Question

Question 1 (16 marks) (a) Are the following statements true or false? Briefly explain your answer. i) “The duration of a zero-coupon bond equals its time to maturity.” ii) Holding maturity constant, a bond's duration is lower when the coupon rate is higher.” iii) “Holding other factors constant, the duration of a coupon bond is higher when the bond's yield to maturity is lower.” (12 marks) (b) “It is not possible to forecast stock returns in an efficient market.” (4 marks)

Answer 1

(a)

i) Duration of a zero coupon bond equals to its time to maturity - it was true

duration of a bond is weighted duration where the weights are proportion of the bonds discounted cash flows to the bondprice discounted at yield to maturity.

ii) The given statement is False.

Duration formula for annuity paying bond = (1+y)/y - (1+y)+T(c-y)/c((1+y)^t-1)+y

where y = yield to maturity, t= term, c= coupon rate

we can do it by taking examples and finding duration.

iii) The given statement is True

by taking some examples we can find it by substituting in duration formula

Let y = 17%, t = 6, c = 16%

duration = 1.17/0.17 - 1.17+6(0.16-0.17)/0.16((1.17)6-1)+0.17 = 4.2424 years

if all same but y =16% then

duration = 1+0.16/0.16 - 1.16+6*(0.16-0.16)/0.16((1.16)6-1)+0.16 = 4.684 years