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P1.T4.315. Tuckman's bond spreads


AIMs: Distinguish between gross and net realized returns, and calculate the realized return for a bond over a holding period including reinvestments. Define and interpret the spread of a bond, and explain how a spread is derived from a bond price and a term structure of rates.


315.1. For a June 1st settlement, an investor finances the entire purchase of a bond with a price of $115.00 at a semiannually compounded borrowing rate of 0.60%. Six months later, on November 30th, the 3 1/8 bond pays a $1.56250 coupon (i.e., $3.125/2 = $1.56250) and its price has "pulled to par" by dropping to $114.00. Which is nearest to the six-month net realized return?

a. -0.87%
b. -0.57%
c. +0.19%
d. +0.49%

315.2. An investor buys a US Treasury 4s of May 31, 2023 at a price of $922.05 for settlement on June 1st, 2013. The yield on this 10-year bond is 5.00% as, per the TI BA II+ calculator, N = 20, I/Y = 2.50, FV = 1000, PMT = 20 returns a present value of about $922.05. Over the subsequent one-year period, the bond pays a $20.00 coupon on November 30th and another $20.00 coupon on May 31st. The November coupon is reinvested at a semiannually compounded rate of 2.00%. If the bond's yield remains perfectly flat at 5.00%, which is nearest to the bond's gross realized return over the one year period?

a. 4.88%
b. 4.97%
c. 5.00%
d. 5.03%

315.3. Assume the reference term structure, which happens to be the theoretical Treasury spot rate curve, is flat at a semiannually compounded rate of 1.30% per annum. A $100 par bond with a 20-year maturity pays a 4 3/8 coupon (4.375% coupon rate) and has a current price of $95.82. Which is nearest to the bond's spread with semi-annual compounding; a.k.a., bond-equivalent basis?

a. 1.74%
b. 3.40%
c. 4.00%
d. 4.70%


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