Question

At t=0, you purchase a five-year, 8 percent coupon bond (paid annually) that is priced at par. The face value of the bond is $1,000. You are also given that your investment horizon is also five years. Suppose that the market interest rate increases to 9 percent (increase by 100 basis points) during the first year of your purchase (within year 1), and it remains at that level (9 percent) for the next four years. You decided to sell the bond at the end of year 1.

b) What is your holding period return at the end of your investment horizon (t=5)? Assume that the reinvestment rate for the first coupon payment and sale proceeds is the new interest rate, that is, 9 percent

Answer 1

The bond pays 8% of $1000 i.e $80 at the end of each year

At the end of 1 year , there are 4 years left to maturity of bond and hence, the price of the bond is

P = 80/1.09+ 80/1.09²+ 80/1.09³+80/1.09⁴ + 1000/1.09⁴

= $967.60

So, at the end of 1st year, the bond can be sold at $967.60 and the proceeds along with a coupon amount of $ 80 can be reinvested at 9%

So, amount invested after 1 year = $967.60+$80 = $1047.60

After 5 years, this amount becomes = $1047.60 * 1.09⁴ =$1478.78

In total, an amount of $1000 invested turned out to be $1478.78 after 5 years

So, the total return r can be calculated as

1000 * (1+r) ⁵ = 1478.78

=> 1+r = 1.478^(1/5)

=> 1+r = 1.08138

=> r= 0.08138 = 8.138% apx

So, the holding period return at the end of investment horizon of 5 years is 8.138%