To compute the total returns we need the investment horizon, reinvestment rate and the price of the bond at the end of the investment horizon. Steps involved in computing total return over the investment horizon are as follows:
First, we need to compute the total coupon payments and the reinvestment income based on an assumed reinvestment rate. Reinvestment income is the amount that can be earned by reinvesting the coupon interest received on the securities. Mostly, bond interest is paid semiannually; so let us assume that the coupon payment is reinvested every six months. Therefore, the reinvestment rate can be calculated by dividing the annual interest rate that the investor assumes can be earned by reinvestment with two.
Next, we need to determine the projected sale price at the end of the investment horizon. This is referred to as horizon price.
By adding the value computed in (i) and (ii) and deducting the cost to obtain the funds we arrive at total future return that will be received from the investment. The reinvestment rates are assumed.
Then we need to calculate semiannual total return using the formula
(Total future return/ full price of the bond)^{ 1/n} - 1
Full price is obtained by adding accrued interest to the price. And n is the number of semiannual periods in the investment horizon.
The total return for semiannual-pay bonds can be expressed on a bond-equivalent basis by simply doubling the interest rates found in step 4.To express the total returns on an effective rate basis - the formula used is(1 + Semiannual total return)^{ 2} -1.
The total return can either be calculated on a bond-equivalent basis or on an effective rate basis. If the total returns are compared to a benchmark index that is based on bond-equivalent basis, then the total return is also to be calculated on the basis of bond-equivalent. But if liabilities are calculated on an effective rate basis and the bond is being used to satisfy liabilities, then the total return should be calculated on the basis of effective rate.