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# P1.T4.905. Gross versus net bond returns, bond spread and bond yield (Tuckman Ch. 3)

#### Nicole Seaman

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Learning objectives: 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. Define, interpret, and apply a bond’s yield-to-maturity (YTM) to bond pricing.

Questions:

905.1. On June 1st, 2018, Jack borrowed the entire purchase price to buy a bond with a price of $103.20 which matures on November 30th, 2019. The bond pays a semi-annual coupon with a coupon rate of 5.50% per annum; this bond can be referred to as "5 1/2 of November 30, 2019." On November 30, 2018, the price of the bond was$106.90. At that time, Jack collected the coupon and sold the bond. His borrowing rate was 40 basis points per annum. Compound frequency is semi-annual to match the coupon cash flows (consistent with the entirely of Tuckman). What was Jack's net realized return?

a. 6.050%
b. 8.715%
c. Infinite due to 100% financing
d. Cannot solve because we need the bond's full/flat price at time of sale

905.2. Let the two-year term structure of zero rates include the following four spot rates: 1.0% @ 0.5 years, 2.0% @ 1.0, 3.0% @ 1.5, and 4.0% @ 2.0 years. Using these discount rates, the price of a two-year $100.00 face value bond with 4.0% coupon rate is$100.10 (see blue cell) as shown in the exhibit below, where $100.10 is the sum of four discounted cash flows: Assume the term structure above (i.e., 1.0% @ 0.5 years, 2.0% @ 1.0, 3.0% @ 1.5, and 4.0% @ 2.0 years) remains valid, but a different bond trades at a price of only$95.12. Which of the following is nearest to this bond's spread?

a. 30 basis points
b. 90 basis points
c. 140 basis points
d. 270 basis points

905.3. Peter paid \$93.40 to purchase a bond on June 1st, 2018; the bond pays a semi-annual coupon with a coupon rate of 3.0% per annum and matures in 10.0 years on June 1st, 2028. One year later, on June 1st, 2019, the bond's yield is unchanged; aka, unchanged yield assumption. Peter can reinvest his received coupons at a rate of 4.0% per annum. If Peter were to sell the bond on June 1st, 2019, which of the following is nearest to his gross realized return over the one year period since he purchased the bond?

a. -1.09%
b. 2.50%
c. 3.84%
d. 4.11%