Question

Suppose that an investor with a 3-year investment horizon is considering buying an 8-year 6% coupon bond selling at par (semi-annual coupon payments). The investor expects that she can reinvest the coupin payments at an annual interest rate of 7% and that at the end of the investment horizon all bonds will be selling to offer a YTM of 9%.

What is the (annualized) expected holding period return for this bond?

Answer 1

First, we calculate the price of the bond after 3 years.

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 9%/2 (Semiannual YTM of bonds = annual YTM / 2)

nper = 5 * 2 (5 years remaining until maturity with 2 semiannual coupon payments each year)

pmt = 1000 * 6% / 2 (semiannual coupon payment = face value * coupon rate / 2)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $881.31

A1 * V fox =PV(9%/2,5*2, 1000*6%/2,1000) D E F G A B C

The cash outflow today is the price paid to buy the bond. As it is selling at par, the price paid is $1,000.

The cash inflow at the end of each semiannual period (upto 2.5 years, or 5 semiannual periods) = face value * coupon rate / 2 = $1000 * 6% / 2 = $30

The cash inflow at the end of the final semiannual period (3 years, or the 6th semiannual period) = semiannual coupon payment + price of bond at that time

The cash inflow at the end of the final semiannual period = $30 + $881.31 = $911.31

The annualized expected holding period return is calculated using MIRR function in Excel :

cash outflow today = price paid to buy the bond = $1000

cash inflow at end of 1st to 5th semiannual period = $30

cash inflow at end of 6th semiannual period = $911.31

Finance_rate and reinvest_rate are the rate at which coupon payments are reinvested. Here, we have to take the semiannual rate, as the coupon payment is semiannual. Semiannual rate = annual rate / 2 = 7% / 2 = 3.5%.

MIRR is calculated to be 1.26%. This is the semiannual expected holding period return. To get annual expected holding period return, we multiply by 2.

Annual expected holding period return = 2.51%

AB Semiannual 1 Period Cash Flow 0 $ (1,000.00) 1 $ 30.00 2 $ 30.00 3 $ 30.00 4 $ 30.00 5 $ 30.00 6 $ 911.31 9 MIRR 2.51%! 10

B Semiannual 1 Period Cash Flow 20 -1000 3 1 30 30 30 =30+881.31 =MIRR(B2:38,3.5%,3.5%)*2 9 MIRR