Question

A mutual fund is holding a portfolio consists of four bonds. Duration of Bond A is 1.22-year, of Bond B is 2.75-year, of Bond C is 3.11-year, of Bond D is 5.16. The proportion of Bond A in the portfolio is 30%, Bond B is 25%, Bond C is 15%, and the rest goes to Bond D.

a) Which bond in the portfolio is exposed to the lowest interest rate risk? Briefly explain.

b) What is the duration of the portfolio?

Answer 1

1. Which bond in the portfolio is exposed to the lowest interest rate risk? Briefly explain.

Answer: Bond A

Reason

Duration of bond A is lower

Interest rate risk refers to the risk that affects the bond owners from fluctuating interest rates. Interest rate risk of a bond depends on how sensitive its price is to interest rate changes in the market. The sensitivity depends on two things, the bond's time to maturity, and the coupon rate.

Duration of the bond: The concept of duration is straightforward. It measures how quickly a bond will repay its true cost. The longer the time it takes the grater exposure the bond has to change in the interest rate environment. It is an important tool in structuring and managing fixed income securities.

2. What is the duration of the portfolio?

Answer: 3.068 years

Formula for calculating Portfolio Duration (PD) is as follows

PD = DA *WA + DB * WB +DC * WC +DD * WD

Where

DA = Duration of Bond A = 1.22 years

DB = Duration of Bond B = 2.75 years

DC = Duration of Bond C = 3.11 years

DD = Duration of Bond D = 5.16 years

WA = Weight of Bond A = 30%

WB = Weight of Bond B = 25%

WC = Weight of Bond C = 15%

WD = Weight of Bond = 30% (i.e. 100 – 30 – 25 – 15)

PD = DA *WA + DB * WB +DC * WC +DD * WD

            = (1.22 * 30%) + (2.75 * 25%) + (3.11 *15%) + (5.16 * 30%)

            =.366+.6875+.4665+1.548

            =3.068 years