...more cash. However, do hot find that fund managers with better stock-picking skills hold less cash. Aggregate cash holdings by equity mutual funds are persistent and positively related to lagged aggregate fund flows. Aggregate cash holdings do not forecast future market returns, suggesting that equity funds as a whole do not have market timing skills.

Cash is a critical component of equity mutual funds' portfolios. At the end of 2000, US equity funds held $228 billion, or 5.8% of their total assets under management, in cash. To put this amount in perspective, the equity fund industry as a whole had only $240 billion in total assets in 1990 (Investment Company Institute, 2002). And yet, despite their practical importance, fund cash holdings have received little direct attention in the academic literature. (1)

The purpose of this article is to examine the determinants and implications of equity mutual funds' cash holdings at both the fund level and the aggregate level. In particular, I address the following questions: How do transaction costs and investor flows affect fund cash holdings? Do managers with better stock-picking skills hold less cash? Do equity funds as a whole display market timing skills by holding more cash prior to down markets?

Equity mutual funds hold cash for several purposes. First, funds hold cash to meet shareholders' redemption needs. Second, funds use cash to pay management fees and other expenses, and to make dividend and capital gain distributions. Third, fund managers may hold cash when they expect future stock market returns to be low (market timing).

The primary cost of holding cash is the opportunity cost. Between 1926 and 2002, stocks outperformed cash by approximately 7.5% per year in the US. (2) Therefore, cash tends to be a drag on long-term fund performance. For example, Wermers (2000) estimates that for the period from 1975 to 1994, cash and bond holdings lower the performance of an average equity fund by 70 basis points per year.

Therefore, there is a trade-off between the costs and benefits of funds' cash holdings. Funds that maximize shareholder wealth should set the fund's cash holdings at a level such that the marginal benefit of cash holdings equals the marginal cost. To formalize this idea, I develop a static model of optimal cash holdings. For tractability, the model considers the trade-off between two factors, the expected trading cost of liquidating stocks to meet redemptions and the opportunity cost of cash.

The model produces four principal predictions. First, that funds with less-liquid stock holdings hold more cash because it is more costly for these funds to liquidate their stock holdings. The model predicts that small-cap funds hold more cash because small-cap stocks have higher transaction costs. Second, that funds with more-volatile fund flows hold more cash. Intuitively, funds with more-volatile fund flows have a greater probability of experiencing a cash shortage. Third, that funds expecting higher fund inflows hold less cash. Fourth, that managers with better stock-picking skills hold less cash. The intuition for this result is that the opportunity cost of holding cash is higher for more skilled managers.

Earlier studies on dynamic portfolio choice in the presence of transaction costs (e.g., Constantinides, 1986) suggest that funds' cash holdings should be persistent and positively related to recent fund flows. In a frictionless world, a fund rebalance its portfolio continuously to maintain an optimal level of cash. Therefore, past fund flows have no impact on a fund's current cash holding. However, in the presence of transaction costs, it is not optimal for a fund to rebalance its portfolio continuously. The optimal strategy for a fund is to adjust its cash holdings only when they are either too high or too low. As a result, fund cash holdings are persistent and positively related to recent fund flows.

I test the above predictions by using a comprehensive sample of US equity mutual funds for the period 1992 to 2001. I find that small-cap funds, funds with higher recent fund flows, and funds with more-volatile fund flows hold more cash. These cross-sectional results are consistent with models of optimal cash holdings. I do not find evidence of a systematic relation between fund cash holdings and risk-adjusted fund performance. This result does not support the static model's prediction that fund managers with better stock-picking skills tend to hold less cash.

To provide additional insight into the predictions of models of optimal cash holdings, I also examine aggregate cash holdings by equity mutual funds. Consistent with dynamic models of optimal fund cash holdings, I find that aggregate fund cash holdings are persistent and positively related to lagged aggregate fund flows. Aggregate fund cash holdings are also negatively related to lagged market returns. This finding is consistent with the idea that equity funds as a whole engage in positive-feedback trading at the market level. I find that aggregate cash holdings are not significantly related to future market returns, suggesting that equity funds as a whole do not have market timing skills.

This article is related to a growing literature that examines the determinants of corporate cash holdings (see, e.g., Kim, Mauer, and Sherman, 1998; Opler, Pinkowitz, Stulz, and Williamson, 1999 and Almeida, Campello, and Weisbach, 2004). Kim et al. (1998) and Opler et al. (1999) find that corporate cash holdings are higher among firms with riskier cash flows. Similarly, in this paper I find that equity mutual funds hold more cash when fund cash flows are more volatile. In addition, many papers in the corporate cash holding literature find that cash holdings increase in the cost of external financing. This result is similar to my result that fund cash holdings increase in transaction costs. Finally, Almeida, Campello, and Weisbach (2004) find that cash flow sensitivity of cash is positive, especially among financially constrained firms. In this article, I document a significant and positive relation between fund cash holdings and recent fund flows. These parallels suggest that industrial corporations and mutual funds are similar in many ways when it comes to managing liquidity.

The article proceeds as follows. I develop my static model of optimal cash a holdings in Section I. I describe the mutual fund sample and present summary statistics in Section II. I examine the determinants of fund-level cash holdings in Section III and present the results for aggregate cash holdings in Section IV. Section V concludes the article.

I. A Static Model of Optimal Cash Holdings

In this section, I first develop a static model of optimal cash holdings and then present the predictions of this model. I also discuss the implications of dynamic models of optimal cash holdings.

A. The Model

I consider a two-period model. At t=0, the fund allocates its money between a risky asset (or portfolio) and a risk-free asset. Without loss of generality, I assume that the total net asset (TNA) of the fund is $1 at t=0, and that the risk-free rate is zero. The expected return of the risky asset is E(R)>0, which is also the equity premium because the risk-free rate is zero. I denote the fund's cash allocation as c. In addition, I denote the fund manager's stock-picking ability as [alpha].

At t=1, the return to the risky asset is realized, so is the net fund flow (denoted as x). The net fund flow can be positive or negative. When redemptions are greater (less) than new sales, the fund flow is negative (positive). For tractability, I assume that the net fund flow is drawn from a normal distribution.

(1) x ~ N([mu],[[sigma].sup.2])

When the fund does not have enough cash to meet redemptions (when c<-x), the fund must liquidate a portion of its risky asset to raise cash. I assume that there is a proportional cost (denoted as g) associated with liquidating the risky asset. This cost includes brokerage commissions, bid-ask spreads, and price impact.

The objective of the fund is to maximize the expected TNA at t=1, as the fund management fees are typically a fixed percentage of total assets under management. Since the fund starts with a TNA of $1, maximizing expected TNA at t=1 is equivalent to:

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

That is, the fund minimizes the sum of the expected cost of liquidating the risky asset and the opportunity cost of cash holdings. The first term on the right-hand side of Equation (2) captures the expected cost of liquidating the risky asset to meet redemptions. The upper limit of the integral is -c, reflecting the fact that, when net redemption is greater than the level of cash holding c, the fund must sell the risky asset to meet redemption needs. The lower limit of the integral is -1 because the fund starts with a TNA of $1. The second term on the right-hand side of Equation (2) captures the opportunity cost of cash holdings, and is increasing in the expected return of the risky asset E(R), the manager's alpha, and the level of cash holding c. This model is admittedly simple, and does not capture many important features of mutual funds. My objective is to focus on fund cash holdings.

Using properties of truncated normal distributions, I can rewrite L(c) as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where Z(*) is the probability density function of the standard normal and [PHI](*) is the cumulative distribution function of the standard normal.

To obtain closed-form solutions, I make two simplifying assumptions. First, I assume that the mean fund flow [mu] is zero. This assumption is reasonable when the evaluation period is relatively short. For example, Greene and Hodges (2002) report that the average daily percentage fund flow is -0.02% for a large sample of US mutual funds during the period 1998-2000. Second, I approximate the lower limit of the integral -1 with -[infinity]. In practice, the probability of x being less than -1 is negligible for...

NOTE: All illustrations and photos have been removed from this article.




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