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

In a one-factor, binomial term structure model, a risk-averse market prices a 2-year zero-coupon bond. The expected price of the bond one year from now, discounted at the current one-year rate, gives a price of 90.00. The bond's actual market price today is 89.00. What does this difference imply?

The market price being below the expected-value price discounted at the short rate means investors demand compensation for interest rate risk. This is a positive risk premium on the longer bond. It reflects risk aversion rather than an arbitrage opportunity.

  1. AThe market requires a positive risk premium for holding the longer-term bondCorrect
  2. BThe market is pricing the bond with an arbitrage opportunity
  3. CThe one-year rate is expected to fall to zero
  4. DThe bond has negative convexity that raises its price

Explanation

Discounting expected future price at the risk-free short rate gives a value that ignores risk aversion. Investors who are risk averse pay less, so the market price (89.00) is below 90.00. The gap is compensation for bearing interest rate risk, i.e., a positive risk premium. It is not an arbitrage, because the pricing is consistent with a risk-adjusted measure.

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