Question

Suppose you are considering an investment in two bonds. Bond A has a duration of eight years and a market price of $950, and a bond B has a duration of four years and a market price of $1050. How should you invest $10 000 in these bonds if you have a desired holding period of seven years and wish to minimise interest rate risk?

Answer 1

Bond A duration = 8 years

Bond A market price = $950

Bond B duration - 4 years

Bond B market price = $1,050

Investment Amount = $10,000

Desired Holding period = 7 years

Let the investment in Bond A be X, thus the investment in bond B is (1-X)

Duration of portfolio = (Duration of Bond A * Investment in Bond A)+(Duration of Bond B * Investment in Bond B)

7 = (8*X)+(4*(1-X))

7 = 8X+4-4X

7-4 = 8X-4X

3=4X

X=3/4 = 75%

Thus, investment in Bond A = 75% and investment in Bond B = (1-75%) = 25%

Investment in Bond A = $10,000*75% = $7,500

Bond A market price = $950

Number of Bonds Purchased = $7,500/$950 = 7.89 or 8

Investment in Bond B = $10,000*25% = $2,500

Bond A market price = $1,050

Number of Bonds Purchased = $2,500/$1,050 = 2.38 or 2

Interest rate risk is minimised by investing in bonds of different durations. Since the desired holding period is seven years, 75% investment in Bond A and 25% investment in Bond B will help in minimising the interest rate risk and also meeting the desiring holding period of seven years.