Pricing a Risky Bond 5. Pricing a Risky Bond You are thinking about investing in

Question

Pricing a Risky Bond

5. Pricing a Risky Bond You are thinking about investing in a bond issued by Google. It is a zero-coupon bond, has a maturity date of 3 years. and a face value of $100. If you were going to invest in a bond with no default risk, you would to receive a nominal interest rate of 3%. Finally, you believe the following about how likely repayment is: (a) If you were risk neutral, how much would you be willing to pay for this bond? (b) If you were risk averse, with a utility function given by 2 root c, how much would you be willing to pay r this bond? (e) Comment on the difference between part (a) and (b). (d) Suppose you bought the bond at the price computed in part (b). Three years pass. and full repayment occurs (i.e. you receive S100). What was your ex-post return. expressed as an annual percentage? What is the default risk premium on this bond. compared to a risk-free bond?

Explanation / Answer

a)
Full payment = 100 x .85 = 85
Partial Payment = 80 x .10 = 8
Zer0 Payment = 0 x .5 = 0
Risk Neutral = $93

b) Risk Averse = 2 x square root $93 = $19.29

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