Question

100 19 00 8 Security #1 is a 15-year bond with a face value of $1,000 that pays a 5% coupon semi-annually. Security #2 is a 5-year bond with a face value of $1,000 that pays a 6% coupon quarterly. Assume a sequence of three liabilities of $100,000, $200,000 and $300,000 that are 3, 5 and 10 years away, and assume r=5% for all instruments. You build a portfolio of Security #1 and Security #2 to match the duration of the liabilities. What is the optimal weight of Security #2 in your portfolio? O 62.58% 56.89% None of the provided answers is correct O 32.54% O 43.54% T- . E-

Answer 1

Concept Applied - Bond Immunization

Bond Immunization

Weighted Average Duration of Asset = Weighted Average Duration of Liability

In this case, Weighted Average Duration of Bond must be equal to Weighted Average Duration of Liabilities.

Calculation of Weighted Average Duration of Bond

Formula for Calculation of Duration of Security 1:

Duration = (n $\sum$ t=1 t*c/(1+i)^t + n*M/(1+i)^n)/ P

n = no. of cash flows

t = time to maturity

i = required yield

M = Maturity Value

P = Price of Bond

Security 1 - Based on above Duration of Security 1 = 10.72

Security 2 - Based on above Duration of Security 2 = 4.48

Weighted Average Duration of Liabilities

= (1,00,000 * 3 + 2,00,000 * 5 + 3,00,000 * 10) / (1,00,000 + 2,00,000 + 3,00,000) = 7.17

Hence Weights of Security 1 = 43.54% & Weight of Securiy 2 = 56.46%.

Hence Answer is Option 5