Earlier researchers have found either no relation or a positive relation between the conditional expected return and the conditional variance of the monthly excess return on stocks when they used the standard GARCH-M model. This is in contrast to the negative relation found when other approaches were used to model conditional variance. We show that the difference in the estimated relation arises because the standard GARCH-M model is misspecified. When the standard model is modified allow for (i) the presence for seasonal patterns in volatility, (ii) positive and negative innovations to returns to having different impacts on conditional volatility, and (iii) nominal interest rates to affect conditional variance, we once again find support for a negative relation. Using the modified GARCH-M model, we also show that there is little evidence to support the traditional view that conditional volatility is highly persistent. Also, positive unanticipated returns result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility of a similar magnitude. Hence the time series properties of the monthly excess return on stocks appear to be substantially different from that of the daily excess return on stocks.
- Federal Reserve Bank of Minneapolis. Research Division.
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