The yield to maturity (YTM) on 1-year zero-coupon bonds is 6% and the YTM on 2-y
ID: 2783766 • Letter: T
Question
The yield to maturity (YTM) on 1-year zero-coupon bonds is 6% and the YTM on 2-year zeros is 7%. The yield to maturity on 2-year-maturity coupon bonds with coupon rates of 9% (paid annually) is 6.5%.
What arbitrage opportunity is available for an investment banking firm? (Omit the "$" sign in your response.)
The arbitrage strategy is to buy zeros with face values of $ and $ , and respective maturities of one year and two years.
What is the profit on the activity? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)
The yield to maturity (YTM) on 1-year zero-coupon bonds is 6% and the YTM on 2-year zeros is 7%. The yield to maturity on 2-year-maturity coupon bonds with coupon rates of 9% (paid annually) is 6.5%.
Explanation / Answer
Face Value=1000
Coupons=9%*1000=90
Price of the coupon paying bond must be 90/1.06+1090/1.07^2=1036.954
However, we see the price of the coupon paying bond=90/1.065+1090/1.065^2=1045.516
So, the bond is overvalued. We would sell the coupon paying bond
We would buy $90 par value 1 year zero coupon bond and $1090 par value 2 year zero coupon bond
The total cash outflow=90/1.06+1090/1.07^2=1036.954
Total cash inflow from coupon paying bond=1045.516
Net cash inflow=1045.516-1036.954=8.562
This we would invest for 2 years at 7% so the amount would become 8.562*1.07^2=9.8026
We have sold the coupon paying bond, so we would need to pay the coupons. We would pay the first coupon from zero coupon bond which will mature in 1 year. And the second coupon & par value will be paid from zero coupon bond which matures in 2 years.
So, net profit=$9.8026 at the end of 2 years
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