## Realized Compound Yield versus Yield to Maturity

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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### Responses

• iida
What is the difference between the yieldtomaturity (ytm) and the realized compound yield (rcy)?
1 year ago
• Paul
Is yield to maturity compound rate?
1 year ago
• fastolph brandagamba
What is ytm an compound return?
9 months ago
• bisrat
When does ytm exceed realized rate of return?
8 months ago
• domenico ricci
Is payment o for realized compound return?
8 months ago
• Julia
How to find the realized compound yield?
8 months ago
• Lorenzo
Why do people calcualte the realized compund yeild?
6 months ago
• Bryan
What is compound yeild to maturity?
4 months ago
• fnan
How to calculate therealized compound yield?
2 months ago
• penelope
Why is realized rate of return different from yield to maturity?
2 months ago
• bob
Why do stated yield to maturity and realized compound yield to maturity must always be equal?
1 month ago
• Dominic
Why does realized yield on a bond differ from yield to maturity?
25 days ago
• kate mitchell
How to calculate realized yield to maturity?
13 days ago
• Fatima
How to calculate realized compound yield?
2 days ago