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typora-copy-images-to: Risk Management and Financial Institution

Risk Management and Financial Institutions

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Chapter 1

• The risk management function’s primary responsibility is to understand the portfolio of risks that the company is currently taking and the risks it plans to take in the future.

• 步骤：

  • concerning the risk‐return trade‐offs
  • whether the same arguments can be used by a company in choosing new projects and managing its risk exposure
  • Why companies should be coucerned with the total risk they face

1.1 Risk vs. Return for Investors

• The trade‐off is actually between risk and expected return, not between risk and actual return
• Expected return is therefore a weighted average of the possible returns, where the weight applied to a particular return equals the probability of that return occurring

• In 1976, Ross developed arbitrage pricing theory, which can be viewed as an extension of the capital asset pricing model to the situation where there are several sources of systematic risk(APT 模型)

1.1.1 Quantifying Risk

• A convenient measure that is often used is the standard deviation of the return over one year(年回报标准差)

1.1.2 Investment Opportunities

• Portfolio expected return is:
  • μ1 is the expected return from the first investment
  • μ2 is the expected return from the second investment

• The standard deviation of the portfolio return is:
  • ρ is the coefficient of correlation between the two

• Most investors are risk‐averse

1.2 The Efficient Frontier

• For any point in this area that is not on the efficient frontier, there is a point on the efficient frontier that has a higher expected return and lower standard deviation of return

• the line FJ is our new efficient frontier

• From the perspective of both expected return and standard deviation of return, point I is β_I of the way from F to M

• the distance of J from F is β_J times the distance of M from F (β_J > 1)

• The investment represented by point M is therefore usually referred to as the market portfolio

1.3 The CAPM

• RM is the return from the market portfolio, a and β are constants, and ε is a random variable equal to the regression error
• An investor should not be concerned about nonsystematic risk and should not require an extra return for bearing nonsystematic risk
• When a large well‐diversified portfolio is held, the systematic risk represented by βR_M does not disappear

• This is the capital asset pricing model
• The excess expected return over the risk‐free rate required on the investment is β times the excess expected return on the market portfolio

• The parameter β is equal to ρσ/σM,pho 是投资回报与市场组合投资回报的相关性，sigma是指投资回报的标准离散程度，sigma M是指市场组合的标准离散程度，Beta衡量的是敏感性

1.3.1 Assumptions of the CAPM

• Assumptions：
  • 假设投资者只关注组合的预期收益以及回报标准差，或者说，投资者只关注第一第二阶距。如果回报是整体分布的，那么没什么问题。但大多数资产是有偏度和峰度的，也就是第三第四阶距。Most investors are concerned about the possibility of extreme negative outcomes. They are likely to want a higher expected return from investments with negative skewness or excess kurtosis，负偏、高峰都会降低极端不利情况发生的概率
  • 假设不同投资工具的 ε变量是独立的，福特和通用的股票有同质性，不太可能是独立的
  • 假设投资者关注的时间跨度是一致的，long time horizon and short time horizons
  • 假设投资者可以以无风险利率借贷，使用与良好信用评级的大型金融机构，在市场正常的情况下
  • 假设不考虑税收，养老基金投资不用交税
  • We assumed that investors have homogeneous expectations 同质性的预期
• the expected return on a portfolio estimated by the capital asset pricing model is a commonly used benchmark for assessing the performance of the portfolio manager，CAPM测算出的预期回报成为benchmark

1.3.2 Alpha

• This is commonly referred to as the alpha created by the portfolio manager

• To produce a positive alpha:

  • trying to pick stocks that outperform the market
  • or by market timing
  • something else in chapter 4
    • trying to anticipate movements in he market upturn
    • trying to anticipate movements in he market downturn

• Beta describes the amount of systematic risk,Beta 越大，系统风险越大，回报多少的程度取决于市场表现

• The weighted average alpha of all investors must be zero，alpha的均值一定为零

1.4 APT Arbitrage Pricing Theory

• APT 可以看做CAPM的拓展插件，CAPM中，资产回报只取决于一个因子。APT是多因子模型

• arbitrage pricing theory shows that the expected return from an investment is linearly dependent on the factors，预期收益与各种因子是线性依赖关系

• **Each factor is a separate source of systematic risk **,unsystematic risk in APT is the risk that is unrelated to all the factors

1.5 Risk vs Return for Companies

• The company should calculate the beta of the investment project and its expected return. If the expected return is greater than that given by the capital asset pricing model, it is a good deal for shareholders and the investment should be accepted. Otherwise it should be rejected

• 非系统性风险同样重要，对冲汇率风险、利率风险、商品价格风险以及其他市场变量

• 收入稳定性以及企业生存意志是重要的风险管理目标，总风险不宜太高

• 个人持有的应该是一个充分风险分散化的组合

1.5.1 Bankruptcy Costs

• 完美世界中，破产程序流畅，资产以公平的价格售卖并按规划好的方式分配，如此并不会破坏股东的价值。

• The bankruptcy process itself invariably reduces the value of its assets，This further reduction in value is referred to as bankruptcy costs

  • customers and suppliers become less inclined to do business with company
  • intangible assets 无形资产灭失了
  • 会计和律师需要支付费用

• example： bankruptcy of Lehman Brothers 20亿美元的审计和律师费用

• creditors 争相 get paid

• When expected bankruptcy costs are taken into account, projects that have a high total (systematic plus nonsystematic) risk are liable to be rejected as unacceptable

• When a major new investment is being contemplated, it is important to consider how well it fits in with other risks taken by the company.加入新投资，总风险小概率下降，因为分散性便利，大概率提升总风险

1.5.2 Financial Institutions

• Confidence is the key to Financial Institutions survival.
• 如果市场发现违约风险不低，则很快市场信心丧失，流动性枯竭，并*清算即使在有偿付能力的情况下

1.5.3 Regulation

• Unlike other companies, many financial institutions are heavily regulated

• Regulated financial institutions are forced to consider total risks

• 监管试图确保银行有足够的资本应对吸收损失，提供充分的缓冲

• 监管者使用的模型在后续章节叙述

• 监管者关注的不仅仅是系统性风险，目标是使得破产是一件极低概率事件

1.6 Risk Management by Financial Institutions

• Two broad risk management strategies:

  • handle each risk separately——risk decompositon 风险分解
  • reduce risks by being well diversified——risk aggregation 风险加总

• The risk managers, working in what is termed the middle office of a bank.implement the risk aggregation approach for the market risks being taken

• If risks are unacceptably high,then the reasons must be determined and corrective action taken

• 保险公司使用的一般是风险加总的方式，1辆车的赔付不好预测，10000辆车可以预测

• 信用风险也经常以风险加总的方式进行管理

• 分散化的好处可以通过不同的地理区域，不同的行业进行最大化

• 即使分散化做得很好的银行依然会有系统性风险

• 信用衍生品可以使银行在对冲风险时使用risk decomposition的方式，进行一对一的对冲

1.7 Credit Rating

• A credit rating is a measure of the credit quality of a debt instrument such as a bond

• Moody and S&P and Finch

• Those with ratings below BBB− (Baa3) are termed noninvestment grade speculative grade or junk bonds

Summary

• There is a trade-off between return and risk

• Companies do not ignore the unsystematic risk that the shareholders can diversify away

• regulators aim to ensure that financial institutions keep enough capital for the total risks they are taking