The following question illustrates diversification and risk sharing. Suppose that there two possible states of the...

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The following question illustrates diversification and risk sharing. Suppose that there two possible states of the world, state 1, and state 2 (say, state 1 is a contraction in the real estate and state 2, a boom in real estate). Suppose there are two types of borrowers, Type A and Type B. The default rate for Type A and Type B borrowers depends on the realized state. When default occurs, the borrower does not repay the principal nor the interest. Default rates are given by: State 1 State 2 10% 5% Type B 1% 15% Each state is equally likely to occur: there is a 50% chance that a contraction or a boom in the real estate sector will happen in a year. Suppose there are 500 Type A borrowers, and 500 Type B borrowers, each asking for a $200 loan to be paid one year from now. There are two investors, each with $100,000 excess funds. a Briefly explain why direct finance might not be a suitable option. Hint: Con- sider the functions of financial intermediaries b Suppose the investors decide to deposit their funds in a bank. The bank will extend the loans and charge a 5% annual lending rate. (a) What is the return of the loan portfolio when State 1 is realized. (b) What is the return of the loan portfolio when State 2 is realized. (c) What is the expected return of the portfolio? c What lending rate should the bank charge to attain an expected return of 10%? d Without calculating any return, would you say that the portfolio is diversified? Hint: In this case, the collection of assets is 500 Type A loans, 500 Type B loans. For a given state, consider the repayment rates. The following question illustrates diversification and risk sharing. Suppose that there two possible states of the world, state 1, and state 2 (say, state 1 is a contraction in the real estate and state 2, a boom in real estate). Suppose there are two types of borrowers, Type A and Type B. The default rate for Type A and Type B borrowers depends on the realized state. When default occurs, the borrower does not repay the principal nor the interest. Default rates are given by: State 1 State 2 10% 5% Type B 1% 15% Each state is equally likely to occur: there is a 50% chance that a contraction or a boom in the real estate sector will happen in a year. Suppose there are 500 Type A borrowers, and 500 Type B borrowers, each asking for a $200 loan to be paid one year from now. There are two investors, each with $100,000 excess funds. a Briefly explain why direct finance might not be a suitable option. Hint: Con- sider the functions of financial intermediaries b Suppose the investors decide to deposit their funds in a bank. The bank will extend the loans and charge a 5% annual lending rate. (a) What is the return of the loan portfolio when State 1 is realized. (b) What is the return of the loan portfolio when State 2 is realized. (c) What is the expected return of the portfolio? c What lending rate should the bank charge to attain an expected return of 10%? d Without calculating any return, would you say that the portfolio is diversified? Hint: In this case, the collection of assets is 500 Type A loans, 500 Type B loans. For a given state, consider the repayment rates.