Question

a. Suppose a 7.2% semi-annual coupon 20-year Treasury issue with a par value of $100 issue is priced in the market based on the on-the-run 20-year Treasury yield. Assume further that this yield is 5.60%, so that each cash flow is discounted at 5.60% divided by 2. What is the market price of the Treasury issue based on this assumption?

b. Suppose also that the price of the same Treasury issue would be $115.285 if it is calculated based on the prevailing Treasury spot rate curve. What action would a dealer take and what would the arbitrage profit be? Can this situation persist in the long run?

Answer 1

a:

Market price of the bond is the present value of its future cashflows

Here coupon= 7.2% semi annual =3.6 per half year ; term=20 years=40 half year

yield=5.6% per annum =2.8% per half year

To calculate price, discount the cashflows using yield/2 ( since cash flows happens each half year) as shown

Bond A
Years	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40
Price
Coupon payment		3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6
Par value																																									100
Total cashflows	0	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	3.6	103.6
Price/NPV	$119.10

From npv caluclation @ yield/2 discount rate ; Price= 119.1 $

b:

If the current price of the treasury issue is 115.285 , the buyer will benefit from purchasing the bond since the actual value is 119.1$ . By purchasing the bond and holding it till expiry the buyer will have an arbitrage opportunity and the yield obtained will be higher than the calculated yield.