Question

Betty and Bob a 2-year coupon bond with a face and maturity value of $1,000 and a coupon rate of 8% per annum payable semiannually and a yield to maturity of 10% per annum compounded semiannually.

A. Algebraically find the price of the bond. Your final answer should be correct to 2 places after the decimal point. The price of the portfolio is __________________.

B. Algebraically find the exact Macaulay Duration of the portfolio. Your final answer should be correct to 2 places after the decimal point and expressed in years. The Macaulay Duration is ______________ years.

Answer 1

A)

Price of a bond is equal to the PV of the coupon payments and PV of the principal received on maturity. The discount factor used should be the minimum required return expected by investors, for eg, discount factor can be the YTM of the bond.

Current price in this case = Coupon payment*annuity factor(5%,4 periods)  + Principal amount*discount factor (5%, 4th period)

= (1000*0.08/2) * 3.546 + (1000* 0.8227) = 141.84 + 822.70= $ 964.54 (here, we have taken teh discounting rate as

10/2=5% due to semi annual coupon, and the no.

of periods has increased to 2*2= 4 periods)

B) Macaulay Duration=

Periods	Cash Flow	PV @ 5%	(PV/Total PV)*time in yrs
1	40	38.10	38.10/964.54= 0.0395
2	40	36.28	0.0376
3	40	34.55	0.0358
4	1040	855.61	0.8870
TOTAL		964.54	0.9999

hence, duration= 0.99