Unless otherwise stated, assume bonds quote coupon rates and YTM as APR with sem
ID: 2811795 • Letter: U
Question
Unless otherwise stated, assume bonds quote coupon rates and YTM as APR with semi-annual compounding 1. Today is 25 September 2018 and the following two US Treasury bond are observed Matur 15 August 2028 15 Coupon | 2.875% PA APR 15.50096 PA APR Bid | 98.2891 Asked 98.3047 120.5547 Asked Yield 3.075% PA APR 3.073% PA APR st 2028 120.5391 easury.html If you buy $10,000 of the second bond today: (a) What will be the dates of your next three coupons? (b) How much will each coupon payment be? (c) How much accrued interest is payable in the purchase price, given US T-Bonds use Actual/Actual, and (d) (e) the settlement procedure T+1 means the settlement will occur the next day 26 September 2018? If instead the accrued interest was $100, how much would you be paying for the bond tomorrow? Is there an arbitrage opportunity between these two bonds?Explanation / Answer
Soln : a) Generally the maturity of the US treasury bonds is 10 years, 20 years, 30 years etc........
So, as the maturity date is 15th Aug. 2028, we are assuming that it is 10 year bond on semi annual payment coupon. We can check it by using the asked yield and ask price, calculting the time period = 10 years.
So, we can say that the next coupon payment will happen after 6 months from 15th Aug. 2018 i.e. 15th Feb.2019, and other next 2 payments will happen on 15th Aug. 2019 and 15th Feb.2020
(b) Each coupon payment will be = 10000*5.5%/2 = $275
c) Accrued interest will be of the coupon due for the no. fo days from the date of its issuance.
So, we can say accrued interest for 41 days (from 15th Aug. 2018 to 25th Sept. 2018)
AI = 5.5%/365 *41 *10000 = 61.78 = 62 (approx.)
d) In case if accrued interest was $100 , need to pay an amount of 120.5547*100 + 100 = 12155.47
e) As we have calculated the values coming near to the ask price based on evaluation on coupon payments, we can say there is an opportunity of arbitrage. Like for 2nd bond as per coupon payments , fundamentally the price should be = 120.75 and its bid/ask price = 120.53/55.
Similarly for the 1st bond the value seems to be 98.289, , no arbitrage opportunity in this case.
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