13. Convexity bias is closely related to the distinction between different versions of the pure expectations hypothesis. Earlier we referred to the pure expectations hypothesis. In fact, there are alternative versions of this hypothesis that are not exactly consistent with each other. The local-expectations hypothesis (LEH) assumes that “all bonds earn the same expected return over the next period” whereas the unbiased-expectations hypothesis (UEH) assumes that “forward rates equal expected spot rates.” In panel b of Exhibit 36–4, the LEH is assumed to hold; thus UEH is not exactly true. The expected future short rates are flat at 8% even though the curve of one-year forward rates is inverted. In yield terms, the difference between the LEH and the UEH is the convexity bias.

14. For detailed discussion of this topic, see Ilmanen, “Convexity Bias in the Yield Curve,” op. cit.

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