Buying Mortgage-Backed Securities: A bank has bundled mortgages of face value 1000 into a mortgage-backed security which can be either

-performing with a high value of 950, or

-non-performing with a low value of 800

It needs liquidity and wants to sell the security to an investor (maybe the treasury) who is liquid and values the security 25 higher. As there are known gains from trade, i.e. the liquidity premium of 25, the bank and the investor would like to trade the security. Assume that some market maker offers them to trade the security at price p. At this price, the investor chooses whether or not to buy the security and the bank decides whether or not to sell the security. The security is only traded if both parties agree to trade. Assume that both the bank and the investor are risk-neutral.

Assume that neither the bank nor the investor know whether or not the security is performing or not but they both believe that each case is equally likely.

(a) For which prices p will the security be traded?

Now assume that the bank knows whether or not the security is performing but the investor does not but he believes each case equally likely.

(b) For which range of prices p is a non-performing security traded in equilibrium?

(c) For which range of prices p is a performing security traded in equilibrium?

(d) Now assume that the security is perform