# Schweser sample exam 2 am question 120

A manager establishes a collateralized commodity futures position with a contract value of \$20 million. He purchases 60-day Treasury bills (T-bills) with a bank discount yield of 8.867% to collateralize the futures position. After 60 days, the loss on the futures position is \$100,000. The holding period return on the position, is closet to: A. -0.5000% B. 0.9978% C. 1.0000% D. 1.2254% The answer is D. I can not reach this answer. I did the following: The value of T-bill should be equal to \$20 m, F = 20 million (F-P)/F*360/60 = 8.867%, I get P = 19.704433 million Gain: T-bill: 20 million - 19.704433 million = 0.295567 million Future: -0.1 million Holding period return: 0.195567 / 19.704433 = 0.99% Any suggestions, thanks.

I tried to search this before, but did not find it. Thanks a lot, barthezz.

This question still seems a bit fishy to me. I would be grateful if someone could identify any breakdown in the following logic: 1. The bank discount yield is 8.867%. 2. De-annualized, that means the discount from face was 60/360 x 8.867% = 1.478% 3. From \$20 million, that means a discount of \$295,567. 4. So the manager paid \$19,704,433 for the t-bills. 5. At the end of 60 days, the manager lost \$100,000 on the future. 6. At the end of 60 days, the manager got the \$295,567 appreciation on the t-bills. 7. Thus at the end of 60 days, the net gain is \$195,567. 8. \$195,567/19,704,433 is 0.9925%. I understand how one can calculate that the holding period return on the t-bills was 1.5% and the loss on the future was .5%, so the result is 1%. I’m not sure the calculation to get the .5% loss on the future is sound, however, since no money changes hands at the inception of a future, leaving aside the provision of margin (calling into question the appropriateness of the denominator of \$20 million in the .5% calculation). Can anyone point out the flaw in the logic above?

Any takers on identifying the flaw in the reasoning above? I assume there is a mistake somewhere along the way as the answer is not provided as an alternative.

Chebychev, There is detailed discussion in http://www.analystforum.com/phorums/read.php?11,627769,627769#msg-627769 B is the closest.

Thanks Superfluid. I’m not sure that thread provides a conclusive answer, but perhaps people have had enough of this question.

Actually per the previous thread answer is C. C 1% Here is the explaination: Establishing a collateralized position in commodities futures requires simultaneously purchasing government securities in a value equal to the contract value of the futures contracts. The actual discount on the 60-day T-bills 0.08867 (60/360) = 0.014778, so the effective 60-day yield is 1/(1 – 0.014778) – 1 = 1.5%. The return from the futures contracts is -100,000/20,000,000 = -0.5%. The net holding period yield is 1% = 1.5% – 0.5%. I know it is weird

Okay, if people are satisfied with the percentage approach described above that’s fine with me. But it leads to some funny results, since if the notional amount of the future was 6.67 million instead of 20 million but all other facts are unchanged, you would calculate a holding period return of 0%. That’s odd considering you would have made \$195,567 in 60 days on an investment of \$19,704,433. Somehow the holding period return changed with no change in cash flows. I think the holding period return should be unaffected by differences in the notional amount of the future, since it isn’t a cash flow. The approach I went through above would produce the same holding return regardless of the notional amount involved. In any event, I’ll leave this topic be.

cheby, there’s a flaw in point 4. The manager paid \$20m for the t-bills, which then appreciated to \$20,300,0034.50. With a collateralised futures position, you pay the face of the contract now. So point 6 should be gained \$300,000 7 should be \$200k, 8 should be 1%. I know because I made the same mistake as you!

Many thanks, Chrismaths!