Question

You’re considering investing in a 2-year 7% annual coupon bond priced at par. Alternatively, you’ll consider a 1-year 5% annual coupon bond priced at par and subsequently reinvesting all your proceeds in another identical 1-year bond. You expect the 1-year bond will yield 9% next year. Assuming you turn out to be right, which approach would generate the higher return?

• Invest in the 2-year bond.
• Invest in the 1-year and reinvest the proceeds in another 1-year.

Answer 1

We will find the Total return over 2 year period of both the approaches and compare the results.

Approach 1: Invest in the 2 year bond

Coupon rate of 2 year bond = 7%

Since the bond is priced at par, therefore coupon rate will be equal to yield to maturity

Total Return over two year period = (1+YTM)² - 1 = (1+7%)² - 1 = (1.07)² - 1 = 1.1449 - 1 = 0.1449 = 14.49%

Approach 2: Invest in 1 year bond and reinvest the proceeds in another 1 year bond

Coupon rate for 1 year bond = 5%

Since 1 year bond is priced at par, therefore coupon rate will be equal to yield to maturity

Hence Yield of 1 year bond = YTM1 = 5%

It is given Yield of one year bond next year = YTM2 = 9%

Total return over two year period = (1+YTM1)(1+YTM2) - 1 = (1+5%)(1+9%) - 1 = 1.05 x 1.09 - 1.1445 - 1 = 0.1445 = 14.45%

It can seen that total return over 2 years in Approach 1 is greater than Approach 2. Hence Approach 1 generates higher return.

Answer: Invest in a 2 year bond