This paper models weekly excess returns of 10-year Treasury notes and long-term Treasury bonds from 1968 through 1993 using an exponential generalized autoregressive conditional hetroskedasticity in mean (EGARCH-M) approach. The results indicate the presence of conditional hetroskedasticity and a strong tendency for the ex-ante volatility of excess returns to increase more following negative excess return innovations compared to positive innovations of equal magnitude. In addition, increases in ex-ante volatility are associated in some subperiods with rising excess returns on longer-term instruments, although the slope of the yield curve and lagged excess returns generally remain significant predictors of excess returns.
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Brunner et al. (1995) studied this question.