We have noted that yield to maturity will equal the rate of return realized over the life of the bond if all coupons are reinvested at an interest rate equal to the bond's yield to maturity. Consider, for example, a two-year bond selling at par value paying a 10% coupon once a year. The yield to maturity is 10%. If the $100 coupon payment is reinvested at an interest rate of 10%, the $1,000 investment in the bond will grow after two years to $1,210, as illustrated in Figure 14.5, A. The coupon paid in the first year is reinvested and grows with interest to a second-year value of $110, which together with the second coupon payment and payment of par value in the second year, results in a total value of $1,210. The compound growth rate of invested funds, therefore, is calculated from
With a reinvestment rate equal to the 10% yield to maturity, the realized compound yield equals yield to maturity.
But what if the reinvestment rate is not 10%? If the coupon can be invested at more than 10%, funds will grow to more than $1,210, and the realized compound return will exceed 10%. If the reinvestment rate is less than 10%, so will be the realized compound return.
Suppose, for example, that the interest rate at which the coupon can be invested equals 8%. The following calculations are illustrated in Figure 14.5, B.
CONCEPT CHECK ^ QUESTIONS 4 and 5
PART IV Fixed-Income Securities
Figure 14.5 Growth of invested funds.
PART IV Fixed-Income Securities
Figure 14.5 Growth of invested funds.
Future value of first coupon payment with interest earnings $100 X 1.08 = $ 108 Cash payment in second year (final coupon plus par value) $1,100
Total value of investment with reinvested coupons $1,208
The realized compound yield is computed by calculating the compound rate of growth of invested funds, assuming that all coupon payments are reinvested. The investor purchased the bond for par at $1,000, and this investment grew to $1,208.
This example highlights the problem with conventional yield to maturity when reinvestment rates can change over time. Conventional yield to maturity will not equal realized compound return. However, in an economy with future interest rate uncertainty, the rates at which interim coupons will be reinvested are not yet known. Therefore, although realized compound yield can be computed after the investment period ends, it cannot be computed in advance without a forecast of future reinvestment rates. This reduces much of the attraction of the realized yield measure.
14.4
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