Question

Consider a 3-year risk-free bond, which pays annual coupons. The coupon rate is 3.5% and the face value is 500. The bond is issued at time t=0, pays coupons at time t=1,2,3 and face value at time t=3. You purchase the bond at time t=0. While holding the bond, you do not reinvest the coupon payments.

You resell the bond in one year, after getting the first coupon payment.

The yield to maturity when you sell is 3.6%.

What is your annualized holding period return?

Answer 1

Face Value = $500

Annual Coupon payment = $500*3.5%

= $17.50

Yield to Maturity at t=1 = 3.6%

No of years to maturity at t=1 = 3yrs -1yrs=2

Calulating the Price of Bond at t=1:-

$Price = \frac{CouponPayment}{(1+YTM)^{1}}+\frac{CouponPayment}{(1+YTM)^{2}}+\frac{FaceValue}{(1+YTM)^{2}}$

$Price = \frac{17.5}{(1+0.036)^{1}}+\frac{17.5}{(1+0.036)^{2}}+\frac{500}{(1+0.036)^{2}}$

Price = $33.1968 + $465.8547

Price = $499.05

SO, Prica at which bond is sold is $499.05

- Since, there is no mention of Yield to maturity at the time of buying assuming it to be same as Coupon rate. Thus, Buying price is same as face Value.

Annualized rate of Return = [(Sell price - Buy Price) + Coupon Income]/Buy Price

=[($499.05 - $500) +$17.50]/500

= 3.31%

So, annualized holding period return is 3.31%

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