Question

The bid and ask bond equivalent yields of a U.S. T-bill are 7.8% and 7.6% respectively. The maturity of the T-bill is 120 days. 1. Calculate the bid and ask bank discount yields of the T-bill. 2. Find the bid-ask spread of the T-bill. 3. Find the effective annual yield based on a. the bid price of the T-bill. b. the ask price of the T-bill.

Answer 1

Let P_bid and P_ask be the bid and ask price of the bond respectively.

Bid bond equivalent yield = (F - P_bid) / P_bid x 365 / N where N = days to maturity, and F = face value of the bond

Hence, 7.8% = (F - P_bid) / P_bid x 365 / 120

Hence, (F - P_bid) / P_bid = 7.8% x 120 / 365

Hence, F / P_bid = 1 + 7.8% x 120 / 365 = 1.0256

Similarly, F / P_ask = 1 + 7.6% x 120 / 365 =  1.0250

Part (1)

Bid bank discount yield = (1 - P_bid / F ) x 360 / N = (1 - 1 / 1.0256) x 360 / 120 = 7.50%

Ask bank discount yield = (1 - P_ask / F ) x 360 / N = (1 - 1 / 1.0250) x 360 / 120 = 7.31%

Part (2)

Bid ask spread = P_ask - P_bid = F / 1.0250 - F / 1.0256

Face value is not given. We assume the same to be $ 10,000 (standard assumption)

Hence, Bid ask spread = 10,000 / 1.0250 - 10,000 / 0.0256 = $ 6.25

Part (3)

P_ask = F / 1.0250 = 10,000 / 1.0250 =  9,756.23

P_bid = F / 1.0256 = 10,000 / 1.0256 =  9,749.97

the effective annual yield based on

a. the bid price of the T-bill = [1 + (F - P_bid) / P_bid]^365/N - 1 = (F / P_bid)^365/N -1 = 1.0256^365/120 - 1 = 8.01%

b. the ask price of the T-bill = 1.0250^365/120 - 1 = 7.80%