital, it was expected to have a strong association with other financial aspects such as “financial constrain” which is second most topics examined concerning cash holding (67 occurrences, 43 link strength). Furthermore, liquidity (55 occurrences) was noted to be also highly related to cash holding (30 link strength). We also encountered general terms such as ‘investment’ (46 occurrences, 47 links), 'cash" (36 occurrences, 28 links). Table 11 provides a summary of the most frequent keywords.

The colour in Fig.  6 shows the average year of publications in which the keyword has occurred, overlay visualization mode with five as minimum occurrences. We also illustrate the most recent and oldest extremes of keywords in cash holding in Table 12 with three minimum keyword occurrences. It is noteworthy that, in our unit analysis, taxation, risk management, and initial public offer are the oldest topics to be investigated in relation to cash holding. The interest in the taxation theme has been renewed in recent years but tax avoidance aspects. Additionally, it is worth noting that advanced methodological techniques were introduced in 2015, with terms such as quantile regression and generalized method of moments (GMM). Hence, it is expected in the future to see more work with these methods and others, such as structural equation modelling and difference-in-differences techniques that have been overlooked in the literature.

Furthermore, corporate governance is the most frequent key-term, and scholars are moving toward more specific governance mechanisms such as board independence (3 occurrences; 2018), country governance (3 occurrences; 2018), and board of directors (12 occurrences; 2016). Finally, corporate social responsibility has drawn researchers' attention recently, and it can be a potential hot topic for future studies due to the limited work on this association. From the keywords’ frequency, two topics of interest were selected for the content analysis including payout policy and corporate social responsibility, while corporate governance as the most examined area in relation to cash holdings is discussed in the cluster analysis later. To evaluate these topics, we searched within our literature sample for specific terms that are related to each output separately.

5.1 Topics of interest and thematic evolution

5.1.1 cash holding and payout policy.

Payout policies (dividends payment and share repurchase) are common ways for corporations to re-balance their capital structure by either reducing or increasing the cash holdings. The association between cash holding and payout police is well documented in the literature, as evidenced by the number of keyword occurrences. However, there are very few studies on share repurchase and cash holdings (Almeida et al. 2016 ; Haw et al. 2011 ; Moon et al. 2015 ). The majority of researches has focused on dividend as the mean of cash distribution (Jia and McMahon 2019 ; Kumar and Ranjani 2019 ; Yang et al. 2020 ). Yet, the finding of prior studies is still inconclusive. The association between cash holding and dividend payment is suggested to be positive (Jia and McMahon 2019 ; Kuldeep and Misra 2019 ). On the other hand, Ahmad and Adaoglu ( 2019 ) focus on the determinant of cash holding and find the association between dividend and cash reserving to be negative and these findings were further supported by Lee and Lee ( 2019 ). However, Palazzo ( 2012 ) stressed that companies tradeoff between the dividends distribution and cash reserve, reaching the optimal cash holding level, which helps firms to lower the costs of external financing.

Scholars start to examine the interaction between different factors in an attempt to solve the puzzle of cash holding. Yang et al. ( 2020 ) examine the innovation and payout policy relationship and find that R&D company with higher internal financing deficit and lower cash holding have pay-for-finance incentives where it pays dividends to facilitate the access external financing activities (Yang et al. 2020 ). Doan and Iskandar-Datta ( 2020 ) focus on the gender diversity of top management and its impact on cash holding. They find that corporates with surplus cash and female CFOs distribute more dividends among shareholders. Furthermore, Lee and Lee ( 2019 ) examine the interrelationship between research and development intensity, dividend, cash holding, and company value in biotech corporates. They suggest reserve extra cash can be achieved by lowering dividends level, and this cash hoarding is positively linked with the firm valuation in the long-term. At the same time, Jia and McMahon( 2019 ) suggested dividend payments decline in companies where the increase of cash holding is a result of a permanent-growth of in corporate profitability. However, although it is well documented in the literature that the relationship between payout policies and cash holding is significant, the sign of their effects is unclear.

5.1.2 Cash holding and corporate social responsibility

The primary concern of corporate social responsibility (CSR) is to achieve the ultimate satisfaction of various stakeholders of corporations. Stakeholders are defined as a different group of individuals engaged in the activities of a business, including competitors, employees, customers, suppliers, creditors, shareholders and society. However, despite the importance of this aspect in today’s business environment, only a handful of research has been carried out to examine the relationship between corporate social responsibility and cash holdings. Yang et al. ( 2019 ) investigate the effect of CSR on the cash holding valuation and find that in the capital market, CSR does enhance the cash holdings’ value, and this positive effect increases with the firm's market value. This result supports the conclusion of Arouri and Pijourlet ( 2017 ) firms with a high corporate social responsibility rating associated with higher value to cash held from investors. Another study by Lu et al. ( 2017 ) dedicated to examining the CSR report relationship with cash holding, suggested that information in CSR reports can facilitate monitoring and thus induce more efficient use of cash holdings. Hence, the issuance of a standalone CSR report increases the marginal value of cash holdings. Lastly, one study identified to examine the association between cash holdings and CSR by Cheung and Wai ( 2016 ) suggesting a positive relationship between cash holdings and CSR. To our knowledge and based on the study results, very few studies have been conducted to examine the relationship between corporate social responsibility and cash holdings and as such, this warrants future investigation.

6 Conclusion, limitations and further research

Cash holding is considered as a significant aspect at the heart of corporates' financial policy. In fact, cash holding is the most popular mean of maintaining enough liquidity within corporations. In the past two decades, corporates around the globe have substantially increased their cash holding. Consequently, a growing interest of researchers has been devoted to cash holding topics, especially after the global financial crisis of 2007 and it is expected to see more work on cash holdings in the recent future evaluating the Covid-19 pandemic impact on the different aspects of cash holding (Khatib and Nour 2021 ). Despite the growing number of empirical studies on cash holdings, there is a lack of review work that analyzing and evaluating the cash holding publications from an international perspective and different aspects of this topic.

We have used a bibliometric and content analysis to assess the development of global cash holding research from several aspects. The data used in this study were retrieved from Scopus (874 journal articles in total). 145 articles were excluded from the keyword analysis due to the lack of the keywords. Furthermore, the content analysis was limited to four themes that emerged from the keyword and cluster analysis, namely, corporate governance, determinants of cash holdings, payout policy, and corporate social responsibility.

Overall, the results suggest that the number of articles has been rapidly increasing since the financial crisis. Interestingly, about 50% of the total global publications were contributed by developed countries (the USA, the U.K., and China), while that few studies taking place in the African region, Latin America, and the Middle East countries. We, therefore, encourage scholars to explore more the cash holding topic from emerging countries especially a single-industry research as it has been suggested that industries might differ in terms of liquidity needs and other factors influencing the cash holdings level. Similarly, there is a lack of focus on small-medium firms. Surprisingly, SMEs occurred nine times only, and researchers tend to concentrate on significant industries and firms due to data availability. Therefore, we highly encourage scholars to explore cash holdings topics in different industries and SMEs.

Regarding payout policy, there is a lack of work on share repurchase and cash holding relationship and more research on cash holding and payout policy (dividend and share repurchase) is highly recommended. We do not recommend merely replicating previous research. Future studies may take advantage of including more socio-economic factors and cultural aspects to extend the understanding of cash holding. Moreover, corporate governance is the most examined topic in relation to cash holdings. Yet, the findings of prior studies are mixed, especially when it comes to different governance attributes. Besides, some mechanisms have been overlooked by scholars such as CEO characteristics, ownership attributes and board diversity in terms of ethnicity, education, tenure, experience, national diversity. Pointing to a need for further work to consider the impact of governance attributes that are less addressed in the literature and the interaction between them. Finally, in the last five years, only a handful of researches have been conducted to explore the association between cash holdings and corporate social responsibility. We, therefore, encourage studies to explore further the influence of cash holdings on CSR, sustainability, and environmental performance/disclosure.

This article contributes to this topic for being the first of its kind to provide a comprehensive evaluation of the development of cash holding research form from the international perspective. By using a large number of articles, this study presents an overview of the research landscape in the area of cash holdings that provides interesting insights and directions for future research offering a complementary approach to the more traditional literature review. Our study underlines the dominating topic related to cash holding (corporate governance) and the recent research trends which would be useful for both academics and professionals. From an application viewpoint, this study will serve as basic groundwork for understanding research into the cash holdings, its current stage and the direction in which the research is growing. Also, it highlights the gap in the current body of knowledge and proposes several actionable avenues for future research in the subject. Indeed, within the concept of cash holdings itself lies the implication that it may affect several organizational aspects, as far as cash holding involves all the companies’ management bodies with decision-making powers.

Like other researches, our literature review has some limitations. First, the search technique used in this study was restricted to cash* holding* within the titles, abstracts, and keywords. However, some research might not refer to the cash holding within the searching scope. Also, we limited our search to the search scope to the Scopus database as it is considered as the most extensive citation and abstract database of peer-reviewed articles. Hence, the finding of the search string used in this study may not cover all publications on cash holding. Further research could make a comparison of the outputs from multiple databases.

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Khatib, S.F.A., Abdullah, D.F., Hendrawaty, E. et al. A bibliometric analysis of cash holdings literature: current status, development, and agenda for future research. Manag Rev Q 72 , 707–744 (2022). https://doi.org/10.1007/s11301-021-00213-0

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DOI : https://doi.org/10.1007/s11301-021-00213-0

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