Question

The stated yield to maturity and realized compound yield to maturity of a (default –free) zero coupon bond will always be equal. Why?

Answer 1

Because the coupon rates are reinvested at the rate of interest which is equal to the yield to maturity of the bond that is why the stated yield to maturity and realized compound yield to maturity of a (default –free) zero coupon bond will always be equal because

Let’s try understand with example

A two-year bond selling at par, in which coupon rate is paid once in a year is around 20%, YTM is 20%, the coupon payment reinvested is $200 and the initial value of investment is around $2000

For calculating the value of the zero-coupon bond when reinvested at reinvestment rate 20%

Value of Bond = (200 + 200×20%) + (2000 + (200 + 200×20%)

= 240 +2240 = 2480

Compounded rate of return:

V(1+r)² = V?

$2000×(1+r)² = $2480

r = 20%

This implies that the compounded rate of return is 20%