Question

Suppose you purchase a​ 10-year bond with 6.8% annual coupons. You hold the bond for four​ years, and sell it immediately after receiving the fourth coupon. If the​ bond's yield to maturity was 4.9% when you purchased and sold the​ bond, a. What cash flows will you pay and receive from your investment in the bond per $100 face​ value? b. What is the annual rate of return of your​ investment?

Answer 1

Price of a bond = I*(1-(1+r)^(-p))/r +FV/(1+r)^p

Where

I = coupon amout = face value * coupon rate =100×6.8% = 6.8 $per annum

r = yield = 4.9%

P= no. Of periods =10 years

FV = Face value =100$

Price = 6.8(1-1.049^-10)/.049 + 100/1.049^10 = 114.74$

Sale price after four year is

Sale price = 6.8(1-1.049^-6)/.049 + 100/(1.049)^6 = 109.67$

( 4 years have passed ,p = remaining 6 years)

Part b

Annual return earned is given by

Y= (I +(SP -P0)/n)/((SP+P0)/2)

Where

SP = sale price =109.67$

P0 = Purchase price = 114.74$

n= 4 years holding period

Y = holding yield =???

I =6.8$

Y = (6.8 +(109.67 -114.74)/4)/((109.67+114.74)/2)= 4.93% equal to our YTM 4.9%

Is it a coincidence or it had to be ?

It had to be because YTM has not changed from the time of purchase till the time of sale hence realised yield will also be equal to the YTM