Question

You have been pursuing some rather risky money market investment strategies and, as a result,
have been burned more than once. You recently came across an article describing hedging techniques using financial futures contracts and wondered how these might apply to a riding the yield curve strategy.
Suppose that the current cash rate on 180-day Treasury bills is 5.3% and 5% on 90-day bills. The futures rates on 90-day Treasury bills is currently 5.2%. You invest in a 180-day bill today and sell it in 90 days when it becomes a 90-day bill. Rates on 90-day cash bills are 5.25% at the
time it is sold. Assume that the rate on a 90-day Treasury bill futures contract is 5.3% in 90 days.
If you invest $1 million and the futures contract denomination is $1 million, the commission
rate is $100, and the margin is $2,000 per contract, then what is the net position resulting from
the hedge? How does this result compare if you had not hedged? How does the original result
compare to having invested in a 90-day cash T-bill?

Answer 1

Money market investment strategies:

1) Investment in 90-Day Treasury bills

Amount invested = $1,000,000

90 day t bill rate = 5.0%

Return on investment = $1,000,000 * 5% * (90/360) = $12,500

After 90 Days, Net position = $1,000,000 + $12,500 = $1,012,500

2) Investment in Futures:

Amount invested = $1,000,000

Value of each contract is $1,000,000

Therefore no. of contracts to enter = 1

Margin money required = $2,000 * No. of contracts = $2,000 * 1 = $2,000

Commission rate = $100

Therefore the amount to be invested in 180 day T-Bill today at the rate 5.30% and selling it on a 90th day when it becomes a 90 day T-bill,

Total return in Futures = $ 1,000,000 * 5.30% * (90/360) = $ 13,250

Net Position = Amount invested + Return on investment - Commission - Interest paid on margin maintenance

= $1,000,000 +$13,250 - $100 - $0

= $ 1,013,150

If the funds are not hedged in futures the resultant loss would be = $ 1,013,150 - $1,012,500 = - $650

Note : Interest paid on margin maintenance is a cost of borrowing of funds required to maintain margin amount in futures. Since the cost of borrowing funds is not provided it has been assumed to be Zero.

3) If invested in 90 day cash T-bill:

Amount invested = $1,000,000

90 day cash T-bill rate = 5.25%

Return on investment = $1,000,000 * 5.25% * (90/360) = $13,125

After 90 Days, Net position = $1,000,000 + $13,125 = $1,013,125

If the funds are not invested in 90 day cash T-bill the resultant loss would be = $ 1,013,125 - $1,012,500 = - $625

As compared to the futures hedging the cash bills are giving lesser returns , since the loss is lesser in the cash bills when compared to 90 day T-bills i.e., the amount of gain which you would get if you invest in that strategy.

Note: It is assumed as no. of days in a year as 360 Days. This problem can also be solved by taking no. of days as 365.

Thank you.