A Possible Error in the Expectations Theory: Comment
评论了Amihud关于远期利率是未来即期利率有偏估计的观点，指出在完美资本市场中，即使投资者最大化期望现值或收益率，无套利条件仍要求远期利率等于期望未来即期利率。
Looking at the market place we can observe a current spot rate of Rn for a n period discount bond and of R n-l for a n 1 period discount bond. Implied in these two spot rates is a forward rate fn for a loan during the nth period. According to the expectations theory, this forward rate is an unbiased estimate of the expected future one period spot rate rn (which in itself is a random variable), that is, fn = E[rn]. Recently Amihud [1] argued that although the foregoing is correct, if investors are risk neutral and if they seek to maximize their expected terminal wealth, it is not if they seek to maximize the expected present value or, equivalently, the expected rate of return of their holdings. Instead, he claims that in the latter two cases forward rates would be downward biased estimates of the expected future spot rates. The basic proposition of this comment is that E[rn] + fn is inconsistent with an equilibrium in a perfect capital market where discount bonds of different maturities are traded by risk neutral investors. Even if investors seek to maximize the expected present value or the expected rate of return of their holdings, the no arbitrage condition of capital market equilibrium requires that E [rn] = fn. Amihud starts his argument by presenting the so-called Hicks equality [3, p. 145], which states that in equilibrium