In this question, you are immunizing a 100MM portfolio. The acceptable return is 6% over 5 years. Current immunization rates are 8.0% using 10 year semiannual pay bonds. The question asks you: If immunization rates jump to 11%, what rate will be the most likely to make the manager switch to immunization? The answers are: A) 11.0% B) 11.7% C) 12.5% Answer and my question below: The answer is B. The answer states that after you calculate the PV of the liability using the 11% rate as follows (100,000,000x1.03^10)/(1.055^(5x2))=78,676,000, you have to find the rate of return that would push that value to the required value. However, the calculator inputs shown use N = 10x2 = 20 periods, which is the life of the bonds, not the liability. The answer shows: FV=100,000,000 PV= -78,676,000 PMT = 4,000,000 N = 10 x 2 = 20 CPT -> I/Y then double First of all, why do you use FV=100,000,000 in this last part? Why do you want to get to the current portfolio value? Also, why do you not use N = 5x2 = 10 periods, which is the life of the liability? I think my brain is just taking a day off here…but I can’t get it to click. Any help is appreciated.
The reason why we use FV = 100,000,000 in the final step of the equation is because that is what the par value is on the bonds that were purchased to immunize the portfolio. In this case, we are simply going through bond pricing techniques, and thus, we must find the interest rate that would push the current market value of the bonds to equal the PV of the liability to be immunized. Because we know that with rates at 11%, the PV of the liability is 78,676,000, we can figure out what interest rate would push the market value of the bonds to that level. Because this last step involves actually pricing the bond, we need to recognize that the bond has 20 periods. 11.7% is the correct answer.