Question

QUESTION 24

1. Consider the following statements:

I. Macaulay duration indicates the period of time when reinvestment risk and price risk offset each other.

II. Modified Duration = Macaulay Duration × (1 + r).

	a.	Both statements are true.
	b.	One statement is true.
	c.	None of the statements is true.

Answer 1

We will analyze both statements individually

1. Price of a bond is subject to interest rate risk. This means that change in market interest risk will increase or decrease the price of the bond. On the other hand change in market interest rate results change in reinvestment rate of coupons. Thus when market interest rate decreases, price of bond increases and but reinvestment rate of coupons increases. Whereas when market rate increases price of bond decreases and reinvestment rate of coupons increases. Risk of Change in price of bond due to change in market interest rate is called price risk. Risk of Change in reinvestment rate of coupons is called as reinvestment risk. If market interest rate rises, then during life time of bond there comes a point when decrease in price of bond is offset by increase in coupon return due to increased reinvestment rate. Similarly if market interest rate decreases, then during life time of there comes a point when increase in price of bond is offset by decrease in coupon return due to decreased reinvestment rate. This means price risk and reinvestment risk negate each other. Macaulay duration is represented by this time point in bond's life. Thus if investment horizon is equal to Macaulay duration then both risks balance each other. Thus Macaulay duration indicates the period of time when reinvestment risk and price risk offset each other. Thus statement I. is true.

2 We know the

Modified duration = Macaulay duration / ( 1 + r)

where r = Yield to maturity of bond

Hence this statement II. is incorrect

Answer: b. Only one statement is correct