Fund performance and subsequent risk: a study of mutual fund tournaments using holdings-based measures

This table reports the results for the pooled regression (Eq. 1) of the change in return standard deviations, \(\sigma _{[7,12]} -\sigma _{[1,6]} \), on the return rank, \(R_{[1,6]} \), and the first half-year’s standard deviation, \(\sigma _{[1,6]} \), for all funds (stocks) \(i\) and calendar years \(t\): \(\sigma _{[ {7,12} ],i,t} -\sigma _{[ {1,6} ],i,t} =\alpha +\beta _1 R_{[ {1,6} ],i,t} +\beta _2 \sigma _{[ {1,6} ],i,t} +\varepsilon _{i,t} \). Return ranks are normalized and expressed as fractional ranks ranging from 0 to 1, with the best-performing funds (stocks) having rank 1. The regression results are displayed for the non-index funds, index funds, and stocks, respectively. The coefficient estimates are shown on the first line, and the t statistics are in parentheses below. Standard errors are simultaneously clustered by year and fund (stock)

***, **, and * indicate significance at the 1 %, 5 %, and 10 % levels, respectively

This table reports the tournament regression for equity non-index funds using three different risk measures: the buy-and-hold portfolio volatility, the volatility gap, and the cross-period term. In Panel A, changes in the buy-and-hold volatility (using the prior year’s December weights), \(\sigma _{0,[ {7,12} ]}^{\mathrm{BH}} -\sigma _{0,[ {1,6} ]}^{\mathrm{BH}} \), are regressed on the fund return rank, \(R_{[ {1,6}]} \) (normalized to range between 0 and 1), and the first half-year’s buy-and-hold volatility, \(\sigma _{0[ {1,6}]}^{\mathrm{BH}} \), for all funds \(i\) and calendar years \(t\) as specified in Eq. (9): \(\sigma _{0,[ {7,12} ],i,t}^{\mathrm{BH}} -\sigma _{0,[ {1,6} ],i,t}^{\mathrm{BH}} =\alpha +\beta _1 R_{[ {1,6} ],i,t} +\beta _2 \sigma _{0[ {1,6} ],i,t}^{\mathrm{BH}} +\varepsilon _{i,t} \). Panel B shows the coefficient estimates for Eq. (10) in which the changes in the volatility gap, \(\mathrm{VG}_{[7,12]} -\mathrm{VG}_{[ {1,6} ]} \), are regressed on the normalized fund return rank \(R_{[ {1,6} ]} \), and the first half-year’s volatility gap, \(\mathrm{VG}_{[ {1,6} ]} \): \(\mathrm{VG}_{[ {7,12,} ]i,t} -\mathrm{VG}_{[ {1,6} ],i,t} =\alpha +\beta _1 R_{[ {1,6} ],i} + \beta _2 \mathrm{VG}_{[ {1,6}],i,t} +\varepsilon _{i,t} \). In Panel C, the differences between the buy-and-hold volatilities using the weights from June and the weights from December of the prior year as initial weights, i.e., the cross-period terms, \(\sigma _{6,[ {7,12} ],i,t}^{\mathrm{BH}} -\sigma _{0,[ {7,12} ],i,t}^{\mathrm{BH}} \) are regressed on the normalized fund rank, \(R_{[ {1,6} ]} \), using Eq. (11): \(\sigma _{6,[ {7,12} ],i,t}^{\mathrm{BH}} -\sigma _{0,[ {7,12} ],i,t}^{\mathrm{BH}} =\alpha +\beta _1 R_{[1,6],i,t} +\varepsilon _{i,t} \). Standard errors are simultaneously clustered by year and fund. The coefficient estimates are in the first line, and the t statistics are in parentheses below

***, **, and * indicate significance at the 1 %, 5 %, and 10 % levels, respectively