Question

Suppose you are an investor in bonds. Consider a corporate bond with a $100 par value, a 5% coupon paid semi-annual coupon, and five years to maturity. The bond presently yields 3% annually. Suppose that interest rates rise shortly, and the yield on comparable bonds is now 4%. After observing this change, you call your broker Jane for a quote on the bond. Jane shows that the bond price is $105. You quickly realize that there is an arbitrage opportunity in this market. Assuming away any transaction cost and tax, you can simultaneously buy and sell the bond and pocket a risk-free profit per $100 of par that is closest to (Hint: you would need to first calculate what the bond price should actually be): A. $1.00 B. $0.51 C. $0.422 D. None of the above

Answer 1

Bond par value: $100, 5% coupon paid semi-annual & Maturity: 5 years

Semi- annual coupon: $ 100 * 5% *6/12 = $2.5 and time period: 5 year * 2 compounding= 10 period

Present yield : 3% annually.

Since in the question interest rates raised to now 4% & broker Jane quote on the bond price is $105.

Calculation of an arbitrage opportunity in this market:-

Current price of bond: Semi annual Coupon * PVAF @2% for 10 Year + Par Value *PVF @10%, 10 year

Current price of bond: $2.5 * 8.9825 + $100 * 0.8204

Current price of bond: $22.45 + $82.04 = $104.49

The same bond is in the market quoted by the broker is $ 105, Hence to gain the risk-free profit we need to sell the bond and pocket the gain of $0.51 (i.e. $105-$104.49)

Correct option is  B. $0.51

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