This common method of estimating idiosyncratic returns is critically dependent upon good estimates of the factor loadings.
We use the factor loading estimates from Equation (2) in Equation (1) to estimate the daily idiosyncratic returns during month t - 1.
We estimate idiosyncratic returns and volatility relative to the eight-factor model rather than the three-factor models from the previous tables.
To estimate idiosyncratic volatility, we first estimate a stock's day d idiosyncratic return:
where [D.sub.t-1] is the number of trading days in month t - 1 and [[??].sup.2.sub.d] is the square of our estimate of the day d idiosyncratic return estimated in Equations (1) and (2).
The idiosyncratic returns of each fund are measured using prior year monthly returns and a four-factor model.
I find a positive relationship between the Overlapping Rate and the Correlation of Idiosyncratic Returns in Column (3) when the average manager overlap rate is not included in the specification.
The Overlapping Rate is treated as endogenous when the dependent variable is the Correlation of Idiosyncratic Returns. Then I perform a 2SLS analysis in which the setup of the model in Column (6) (Column 7) is identical to that of the model in Column (3) (Column 4) except that the Overlapping Rate is instrumented by the four instruments as defined earlier and 2SLS estimates are reported.
Correlation of For each fund in year t, the idiosyncratic returns Idiosyncratic are estimated by using a rolling 12-month window Returns and a four-factor model.
PCA factors Equity common -0.026 0 (0.632) (0.0%) Equity 0.004 30 idiosyncratic (0.954) (15.5%) CDS common -0.279 173 (0.000) (89.6%) CDS -0.009 19 idiosyncratic (0.922) (9.8%) Lagged Equity Returns Idiosyncratic Returns
Coefficient Count Signif.
The evidence of Fama and French (2004) is consistent with the explanation that changes in the idiosyncratic returns volatility could be, in part, due to trends in the entry and exit of firms into the markets.
Pontiff, 2009, "Idiosyncratic Return Volatility, Cash Flows, and Product Market Competition," Review of Financial Studies 22, 1149-1177.