What is duration of a bond? Explain briefly.

A 4 years bond with an annual coupon rate of 5% has a face value of $1000 and is trading for $930. What are the MacD and ModD if the current market interest rate is 8 %? Show your calculations step-by-step.

Duration of a bond

Duration refers to the average time spent by any financial product until the end of the payback period. This method shows that how long it will take a financial asset to pay cash on average. Bond prices change as interest rates change. The bond price consists of the sum of the present value of the cash flows that the bond will provide during the periods, discounted with the interest rate. According to Macaulay, effective maturity is equal to the weighted average of the maturities of the cash flows (payments).

Other things remaining the same, the smaller the difference between the market interest rate and the coupon rate, the shorter the duration of the bond.

Modified duration (MD) = [Macauley duration(MD )1+YTMn] Where: n = number of coupon periods per year YTM = the bond's yield to maturity

Example:

A 5 years bond with an annual coupon rate of 5% has a face value of $1000. What are the Macaulay Duration and Modified Duration, if the current market interest rate is 6%?

Calculating the Macaulay Duration step-by-step

Face value = $1,000

Coupon rate = 5%

Coupon value = 5% x $1,000 = $50

Market interest rate is 6%

Years coupon value DF (6%) PV of CF PV of the time weighted CF

1 50 0.943 47.15 1 x 47.15 = 47.15

2 50 0.890 44.90 2 x 44.90 = 89.80

3 50 0.840 42 .00 3 x 42 = 126

4 50 0.792 39.60 4 x 39.6 = 158.41

5 1050 (50+1,000) 0.743 784.60 5 x784.60 = 3,923.1

958.25 4,344

MacD= 4,344/ 958.25 = 4.53 years

Modified duration:

MD = [MacD1+YTMn] MD = [4.531+ (.122) ] = 4.27