Holding Period Return on Zero Coupon Bonds
Let’s compute the rate of return on each bond. The 1 year bond is bought today for $925.93 and matures in 1 year to its par value of $1,000. Because the bond pays no coupon, total income is $1,000 $925.93 = $74.07, and the rate of return is $74.07/$925.93 .08, or 8%. The 2 year bond is bought today for $841.75. Next year the interest rate will be 10%, and the bond will have 1 year left until maturity. It will sell then for $1,000/1.10 = $909.09. Thus the holding period return is ($909.09 $841.75)/$841.75 = .08, again implying an 8% rate of return. Similarly, the 3 year bond will be purchased for $758.33 and will be sold at year end for 1,000/(1.10)(1.11) = $819.00, for a rate of return ($819.00 $758.33)/$758.33 = .08, again, an 8% return. We conclude from Example 15.1 that when interest rate movements are known with certainty, and all bonds are properly priced, all will provide equal 1 year rates of return. The higher yields on the longer term bonds merely reflect the fact that future interest rates are higher than current rates and that the longer bonds are still alive during the higher rate period. Owners of the short term bonds receive lower yields to maturity, but they can reinvest, or “roll over,” their proceeds for higher yields in later years when rates are higher. In the end, both long term bonds and short term rollover strategies provide equal returns over the holding period, at least in a world of interest rate certainty.