# Forward Contract question

A portfolio manager holds a long position on a forward contract on \$20million face value 80-day T-bills priced at 1.85% on a discount yield basis. At settlement, 80 day T-bills are priced at 1.95% on a discount ield basis. How much will the portfolio manager have to pay at settlement for the T-bills? A. 19,630,000 B. 19,773,890 C. \$19,917,780 D. \$19,913,333 I arrive at 20,000,000 ( (0195-.0185* 80/360)) / (1.0195 * 80/360)) =19,597.80 20,000,000 - 19597.80 = 19,980,402 I can’t seem to figure out what it is that I am doing wrong

I got C (1.85*80/360) = 0.411 % (1-0.411)% * 20 million = C

would you need to de-annualize this since its a bank discount yield?

At time of signing contract = (1-0.0185*80/360) * 200000000 = 19917780 At settlement price of T-Bill = (1-0.0195*80/360) * 200000000= 19913333.33 Bond is delivered at settlement – so 19913333 is the answer, I believe.

I did it, . 80/360 * 1.85 where 1.85 is the annual discount

that is correct…why is the price at expiration not included in this case?? C that is

1.85% means 1-.185(80/360) = 99.85% of Price. These rates are discount rates in T-Bill Futures.

I believe the answer is c. The portfolio manager needs to pay for the t-bills at a 1.85% bank discount yield, pursuant to the forward contract. Thus, the manager pays 20,000,000 - (1.85% x 80/360 x 20,000,000) = \$19,917,778. I believe the portfolio manager would pay this amount for the t-bills regardless of their yield at settlement, since he has contractually obligated himself to do so pursuant to the forward contract. Of course, the yield in effect at settlement could be used to measure the amount the manager saved or lost by having entered the forward. If you do not de-annualize, you get answer A. I think de-annualization is appropriate with bank discount yields, however, since bank discount yield = discount/face x 360/t. If the cost of settling the forward contract depended on the yield in effect at settlement rather then when the forward contract was entered, the forward would serve no purpose in locking in a yield rate.

cpk123 Wrote: ------------------------------------------------------- > At time of signing contract = (1-0.0185*80/360) * > 200000000 = 19917780 > > At settlement price of T-Bill = (1-0.0195*80/360) > * 200000000= 19913333.33 > > Bond is delivered at settlement – so 19913333 is > the answer, I believe. But doesnt the manager have the obligation to buy at the forward rate?

CFALondon0109 Wrote: ------------------------------------------------------- > that is correct…why is the price at expiration > not included in this case?? > C that is Why would you need to know anything about the price at expiration. If I offer to sell you a dozen eggs for \$1.50 in 18 months, how much are you going to pay for the eggs in 18 months? (ans: \$1.50) Now suppose that eggs in the grocery store are selling for \$3.50/dozen in 18 months, how much are you going to pay for the eggs? (ans: \$1.50).

all these derivatives have me beat!!!

JDV you make sense - why do some FRA questions consider the expiration yield too? like LIBOR was x 180 days from now, those kind of questions? is not considering expiration yield restricted to FRA problems involving bonds i.e. T-Bills only instead of LIBOR?

niraj i think chebychev said it best “I believe the portfolio manager would pay this amount for the t-bills regardless of their yield at settlement, since he has contractually obligated himself to do so pursuant to the forward contract.”

Is it because of the fact that FRA’s are cash settled compared to bonds where you are obligated to buy at the forward price mentioned on the contract

i like joeys egg example. it’s great.

niraj_a Wrote: ------------------------------------------------------- > JDV you make sense - > > why do some FRA questions consider the expiration > yield too? like LIBOR was x 180 days from now, > those kind of questions? > > is not considering expiration yield restricted to > FRA problems involving bonds i.e. T-Bills only > instead of LIBOR? Because an FRA unlike any other derivative that I can think of (which doesn’t mean all of them) gives you a payout at settlement date which is a discounted payment of what is really due at some later date.

CFALondon0109 Wrote: ------------------------------------------------------- > niraj > i think chebychev said it best “I believe the > portfolio manager would pay this amount for the > t-bills regardless of their yield at settlement, > since he has contractually obligated himself to do > so pursuant to the forward contract.” ^Yep.

gotcha. will keep in mind. might start CFAI sample 2 right now, lets see if i can find 50 bucks more on the credit line