Question

The spot discount rates for two T-bills, 80-day T-bill and 170-day T-bill, are given below.

A) Based on the two T-bills's discount rates, what should be the quoted equilibrium price of an 80-day T-bill futures contract? Assume $1,000,000 face value. Keep in mind the quoted price is 100 - (discount rate). What should be the dollar amount implied by the futures quoted price (the amount to pay or to be paid at settlement)?

B) You took 10 long T-bill futures contact for delivery in 80 days. It is now 20 days later since you took the long futures position and the T-bill futures for delivery in 60 days is quoted at 95.50. Calculate your gains(losses) on your position.

Spot discount rates
80-day T-bill	6.00%
170-day T-bill	6.25%
Face Value	$1,000,000
Dollar amount for the futures
Price Quoted
Gain(loss)

Answer 1

A)given spot discount rates for 80 days T-bill @ 6% per annum

spot discount rates for 170 days T-Bill @ 6.25% per annum

calculation for price to be quoted for 80days T-Bill

Face Value =$ 1,000,000

quoted price is=$1,000,000-($1000000*6%*80days/365days)

=$9,86,849.3(Approx)

Calculation for Price to be quoted for 170 days T-Bill

Face Value=S1,000,000

Quoted Price is =$1,000,000-($1,000,000*6.25%*170/365days)

=$9,70,890.41(Approx)

Note: 1.Assumed that T-Bill consists only one bill with $1,000,000

2.we can assume T-bill is Face value of $100 then we have divide above figure with 100 .after that same calculation as to do.

398Assumed in a year 365 days

B) given spot discount rates for 80 days @6%

We have taken 10 long futures for delivery in 80 days at a discount price of 6% per annum

one long futures =$100

then =$10*100*6%*80/365days

Discount=$13.15

Value=$10*100-13.15

=$986.84

but after 20 days future for delivery in 60 days quoted at 95.50

then value =$10*95.50

=$955

Calculation for gain or loss

Value of T-bill after 20 days =$986.84+$986.84*6%*20/365

=$990.08

Gain or(loss)=$955-$990.08

=$35.08