Question

Suppose that you just bought a four-year $1,000 coupon bond with a coupon rate of 5.4% when the market interest rate is 5.4%. One year later, the market interest rate falls to 3.4%.

The rate of return earned on the bond during the year was _%

Answer 1

FAce value = 1000

years to maturity at time of purchase(n) =4

annual coupon amount = face value * coupon rate

=1000*5.4% = 54

required return (i) = 5.4%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(54*(1-(1/(1+5.4%)^4))/5.4%) + (1000/(1+5.4%)^4)

=1000

So purchase price = $1000

After 1 year, years to maturity (n) =4-1 =3

annual coupon amount = face value * coupon rate

=1000*5.4% = 54

required return (i) = 3.4%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(54*(1-(1/(1+3.4%)^3))/3.4%) + (1000/(1+3.4%)^3)

=1056.139946

1 year coupon received = $54

Holding period return = (Coupon received + Sale price - Buying price)/Buying price

(54+1056.139946- 1000)/1000

=0.110139946 or 11.0139946 %

So holding period return is 11.014%