1. 一家银行计划向钢铁行业的一家公司提供 5,000,000 美元的贷款。

(a) 使用 RAROC 模型，确定银行是否应该发放贷款。
(b) 贷款获得批准需要多长时间？
(c) 假设久期不能改变，有多少额外的利息和费用收入是否需要使贷款可以接受？
(d) 鉴于提议的收入流和协商的持续时间，什么调整——是否需要调整贷款利率才能使贷款可接受？
2. 你是一名银行家，面对一群贷款申请人，每个人可以是低风险或高风险。低风险申请人600人，高风险申请人400人风险申请人，每个申请人都在申请 100 美元的贷款。低风险借款人将 100 美元的贷款投资于一个项目，该项目将产生 150 美元的概率为 0.8 和没有概率 0.2 一个周期因此。高风险借款人将投资项目中的 100 美元贷款将以 0.7 的概率产生 155 美元，而因此，一个时期的概率为 0.3。您知道 60% 的申请者数量很少风险和 40% 是高风险，但您无法判断特定借款人是否为低风险风险或高风险。你是一个垄断银行家，有 50,000 美元可以借出。

1. A bank is planning to make a loan of \$5,000,000 to a rm in the steel industry.
It expects to charge a servicing fee of 50 basis points. The loan has a maturity of 8 years with a duration of 7.5 years. The cost of funds (the RAROC benchmark) for the bank is 10 percent. The bank has estimated the maximum change in the risk premium on the steel manufacturing sector to be approximately 4.2 percent,based on two years of historical data. The current market interest rate for loans in this sector is 12 percent.
(a) Using the RAROC model, determine whether the bank should make the loan.
(b) What should be the duration in order for this loan to be approved?
(c) Assuming that the duration cannot be changed, how much additional interest and fee income will be necessary to make the loan acceptable?
(d) Given the proposed income stream and the negotiated duration, what adjustment in the loan rate would be necessary to make the loan acceptable?
2. You are a banker and are confronted with a pool of loan applicants, each of whom can be either low risk or high risk. There are 600 low-risk applicants and 400 high-risk applicants and each applicant is applying for a \$100 loan. A low-risk borrower will invest the \$100 loan in a project that will yield \$150 with probability 0.8 and nothing with probability 0.2 one period hence. A high-risk borrower will invest the \$100 loan in a project that will yield \$155 with probability 0.7 and nothing with probability 0.3 one period hence. You know that 60% of the applicant pool is low risk and 40% is high risk, but you cannot tell whether a speci c borrower is low risk or high risk. You are a monopolist banker and have \$50,000 available to lend.
Everybody is risk neutral. The current riskless rate is 8%. Each borrower must be allowed to retain a pro t of at least \$5 in the successful state in order to be induced to apply for a bank loan. You have just learned that 1,000 loan applications have been received after you announced a 45% loan interest rate. You can satisfy only 500. What should be your optimal (pro t-maximizing) loan interest rate? Should it be 45% (at which you must ration half the loan applicants) or a higher interest rate at which there is no rationing? (See Topic 5, Example 5.5 )

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