1] < 0), but if future marginal utility of a dollar is positively correlated with the expected growth rate of marginal utility, then forward premiums and the term premium in rates will be negative.
The second decomposition expressed the bond price in terms of the expected product of the prices of future short-term bonds and the product of individual forward premiums at each maturity.
Very loosely speaking, this expression relates the holding-period premium to the conditional covariance between expected future short prices and expected future forward premiums.
Most importantly, from our perspective, the model-based forward premiums that Wachter computes help to account for the empirical disparity between long-term rates and the corresponding average of expected future short-term rates--that is, the violation of the pure expectations hypothesis.
In terms of marginal utilities, using (11) and (15), the forward premium is
and it is straightforward to show that the forward premium is pinned down by the autocovariance properties of marginal utility, or equivalently by the covariance between the future short-term bond price and future marginal utility:
Note that like the forward premium, the inflation-risk premium can be positive or negative.
For the 19-month forward period, the bonds carried a relatively modest forward premium over the spot bond market.
The difference between the two is called the forward premium, and it is shaped by such factors as the level of long-term and short-term rates and the shape of the yield curve.
As a result, when a contract is renewed/rolled over during a volatility cluster, the risk due to higher volatility is often reflected in higher forward premium, which makes hedging unattractive.
Following the evidence of the presence of volatility clusters, we need to look at forward premium movement during such periods.
We notice that forward premium deviation in all cases (for one, three and six month forwards) was in tandem with volatility figures for the month.