The yield-to-maturity on a bond is the interest rate you earn on your investment if interest rates do not change. If you actually sell the bond before it matures, your realized return is known as the holding period yield. Suppose that today you buy a 9 percent annual coupon bond for $1,000. The bond has 12 years to maturity. Three years from now, the yield-to-maturity has declined to 7 percent and you decide to sell. What is your holding period yield

The holding period yield is 11.87%

Explanation:

First, we need to determine the interest income received in the holding period

Interest income = Face value x Coupon rate x Holding period

Where

Face value = $1,000

Coupon rate = 9% per anum

Holding period = 3 years

Placing values in the formula

Interest income = $1,000 x 9% x 3 years = $270

Now calculate the price of the bond after 3 years as follow

Use the following formula to calculate the price of the bond

Price of the bond = [ C x ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Where

F = Face value = $1,000

C = Periodic coupon payment = $1,000 x 9% = $90

r = Periodic interest rate = 7%

n = Numbers of periods = 12 years - 3 year = 9 years

Placing values in the formula

Price of the bond = [ $90 x ( 1 - ( 1 + 7% )^-9 ) / 7% ] + [ $1,000 / ( 1 + 7% )^3 ]

Price of the bond = $586.37 + $543.93

Price of the bond = $1,130.30

Now determine the holding period return

Holding period return = Interest income + Price appreciation

Holding period return = Interest income + ( Price after 3 years - Purchase price )

Where

Interest income = $270

Price after 3 years = $1,130.30

Purchase price = $1,000

Placing values in the formula

Holding period return = $270 + ( $1,130.30 - $1,000 ) = $270 + $130.30 = $400,.30

Now calculate the holding period return rate

Holding period return rate = Holding period return / Initial investment = $400.30 / $1,000 = 0.40 = 40%

Annualise the rate of return as follow

Annual rate of return = ( ( ( 1 + rate of return )^(1/n) ) - 1 ) x 100

Annual rate of return = ( ( ( 1 + 40% )^(1/3) ) - 1 ) x 100

Annual rate of return = 0.1187 x 100

Annual rate of return = 11.87%

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