Question

You have purchased a bond with 18 year maturity, 4% coupon rate, $1000 face value, and semi-annual payments for $927.09.

Two years later, when the YTM=3.8%, you sell the bond.

What was your average annual realized yield on the bond, if you were able to reinvest coupons at 3%? [Provide your answer in percent rounded to two decimals, omitting the % sign.]

Answer 1

Assuming that the first coupon on bond is due after 6 months.

Bond Purchase Price = $927.09

Bond Sale price Calculation

Semi annual rate = 3.8%/2 = 1.9%

Coupon amount = $1000 x 4% x 6/12 = $20

Number of coupons = 16 years x 2 = 32 coupons

Given the bond was sold yielding a YTM of 3.8%

So Sale Price = 20 x PVIFA(1.9%,32) + 1,000 x PVIF(1.9%,32)

Sale price = 20 x 23.813 + 1,000 x 0.54755

Sale Price = $1,023.81

Coupons value at end of 2nd year is -

= Coupon amount x FVIFA(coupon reinvestment rate per half year, Number of coupons)

= 20 x FVIFA(1.5%,4)

= 20 x 4.0909

= $81.818

Total Value at end of 2nd year = Sale amount + Coupon along with interest

= $1,023.81 + $81.818

= $1,105.628

Total return = ($1,105.628 - $927.09)/$927.09

= 0.1925789 or 19.25789%

This is for two years combined

Annualized return = [ (1+total return)^(1/n) - 1]

= [ (1+0.1925789)^(1/2) - 1]

= 0.09205 or 9.205% or 9.21%

Note :

Alternatively, average annualized return can simply be calculated like 19.25789%/2 = 9.63%

But the method used in problem is more accurate than this