Question

Pension funds can pay life time annuities to recipients. Suppose you work for an investment firm that provides these types of annuities. You need to make 2 million payments per year. Suppose YTM is 16% on all bonds.

Suppose the duration of 5 year bonds with 12% coupon is 4 years and the duration of 20 year bonds with 6% coupon is 10 years and these are the only bonds available to you. You want to immunize the portfolio.

The price of the 5 -year bond will be: (closest to)

• A. 889.23

• B. 407.12

• C. 869.03

• D. 515.40

Answer 1

Correct answer: C. $869.03

5-year Bond:

Face value (F) = $1,000

Annual coupon rate = 12%

Coupon amount(C) = 12%*1000 = $120

Years until maturity (n) = 5

YTM (i) = 16%

Price of Bond = P

We can compute the price of bond with following equation:

P=C* (P/A, 1, n) + F* P/F,,n)

or

P=C* ((1+i)n-1 i*(1+i)n (1+i)n

P = 120 * (1 + 0.16)5 - 1 0.16* (1 +0.165) 1000 (1 + 0.16)

by solving

P= 869,02825385355

P= $869.03

Hope it will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.