Question

Suppose you just purchased a bond with 14 years to maturity that pays an annual coupon of $44.00 and is selling at par. Calculate the one-year holding period return for each of these two cases: a. The yield to maturity is 3.10% one year from now. (Negative value should be indicated by a minus sign. Round your answer to 4 decimal places.) b. The yield to maturity is 2.70% one year from now. (Round your answer to 4 decimal places.)

Answer 1

Since the bond price is currently trading at its par value, it means that the bond's yield to maturity is equal to its coupon rate.

The bond pays an annual coupon, which means the Coupon rate = coupon payment / face value of the bond. In this case, since the face value is not given, it is presumed to be $1000.

Hence, coupon rate of the bond = $44/$1000 = 0.044 or 4.4%

Solution for a)

The yield-to-maturity or YTM after one year is 3.1%. The bond is now 13 years from maturity. The price of the bond is the current value of the future cash flow from the bond

That is, (coupon during year 1)/ (1 + YTM) + {(coupon during year 2)/ (1 + YTM)²} and so on till {(coupon during year 13)/ (1 + YTM)¹³} + {face value of the bond/ (1+YTM)¹³}

={44/(1+0.031)}+ {44/(1+0.031)²} + {44/(1+0.031)³} + {44/(1+0.031)⁴} + {44/(1+0.031)⁵} + {44/(1+0.031)⁶} + {44/(1+0.031)⁷} + {44/(1+0.031)⁸} + {44/(1+0.031)⁹} + {44/(1+0.031)¹⁰} + {44/(1+0.031)¹¹} + {44/(1+0.031)¹²} + {44/(1+0.031)¹³} + {1000/(1+0.031)¹³}

= $1,137.3744. Hence, the price of the bond after one year if YTM falls to 3.1% is $1137.3744

The holding period return of a bond = (total coupon payments + price of the bond at the end of the period - price of the bond at the start of the period) / price of the bond at the start of the period

total coupon payment during the period is $44, as mentioned above. Hence, the holding period return = ($44 + $1,137.3744 - $1,000)/ $1,000 = 0.181374 or 18.1374%

Solution for b

Similarly, we can calculate the holding period return if the YTM is 2.7% after 1 year, that is 13 years to maturity.

The price of the bond is the current value of the future cash flow from the bond

That is, (coupon during year 1)/ (1 + YTM) + {(coupon during year 2)/ (1 + YTM)²} and so on till {(coupon during year 13)/ (1 + YTM)¹³} + {face value of the bond/ (1+YTM)¹³}

={44/(1+0.027)}+ {44/(1+0.027)²} + {44/(1+0.027)³} + {44/(1+0.027)⁴} + {44/(1+0.027)⁵} + {44/(1+0.027)⁶} + {44/(1+0.027)⁷} + {44/(1+0.027)⁸} + {44/(1+0.027)⁹} + {44/(1+0.027)¹⁰} + {44/(1+0.027)¹¹} + {44/(1+0.027)¹²} + {44/(1+0.027)¹³} + {1000/(1+0.027)¹³}

= $1,184.3125. Hence, the price of the bond after one year if YTM falls to 2.7% is $1,184.3125

The holding period return of a bond = (total coupon payments + price of the bond at the end of the period - price of the bond at the start of the period) / price of the bond at the start of the period

total coupon payment during the period is $44, as mentioned above. Hence, the holding period return = ($44 + $1,184.3125 - $1,000)/ $1,000 = 0.228313 or 22.8313%