Question

6. A Treasury bill that settled January 15, 2020 has face value $1 million and matures April 14, 2020. Its yield on a bank discount basis was 3.00%.

1. Show that the actual number of days elapsed between settlement and maturity is 90 days. [Hint: 2020 is a leap year.]
2. Calculate the bond equivalent yield (actual/365 basis).
3. Calculate the coupon equivalent yield (30/360 basis).
4. Calculate the CD equivalent yield (actual/360 basis).
5. Explain why the bond equivalent yield in part b is 365/360 of the CD equivalent yield in part d.

Answer 1

Part (a)

the actual number of days elapsed between settlement and maturity = 16 days from Jan + 29 days from Feb + 31 days from March + 14 days from April = 16 + 29 + 31 + 14 = 90 days

Part (b)

Bank discount = [(F - P) / F] x (360 / n)

3% = [(1,000,000 - P) / 1,000,000] x (360 / 90)

Hence, P = 992,500

Hence, the bond equivalent yield = [(F - P) / P] x (365 / n) = [(1,000,000 - 992,500) / 992,500] x (365 / 90) = 3.06%

Part (c)

On 30/360 basis, time btween settlement and maturity, n = 3 months = 3 x 30 = 90 days

the coupon equivalent yield (30/360 basis) = [(F - P) / P] x (360 / n) = [(1,000,000 - 992,500) / 992,500] x (360 / 90) = 3.02%

Part (d)

the CD equivalent yield  = [(F - P) / P] x (360 / n) = [(1,000,000 - 992,500) / 992,500] x (360 / 90) = 3.02%

Part (e)

Since the number of days in three months = 3 x 30 = 90 = actual number of days between settlement and maturity date, the formula for:

the bond equivalent yield in part b = [(F - P) / P] x (365 / n) = [(F - P) / P] x (365 / 90)

and the CD equivalent yield in part d = [(F - P) / P] x (360 / n) = [(F - P) / P] x (360 / 60)

Divide the two equations to get,

bond equivalent yield in part b / the CD equivalent yield in part d = 365 / 360

Hence, bond equivalent yield in part b = the CD equivalent yield in part d x 365 / 360