What is the implied futures YTM on a March three month T-bill futures contract t
ID: 2714750 • Letter: W
Question
What is the implied futures YTM on a March three month T-bill futures contract trading at 94(IMM index)? Ms. Hunter is a money market manager. In July, she anticipates needing cash in September that she plans to obtain by selling ten $1M-face value T-bills she currently holds. At the time of the anticipated September sale, the T-bills will have a maturity of 91 days. Suppose there is a September T-bill futures contract trading at bank discount yield of RD = 6%. If Ms. Hunter is fearful that short-term interest rate could increase, how could she lock in the selling price on her T-bills? Show in a table Ms. Hunter's net revenue at the futures' expiration date from closing the futures position and selling her 10 T-bills at possible discount yields(BDY) of 5%, 6%, and 7%. Assume no quality, quantity, or timing risk.Explanation / Answer
Answer (1)
Price of a March 3 month T-Bills futures contract = 94
Face Value = 100
Implied yield = Face Value / Price * 100 = ((100/94) – 1) * 100 = 6.3829% or 6.38% (rounded off)
Answer (2)(a)
The money manager is holding the treasury bills which she intends to sell after 3 months to meet a cash requirement. To lock the short term interest rate she could sell T-bill futures with the same maturity at current price at 98.53. On 91st day, she can close out the futures position (by buying the same number of T-Bill futures) at the price on that day and sell T-bill portfolio for a protected return on her T-bill holdings.
Answer (2b)
Discount Yield
Return from sale of Portfolio
Return from closure of futures position
Net Return
5%
- $12,312.27
- $ 2426.16
-$ 14,738.43
6%
-$ 14,738.43
0
-$ 14,738.43
7%
-$ 17,152.70
$ 2,414.27
-$ 14,738.43
Value of the Portfolio = $ 1 Million
At a Face value of $100 total number of bonds held = $1,000,000/$100 = 10,000
Total number of futures contracts held = 10 each representing 100,000 t-bills
Bank discount yield on a 3 month (91 day) T-Bill = 6%
Price of the T-Bill = 100/(1+6%*(91/365)) = 100 /(1+0.0149589) = 100/1.0149589
= 98.52616
Price of 1 T-bill future = 98.52616 * 100000/100 = 98.526157 * 1000
= $ 98526.157
At Discount Yield = 5%
Price at which the T-Bill Portfolio is sold = 100/(1+5%*(91/365)) = 100 / (1+ 5%*0.249315)
= 100 / (1+0.01246575) = 100/1.01246575
= 98.768773
Price of 1 T-bill future = 98.76877 * 100000 (total t-bills)/100 (face value) = 98.76877 * 1000
= $ 98768.773
Amount Received from sale of T-Bill Portfolio = 10,000 * 98.76877 = $ 987, 687.73
Loss on Sale of T-Bill Portfolio = $ 987,687.73 - $ 1,000,000 = - $ 12,312.27
Return from closing of future position = 10 * 98526.157 – 10 *98768.773
= 985,261.57 – 987,687.73
= - $ 2,426.16
Net return = return from sale of investment + return from closing of future position
= - $12,312.27 - $ 2426.16 = -$ 14,738.43
At discount yield = 6%
Price of the bond = 100/(1+6%*(91/365)) = 100 / (1+ 6%*0.249315)
= 100 / (1+0.0149589) = 100/1.0149589
= 98.526157
Amount received from sale of T-Bills = 10000 * 98.526157 = $ 985,261.57
Loss on sale of T-Bill Portfolio = $ 985,261.57 - $ 1,000,000 = -$14,738.43
Return on closure of future portfolio = 10 * 98526.157 – 10 * 98526.157
= 0
Net return = -$ 14,738.43
At discount yield = 7%
Price of the Bond = 100/(1+7%*91/364) = 100/(1+7%*0.249315) = 100/(1+0.01745205)
= 100/1.01745205 = 98.284730
Price of T-Bill Future = 98.284730 * 1000 = 98284.730
Amount received from sale of T-bill portfolio = 10000 * 98.284730 = $ 982, 847.30
Loss on sale of T-bill portfolio = $ 982847.30 - $ 1,000,000 = -$ 17,152.70
Return on closure of Futures position = 10 * 98526.157 – 10 *98284.73
= $ 985,261.57 - $ 982,847.30
= $ 2,414.27
Net return = -$ 17,152.70 + $ 2,414.27 = - $ 14,738.43
Discount Yield
Return from sale of Portfolio
Return from closure of futures position
Net Return
5%
- $12,312.27
- $ 2426.16
-$ 14,738.43
6%
-$ 14,738.43
0
-$ 14,738.43
7%
-$ 17,152.70
$ 2,414.27
-$ 14,738.43
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