Question

Assume an investor purchased a 3-month T-bill with a $10,000 par value for $9,800 and sold it 60 days later for $9,950. What is the yield (or bond equivalent yield)? What is the discount yield? What is the effective annual return?

Answer 1

Since investor purchased the 3-month T-bill for $9,800, the face value for which the t-bill was purchased is $9,800.

Yield is the return on the securiity being held by the investor in the form of dividend, interest, etc.

Using 360 as the number of days in a year in the formules because the ideal number of days for interest calculation of short term instruments whose maturity is within a year is Actual/360.

Formula for yield (Y) = (sales - face value)/face value * 360

Y = (9950 - 9800)/9800 * 360/60 = 0.091837

Discount yield calculates the return of the security being held which was sold ata discount.

Y_D = (Par value - sale price)/Par value * 360/n

Y_D = (10000 - 9800)/10000 *360/60 = 0.12

Effective annual return calculates the return earned on the securities held during the year.

Effective annual return = yield * 365 / maturity period

Return = 0.091837 *365 / 90 = 0.3725