Spreads
Just as we can predict the relationship between spot and futures prices, there are similar ways
to determine the proper relationships among futures prices for contracts of different maturity
dates. Equation 17.2 shows that the futures price is in part determined by time to maturity.
If rf
> d, the futures price will be higher on longer-maturity contracts. When rf
< d, the reverse
will be true. For futures on assets like gold, which pay no “dividend yield,” we can set d = 0
and conclude that F must increase as time to maturity increases.
Equation 17.2 implies that futures prices for different maturity dates should all move in
unison, for all are linked to the same spot price through the parity relationship. Figure 17.6
plots futures prices on gold for three maturity dates. It is apparent that the prices move in
virtual lockstep and that the more distant delivery dates command higher futures prices, as
predicted by Equation 17.2.

概括

我们可以通过类似预测现货与期货价格关系的方法，确定不同到期日期货合约间的合理价差。公式17.2显示期货价格部分取决于到期时间：当无风险利率高于资产收益率时，长期合约价格更高；反之则更低。以黄金为例（其收益率d=0），期货价格必然随到期时间延长而上升。该公式还表明不同到期日的期货价格应同步波动，因其均通过平价关系与同一现货价格挂钩。图17.6展示的三种黄金期货合约价格走势印证了这一规律——各合约价格如齿轮般同步变动，且远期合约价格更高，与理论预测完全一致。