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 collateralized futures position is closest to: A. -0.5000%. B. 0.9978%. C. 1.0000%. D. 1.2254%. Can anybody show a detail calculation for this one? Thanks.

Final value: = Final Value of T-Bills - loss on futures position = 20,000,000-100,000 = 19,900,000 Initial Value: Compute Holding Period Discount Yield: = 8.867% * (60/360) =1.14778% Compute Initial Value of TBills: =(1-Holding Period Discount)* Face Value =(1-1.14778%)* 20mm =19,704,433 Return: =(1-(Final Value/Initial Value)) *100% =(1-(19,900,000/19,704,433))*100% =0.9925% I might have messed something up in there, but I’m going with B

The answer is actually C. I had the same cal too. Not sure which part did I mess up…

I agree with B (.08867*(60/360))*20m=$295,566 20,000,000-$295,566=19,704,434 ((20,000,000-100,000)/19,704,434)-1= .9925%

Well that’s just crap–let us know if you find the answer.

.08867*60/360= 0.014778 20000000* 1.4778%= 295560 295560-100000= 195560 195560/(20000000-295560)= 0.9925%

strange that everybody kinda agrees with B… anybody can justify the answer C?

i agree with B too…unless they rounded it off to 1%

I’m too lazy to do the calculations, but all the calculations above have a $20M futures position collateralized with T-bills worth $19.7 M. If you’re fully collateralizing something worth $20M, I want collateral worth $20M not something worth $20M in 60 days. If you redo the calculations with an initial deposit of $20M and earnings on 20M you will get a better return than depositing 19.7M which probably gets you to the 1%

Yeah - Joey is right. Just ran through the math, and if you buy a 20M T-Bill, it will be worth 20,300,000. Subtract the 100,000 loss. 20.2M/20M = 1.01, or 1% return. .08867=((F-20M)/F)(360/60)

hoofmag2, Yeah - Joey is right. Just ran through the math, and if you buy a 20M T-Bill, it will be worth 20,300,000. Subtract the 100,000 loss. 20.2M/20M = 1.01, or 1% return. .08867=((F-20M)/F)(360/60) where did you get the 300000 from, what yield did you use?

What do you mean? I used the discount yield equation to back out the future value of a 20M T-bill yielding 8.867%. Discount Yield = (F-P)/F * (360/T) Solve for F. (60/360)F(.08867) = F - 20M -0.98522166F = -20M F = 20,300,000.17 So at the end of the period, that is what you will get from the T-Bill. Pay the 100,000 loss on the future, and your HPY is [20.2m/20m - 1], or 1%

ok thanks

Thanks guys. This helps me understand how collateralized commodity futures really work. According to the Schweser notes, “establishing a collateralized commodities futures position requires simultaneously purchasing (going long) a specific futures contract and purchasing government securities, such as T-bills, with a market value equal to the contract value of the futures contract.” The market value of treasuries to collateralize the position is 20M and not something less. Thanks!

Thanks, guys!