Problem. This question asks you to apply concepts from throughout the course. Im

Question

Problem. This question asks you to apply concepts from throughout the course. Imagine there is an investment manager looking for arbitrage opportunities. Any opportunities are found you must explain how to exploit them After looking at the stock market and being unable to find any opportunities, the invest- ment manager moves to the bond market, where he sees the following table for $100 par value zero coupon bonds: Boud Years to Maturity Yield to Maturity Price 2% 5% 7% (a) Fill in the table. Show any formulas you use (b) Suppose there is a $100 face value 3 year coupon bond with a coupon rate of 8% with price $104. Is there an arbitrage opportunity for the investment manager? (c) Under the expectations hypothesis, what is the expected short rate in year 2? (d) Supposing a liquidity premium of 1%, what is the expected short rate in year 2?

Explanation / Answer

a) Price of year 1 = 100/(1+ y) = 100/(1.02) = 98.04

Price of year 2 = 100/(1+ y)^2 = 100/(1.05) = 90.70

Price of year 3 = 100/(1+ y)^3 = 100/(1.07) = 81.63

b) There exists an arbitrage opportunity for the investment manager as the price of 3 year coupon bond is higher than the price of 3 year zero coupon bond in the question.

c) Let r2 be the short rate for year 2

(1+r2) = (1+y2)^2 / (1+y1) = > (1+r2) = (1+0.05)^2 / (1+0.02) => r2 = (1.1025/1.02) -1 => r2 = 8.09%

d)  Expected short rate in year 2

(1+r2) + premium = (1+y2)^2 / (1+y1)

(1+r2) + 0.01 =  1.08 => r2 = 7%

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