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Examples of how to adjust the rate of return on a discount money market instrument calculated on a 360-day year basis (a US T-Bill) such that it can be compared to a yield instrument whose return is calculated on a 365-day year (here a US bond). Q2 A U.S. treasury bill has 180 days to maturity and a price of $9600 per $10000 face value. The bank discount yield, rBD, of the bill is 8%. FV P 360 rBD FV n a) Calculate the bond equivalent yield for the Treasury bill. FV P 365 rBEY P n = (10000 – 9600)/9600 * (365/180) = .0845 8.45% b) [> 8% bank discount yield] Briefly explain why a t-bill’s bond equivalent yield differs from (i.e. is greater than) the bank discount yield. i) The denominator for the discount yield is the face value (i.e. 10000) rather than invested value. Thus the first factor is larger. ii) 360 vs. 365 days. The numerator in the second factor is larger. Q3 A T-bill has a bank discount yield of 6.81% based on the asked price, and 6.9% based on the bid price. The maturity of the bill is 60 days. Find the bid and asked price of the bill. Bank Discount Yield: P = 10000 * [1 – rBD * (n/360)] Thus, Pask = 10000 [1 – 0.0681 (60/360)] ≈ $ 9886.5 Pbid = 10000 [1 – 0.069 (60/360)] ≈ $ 9885 Q4 From Q3, calculate the bond equivalent yield and effective annual yield based on the ask price. Confirm that these yields exceed the discount yield. Bond Equivalent Yield: rBEY = (10000 – P)/ P * (365/n) |use ask Pask = (10000 – 9886.5)/9886.5 * (365/60) ≈ 6.98% [ > 6.81 = rBD] Effective Annual Yield: 1 + rAY = [1 + (10000 – 9886.5)/9886.5]365/60 1 + rAY = (10000/9886.5)365/60 1 + rAY ≈ 1.0719 => rAY ≈ 7.19%