A manager establishes a collateralized commodity futures positoin with a contrace value of $20 million. He purchases 60-day Treasury bills (T-bills) with a bank discount yield of 8.867% to collateralize the futures positoin. After 60 days, the loss on the futures position is $100,000. The holding period return on the position is closest to: A. - 0.5% B. 0.9978% C. 1.0% D. 1.2254%

B?

BDY = 8.8867% so (F-P)/F * 360/60 = .08867 and F=20 so P = 19.70433M Loss = 0.1M So HPR = -.1/19.7043 = -.5% Is that right? (Choice A)?

I got A as well. but I simply did (19.9-20)/20

I got something close to B, but I am not sure I did it correctly.

I looked at it as 2 separate transactions. The return on the futures position is: -100,000 / 20,000,000 = -.005 The return on the t-bill is .08867 x 60/360 = .01477833 So total return is -.005 + .0147783 = .0097783 choice B But I may be totally wrong in my thinking…

Commodity futures positoin ----------------------------------- 19000K - 20000K / 20000K = -0.005 Convert BDY to APY ------------------------ Yield = 0 .08867 * 60/ 360 =0.01477833333 Net gain % ------------- = -0.005 + 0.01477833333 = 0.01977833333 = B? - Dinesh S EDIT: oops, Ryan did the exact same thing!! considering it as 2 separate transactions would make it easy to solve…

I got B.

I guess I made a mistake above… not sure until we see the answer. He gained 20M - 19.704M = 296K on the T-Bill Lost 100K on the Futures position Net Position: 196K on a 19.704M Investment. HPR = 196/19704 = .9947%

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

C on bill 0.08867*60/360= 0.0148 1/(1-0.0148) = 1.5% on future -100,000/20,000,000=-.5 Total 1.5% - 0.5% = 1%

1/(1-0.0148) = 1.5% Why this?

it is essentially 19.704 M = PBegin 20 M = PEnd So HPR = (20 - 19.704)/19.704 = 1.5022%

Can you show me the calculation for 19.704M?

the annualized bank discount yield is BDY=Discount/Face value * 360/t here we have: 0.0867= D/20,000,000 * 360/60 D= 20,000,000*0.08867*60/360 = 295567 bond is trading at: 20,000,000-295567=19,704,433 Holding period yield is: HPY= 295567/19704433= 1.5% now cfaboston to answer your question: 1/(1-0.0148) why is this? HPY=20,000,000/(19,704,433) = 20,000,000/(20,000,000-20,000,000-295567) -1 = 1.015 it is easier to equal 20,000,000 = 1 (in pecentage terms 100%) since you do not have to type in all those numbers… 1/(1-d) hope this helps.