Asset-Liability Matching: In this question, we will investigate the economic reason why insurance companies try to match assets with liabilities. Suppose that in 30 years an insurance company will need to payout L30 = $120M (with certainty). It currently has collected $20 million in premiums, and has equity of $10 million. That is, E0 = $10M and A0 = $30M. It has the option of either (1) investing in a 30-year bond that will give a certain 300% return, or (2) investing in a 15-year bond that will give a certain 100% return, and then investing in another 15-year bond that will have a random return. The random bond will either have a return of 200% or 0%, both with probability 50%.

(a) (10 points) Calculate the expected equity value, expected return, and expected failure probability for the two options.

(b) (5 points) Which investment option will an unconstrained risk neutral insurance company choose? Why?

(c) (5 points) Define risk shifting. Does a risk shifting problem exist in this example, why or why not?

(d) (5 points) Suppose the government requires that all insurance companies must have

a failure probability of less than 0.1%. In this case, which investment option will the insurance company choose? Why?

(e) (5 points) In class we saw that the bonds used for asset-liability matching are more expensive than other bonds. How would this relationship change if the government

allowed insurance companies to operate with a higher acceptable failure probability?