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。
它预计将收取 50 个基点的服务费。贷款期限为8 年，持续时间为 7.5 年。资金成本（RAROC 基准）因为银行是 10%。银行估计了最大的变化钢铁制造业的风险溢价约为 4.2%，根据两年的历史数据。当前市场贷款利率在这个部门是 12%。
(a) 使用 RAROC 模型，确定银行是否应该发放贷款。
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。
每个人都是风险中性的。目前的无风险利率为 8%。每个借款人必须允许在成功状态下保留至少 5 美元的利润以进行诱导申请银行贷款。您刚刚了解到 1,000 份贷款申请在您宣布 45% 的贷款利率后收到。你只能满足500. 你的最佳（利润最大化）贷款利率应该是多少？应该它是 45%（您必须分配一半的贷款申请人）或更高的利息没有配给的比率？ （参见主题 5，示例 5.5）
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 specic 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 prot 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 (prot-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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