# B. Volatility of Excess Cash Holdings and Future Market Returns

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1 In this online supplement, I present additional empirical results and confirm robustness of the positive relation between excess cash and future fund performance using yet another alternative definition of excess cash. A. Transition Probabilities To determine the persistence of excess cash, I estimate the transition probabilities of the excess cash groups, shown in Table S1. Excess cash is rather transitory: for example, the likelihood of remaining in the low excess cash for two more years is just 9.7%. Furthermore, given that a fund was assigned to the middle excess cash group at the end of a year, it is almost equally likely to be in either of the five groups a year later. High excess cash funds have the highest probability among the five groups to remain in the same quintile a year later, yet almost 20% of such funds move to one of the bottom two excess cash groups within a year. B. Volatility of Excess Cash Holdings and Future Market Returns It is interesting to ask whether excess cash holdings of mutual funds predict market returns. 1 The results presented in Table 12 of the paper indicate that funds in none of the excess cash groups exhibit robust evidence of market-timing skills. Yet, it is possible that at least some subset of mutual fund managers possess market-timing abilities. The funds run by such managers are likely to have more volatile excess cash holdings, as the managers adjust cash positions in response to their changing expectations about market returns. Thus, if managers possess any market-timing skills, the evidence will be more pronounced among the funds with high volatility of excess cash holdings. To test this hypothesis, at the end of each quarter τ I calculate volatility of excess cash holdings as standard deviation of excess cash during the past 12 quarters (from τ 11 to τ), requiring at least eight observations to be present. 2 I assign funds into five groups on the basis of this measure, and for each quintile j, compute aggregate excess cash at the end of quarter τ as AEC jτ = i j EC iτ T NA iτ, where EC iτ and T NA iτ are excess cash and total net assets of fund i as of the end of quarter τ, 1 In untabulated results, I confirm the finding of Yan (2006) of no relationship between aggregate raw cash holdings and future market returns. 2 To obtain a meaningful measure of volatility of excess cash holdings, I limit the sample to post-1998 data, when cash holdings are available quarterly.

2 and then estimate the regression R N M,τ+1 = ψ 0j + ψ 1j AEC jτ + ς N j,τ+1, where RM,τ+1 N is the market return during the N-month period starting in the first month of quarter τ + 1, N (1, 3, 6, 12). A significantly negative coefficient ψ 1j can be interpreted as consistent with market-timing ability of group j, whereas a positive coefficient implies poor market-timing skills. The results of this regression are reported in Table S2. At each forecasting horizon, the bottom four groups exhibit either insignificant, or significantly negative market-timing abilities. However, aggregate excess cash holdings of the funds with high volatility of past excess cash holdings relate significantly and negatively to future three- and six-month market return. 3 This evidence is consistent with skillful market timing by those mutual fund managers who frequently adjust their excess cash holdings. Such managers increase their excess cash position prior to market downturns and reduce it prior to a period of strong market returns. C. Excess Cash and Future Performance: Conditioning on Prior Market Return Following a market downturn, financial press abounds with stories of managers who adjusted their cash position in response to poor recent market returns. 4 Surprisingly often, such moves by the managers tend to be portrayed as savvy even though the managers adjusted their cash holdings only after the period of low market returns, rather than prior to it. In untabulated results, I find that this tendency to increase cash holdings following a market downturn is particularly pronounced among unskilled managers (those with lower return gap). For the purposes of my analysis, this implies that following a downturn, the portfolio of high excess cash funds is likely to include the funds run by such managers who are likely to continue to underperform (see Kacperczyk, Sialm, and Zheng, 2008). In such times, the returns of high excess cash portfolio will be dragged down due to the fact that it includes these poorly-performing funds. To account for this, I modify the portfolio formation approach used in the paper. Instead of assigning funds into quintiles on the basis of excess cash in each cross-section when cash holdings are available, I assign funds into quintiles only if the prior 12-month market return was positive. 5 3 Insignificant evidence of market timing at one- and twelve-month horizons is consistent with the findings of Jiang, Yao, and Yu (2007) who use mutual fund holdings data to study market-timing abilities. They find no evidence of market-timing skills at one- and twelve-month horizons, but observe positive timing ability and three- and six-month horizons. 4 For examples, see Fund s extra cash holds opportunities, Wall Street Journal, April 8, 2009; More stocks funds declare cash king, Wall Street Journal, April 9, 2009; Cash regains its asset status, Barron s, August 17, I alternatively consider not including into a high excess cash portfolio those funds that increased their cash holdings by more than half following a 12-month period of negative market returns, and obtain similar results. 2

3 Table S3 reports the resulting future raw and risk-adjusted returns of different excess cash groups. Compared to the findings presented in Table 4 of the paper, where funds are assigned into groups without conditioning on prior market performance, the difference in future returns between high and low excess cash funds is approximately 50 percent larger. For example, the difference in the Ferson- Schadt conditional alphas reaches 0.32% per month (t-statistic of 3.95). Even more interesting, alphas of the high excess cash group are in no case negative, regardless of which performance measure is used. Thus, the relation between excess cash and future fund performance is particularly pronounced when high excess cash portfolio is less likely to include unskilled managers who increase their cash position in response to poor recent market returns. D. Simplified Excess Cash Definition Definition of excess cash as a residual from cross-sectional regression (7) in Table 2 of the paper is very appealing, as it accounts for a wide number of variables that affect corporate cash holdings. To address any concerns about the sensitivity of the results to this particular way of estimating excess cash, I now show that the main empirical conclusions of this paper are robust to yet another alternative measure of excess cash. More specifically, to obtain excess cash for fund i as of the end of month t, I run a simpler cross-sectional regression CASH it = γ 0t + γ 1t RU12 it + γ 2t FF1 it + γ 3t β Mkt Fund,it + ε it, where, as before, CASH it is the percentage of total net assets of fund i held in cash as of the end of month t; RU12 it is the 12-month fund return runup ending at the end of month t; FF1 it is fund flow during month t; and β Mkt Fund,it is market beta of the fund estimated using realized fund returns from t 11 to t. Table S4 shows that controlling for prior return runup, recent fund flows, and fund market beta is sufficient to generate a positive relation between excess cash and future fund returns. 3

4 Table S1. Excess Cash Groups Transition Probabilities Low τ+1 EC2 τ+1 EC3 τ+1 EC4 τ+1 High τ+1 Low τ EC2 τ EC3 τ EC4 τ High τ Notes: This table reports transition probabilities of the five excess cash groups. Excess cash as of the end of calendar year τ is estimated from the cross-sectional regression (7) in Table 2 of the paper. Sample period is

5 Table S2. Market Timing Conditional on Volatility of Excess Cash Low Var(EC) Var(EC)2 Var(EC)4 Var(EC)4 High Var(EC) 1 month [2.11] [0.52] [1.09] [0.56] [-0.56] 3 months [1.14] [2.20] [2.18] [1.81] [-2.00] 6 months [0.09] [2.59] [1.76] [1.36] [-2.04] 12 months [-0.13] [1.80] [0.06] [0.09] [-0.67] Notes: This table reports slope coefficients and t-statistics from the regression of N- month market return beginning in month t + 1, N (1, 3, 6, 12), on aggregate excess cash holdings of five portfolio that are formed on the basis of volatility of past excess cash holdings, Var(EC), which is computed for each fund at time t as standard deviation of excess cash holdings from twelve quarterly observation in months t 33, t 30,..., t 3, and t. Sample period is

6 Table S3. Excess Cash Holdings and Future Fund Performance Conditional On Positive Market Runup Performance measure Low Quint 2 Quint 3 Quint 4 High High-Low R 2 Excess return [0.85] [1.49] [1.47] [1.70] [1.61] [3.02] Market model alpha [-3.53] [-0.74] [-0.93] [0.51] [0.04] [3.33] Fama-French factor alpha [-3.51] [-0.97] [-0.74] [0.63] [0.42] [3.73] Carhart factor alpha [-3.32] [-1.39] [-1.10] [-0.22] [0.02] [3.29] Carhart + liquidity factor alpha [-3.13] [-1.06] [-0.81] [0.11] [0.17] [3.21] Ferson-Schadt conditional alpha [-3.54] [-1.32] [-0.96] [-0.42] [0.31] [3.95] Notes: This table reports average raw and risk-adjusted returns, in percent per month, and the corresponding t-statistics for each of the excess cash quintiles of index funds as well as for the differences between quintiles of high and low excess cash, conditional on the 12-month market return prior to cash measurement being positive. Excess cash is calculated as the residual from the cross-sectional regression (7) in Table 2 of the paper. At the beginning of month t + 4, a total net assets-weighted investment is made in the funds that were assigned to a particular excess cash group as of the end of month t, and the position is held for the following 12 months. The 5-factor model uses Pastor-Stambaugh liquidity factor. R 2 is the adjusted R 2 from regressions using as a dependent variable the difference in returns between high and low excess cash funds. The sample period is

7 Table S4. Fund Excess Cash Holdings and Future Performance: Simplified Excess Cash Definition Performance measure Low Quint 2 Quint 3 Quint 4 High High-Low R 2 Excess return [1.56] [1.64] [1.69] [1.72] [1.71] Market model alpha [-2.35] [-1.06] [-0.56] [-0.33] [-0.03] [1.71] Fama-French factor alpha [-4.59] [-1.63] [0.48] [0.14] [0.03] [3.27] Carhart factor alpha [-3.73] [-1.53] [-0.64] [-0.46] [-0.88] [2.16] Carhart + liquidity factor alpha [-3.55] [-1.25] [-0.50] [-0.31] [-0.64] [2.20] Ferson-Schadt conditional alpha [-4.05] [-1.62] [-0.38] [-0.49] [-0.74] [2.46] Notes: This table reports average raw and risk-adjusted returns, in percent per month, and the corresponding t-statistics for each of the excess cash quintiles of index funds as well as for the differences between quintiles of high and low excess cash. Excess cash of fund i as of the end of month t is calculated as the residual from cross-sectional regression CASH it = γ 0t + γ 1t RU12 it + γ 2t FF1 it + γ 3t β Mkt Fund,it + ε it, where CASH it is the percentage of fund total net assets held in cash as of the end of month t; RU12 it is the 12-month fund return runup ending at the end of month t; FF1 it is fund flow during month t; and β Mkt Fund,it is market beta of the fund, calculated from market model regressions using realized fund returns from months t 11 to t. At the beginning of month t + 4, a total net assets-weighted investment is made in the funds that were assigned to a particular excess cash group as of the end of month t, and the position is held for the following 12 months. The 5-factor model uses Pastor-Stambaugh liquidity factor. R 2 is the adjusted R 2 from regressions using as a dependent variable the difference in returns between high and low excess cash funds. The sample period is

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