3.3 Investors' Response to the Return Gap
3.3.1 Main Eect
We regress quarterly fund ows in quarter t on lagged variables, known to in uence investors' capital allocation decisions, and four lagged return gap measures. More speci cally,
F lowi,t+1= βXi,t+ t (3)
The vector of explanatory variables Xi,tconsists of an intercept, past net returns and fund ows, alpha,
the most recently available expense ratio, and past return gap realizations. The alpha is estimated at the end of quarter t using monthly data over the preceding 12 months from a four factor model, including the return of the market, SMB, HML, and Mom.10 We include the most recently available expense ratio because
the return gap is calculated using fund's expenses. This way, we rule out a mechanical relation between fund ows and the return gap that may be due to a response to the expense ratio. We use two methodological alternatives Fama-Macbeth regressions (Fama and Macbeth (1973)) with Newey-West standard errors and pooled regressions with time- xed eects and standard errors clustered on the fund level.
10The risk factors are obtained from Kenneth French's data library: http://mba.tuck.dartmouth.edu/
3.3. Investors' Response to the Return Gap 41
Table 3.5. Investors' Response to the Return Gap.
The dependent variable in each regression speci cation is fund ow in quarter t. In each speci cation, we include an intercept, alpha (estimated using past one year of monthly fund returns and the excess return on the market, SMB, HML, and Momentum as risk factors), the most recently available expense ratio, four lagged quarterly fund ow measures, and four lagged fund net return measures. In speci cations (2) and (4) we add four lagged return gap scores, calculated according to the procedure described in Section 3.2. In speci cations (1) and (2) we estimate the models using Fama-Macbeth regressions where I report t-statistics based on Newey-West standard errors with 3 lags. In speci cations (3) and (4) we estimate the models using a panel regression approach where we include time- xed eects and cluster standard errors on the fund level.∗denotes statistical
signi cance on the 10% level,∗∗denotes statistical signi cance on the 5% level, and∗∗∗denotes statistical signi cance on the
1% level.
Fama-Macbeth Pooled
(1) Flowt (2) Flowt (3) Flowt (4) Flowt
Coe t-stat Coe t-stat Coe t-stat Coe t-stat Intercept −0.02∗∗∗ −2.91 −0.02∗∗ −2.39 −0.01∗∗∗ −2.82 −0.01∗ −1.82 Alpha 1.19∗∗∗ 4.66 0.97∗∗∗ 3.57 1.40∗∗∗ 8.34 1.29∗∗∗ 7.97 Exp Ratio 0.83∗∗∗ 3.65 1.13∗∗∗ 4.24 0.31 1.23 0.43 1.44 Flowt-1 0.18∗∗∗ 9.86 0.17∗∗∗ 10.01 0.07∗∗∗ 2.71 0.07∗∗∗ 2.72 Flowt-2 0.08∗∗∗ 5.74 0.10∗∗∗ 7.28 0.06∗∗∗ 5.74 0.06∗∗∗ 5.74 Flowt-3 0.08∗∗∗ 4.17 0.09∗∗∗ 4.89 0.02∗∗∗ 3.67 0.02∗∗∗ 3.66 Flowt-4 0.01∗∗∗ 2.92 0.02∗∗∗ 3.77 0.01∗∗∗ 3.55 0.01∗∗∗ 3.52 Returnt-1 0.36∗∗∗ 7.86 0.31∗∗∗ 5.52 0.35∗∗∗ 17.38 0.34∗∗∗ 17.03 Returnt-2 0.25∗∗∗ 6.45 0.20∗∗∗ 5.44 0.17∗∗∗ 9.86 0.15∗∗∗ 9.00 Returnt-3 0.25∗∗∗ 6.17 0.22∗∗∗ 5.49 0.17∗∗∗ 11.12 0.16∗∗∗ 10.35 Returnt-4 0.11∗∗∗ 3.29 0.07∗∗ 2.18 0.10∗∗∗ 6.18 0.09∗∗∗ 5.56 ReturnGapt-1 0.21∗∗∗ 3.39 0.11∗∗∗ 3.08 ReturnGapt-2 0.23∗∗∗ 3.85 0.18∗∗∗ 5.96 ReturnGapt-3 0.22∗∗∗ 3.22 0.14∗∗∗ 4.27 ReturnGapt-4 0.15∗∗ 2.50 0.15∗∗∗ 4.13 R2 0.22 0.24 0.12 0.13 Observations 85914 85914 85914 85914 Time- Period Q1.1990 Q3.2010 Q1.1990 Q3.2010 Q1.1990 Q3.2010 Q1.1990 Q3.2010
The results, using the whole dataset between 1990 and 2010, are consistent across the two methodologies and summarized in Table 3.5. In the restricted models 1 and 3, where we do not include the lagged return gap variables, we nd results largelyconsistent with previous studies on the ow-performance relationship, such as Ippolito (1992) and Chevalier and Ellison (1997). Investors stronglychase past returns and alpha, putting higher weight on more recentlyavailable data. The estimated coe cients on lagged fund returns range from above 0.3 for the most recentlyavailable quarterlyfund return to about 0.1 for fund returns that are four quarters old. Consequently, a 1% fund return in each of the four preceding quarters translates to about 1% quarterlyfund ows. Similarly, the estimated coe cients on lagged fund alpha implythat a 1% yearly alpha translates to a 0.97% to 1.40% increase in fund ows in the following quarter, depending on the speci cation.
Next, in speci cations 2 and 4, we include four past realizations of the return gap measure as explanatory variables. We nd a strong, positive response of ows to the past return gaps. The estimated coe cients of the four lagged return gap measures range between 0.15 and 0.21, with t-stats between 2.50 and 3.39. The results are economicallyimportant. More speci cally, a one standard deviation increase in the return gap in each of the last four quarters is followed bya 0.96% or 1.34% increase in ows in the following quarter, depending on the estimation method. To position this in perspective, a one standard deviation increase in alpha is followed byan increase in expected ows of 0.78% or 1.03% during the next quarter, depending
42 Chapter 3. Do Investors Use Fund Holdings to Infer Managerial Skill? on the estimation method. The results further show that a one standard deviation increase in net returns brings 8.10% or 7.40% expected ows in the following quarter,depending on the speci cation. The evidence presented in Table 3.5 suggests that the economic impact of investors' response to the return gap is important, in order of magnitude similar to investors' response to past alpha.
We also nd a positive response of investors to the lagged expense ratio. At rst sight,this may appear a bit surprising since previous studies document a negative response to management fees (see,for example,Sirri and Tufano (1998)). Yet,the speci cations include total expense ratio,which also contains the marketing and distribution expenses,known as 12b-1 fees. Jain and Wu (2000) and Barber et al. (2005) point that marketing by fund managers seems to work higher marketing expenses attract investors. Furthermore,Barber et al. (2005) show that investors tend to avoid load funds and Haslem (2009) points that fund managers mask payments to brokers and advisors in the 12b-1 fees and market themselves as no-load funds in order to attract naive investors. Thus,12b-1 fees appear to be positively related to fund ows. Note that we include the total expense ratio in our speci cations since we are interested in ruling out a mechanical relation between the return gap and investor ows that is due to a response to the expense ratio. Therefore,it is beyond the scope of this study to examine the response of investors to dierent fund fees.