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FRM Part II · FRM Exam Part II · Expectations, Risk Premium, Convexity and the Shape of the Term Structure

A risk analyst explains why the yield on a long-dated zero-coupon bond is lower than the average of expected future short rates when interest rate volatility is positive and the risk premium is zero. Which statement best describes the source of this effect?

The convexity effect arises from Jensen's inequality. Because discount factors are convex in rates, the expected discount factor exceeds the discount factor at the expected rate, so the implied long yield falls below the average expected short rate even with no risk premium.

  1. AJensen's inequality: the expected discount factor exceeds the discount factor evaluated at the expected rate, so the implied yield is lowerCorrect
  2. BThe liquidity preference of investors, who demand a premium for holding longer maturities
  3. CSegmentation of the market, where long-maturity demand pushes yields below expected short rates
  4. DThe mean reversion of short rates toward their long-run level, which lowers long yields

Explanation

Bond prices are convex in rates, so E[exp(-r)] > exp(-E[r]) by Jensen's inequality. A higher expected price means a lower yield than the average expected rate. Liquidity preference would push yields up, not down, and the question assumes a zero risk premium.

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