Question

12. Consider an insurance company that issues a guaranteed investment contract, called ABC, for $1,000. ABC has a three-year maturity and a guaranteed interest rate of 6%. The market interest rate is 6% for all maturities. Assume the payment is compounded annually a) Calculate the amount the insurance company promises to pay in three years (3 marks) b) Suppose that the insurance company funds this obligation with a two-year zero coupon bond and a bonds to construct a portfolio with a duration of three years. four-year zero coupon bond using $1,000. Show how to use these two (3 marks) assume all market interest rates increase to 7% and stay unchanged for c) Following b), the next three years. Calculate the portfolio value in three years. (6 marks) d) Following b), assume all market interest rates decrease to 5% and stay unchanged for the next three years. Calculate the portfolio value in three years. (5 marks) e) Explain why this portfolio could immunize the interest rate risk of ABC (3 marks)

Hey there, Could you please provide the answers with workings shown. Thank you!

Answer 1

Solution to part A:Future value=present value(1+rate)^Time

Here we need to find the future vale that insurance company promises to pay.

Three year is the time period

Interest Rate-6%pa

Therefore , future amount=1000(1+.06)^3

Payment compounded annually, therefore Future value=1191.016

Solution B: To get the duration of 3 year , suppose w1% invested in 2 year zero coupon bond and Amount invested in 4 year zero coupon bond =(1-w1%) where W1 is weight for 2 year zero coupon bond

=> 2*w1+4*(1-w1)=3

=> 2w1+4-4w1=3

=> 1=2w1

=> w1=50%

Conclusion: to construct the portfolio with 2 year zero coupon bond and 4 year zero coupon bond so as to get duration of 3, Weight of 2 year zero coupon bond will be 50 per and weight of 4 year zero coupon bond will be 50 percent.

Solution C: if interest rate rise to 7 perc.

500 invested in each 2 year zero coupon bond and 4 year zero coupon bond

500- 2 year zero coupon bond par value after 2 year and this 500 reinvested@7% for 1 more year as we are calculating the portfolio value at the end of three year horizon. Amount=500+500*7%=535

500- 4year zero coupon bond market value after 3year, if this 500 discounted @7% for 1 year , as we are calculating the portfolio value at the end of three year horizon. Amount=500/(1+.07)=467.28

Total portfolio value at 3 year horizon=535+467.28=1002.28

Solution D: if interest rate decrease to 5 perc

500 par value- 2 year zero coupon bond par value at 2 year and this 500 reinvested@5% for 1 more year as we are calculating the portfolio value at the end of three year horizon. Amount=500+500*5%=525

500 par value- 4year zero coupon bond market value after 3year, if this 500 discounted @5% for 1 year , as we are calculating the portfolio value at the end of three year horizon. Amount=500/(1+.05)=476.19

Total portfolio value at 3 year horizon=525+476.19=1001.19

Hope this clarifies .....