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1、第9章资本资产定价模型 The Capital Asset Pricing Model,9.1 股票的需求与均衡价格 9.2 资本资产定价模型 9.3 资本资产定价模型的扩展形式 9.4 资本资产定价模型与流动性,资本资产定价模型 Capital Asset Pricing Model (CAPM),The supply and demand for shares determine equilibrium prices and expected rates of return. Imagine a simple world with only two corporations: Bottom
2、 Up Inc. (BU) and Top Down Inc. (TD). Stock prices and market values are shown in Table 9.1. Investors can also invest in a money market fund (MMF) which yields a risk-free interest rate of 5%.,股票的需求与均衡价格DEMAND FOR STOCKS AND EQUILIBRIUM PRICES,Sigma Fund is a new actively managed mutual fund that h
3、as raised $220 million to invest in the stock market. The security analysis staff of Sigma believes that neither BU nor TD will grow in the future and therefore, that each firm will pay level annual dividends for the foreseeable future. This is a useful simplifying assumption because, if a stock is
4、expected to pay a stream of level dividends, the income derived from each share is a perpetuity. Therefore, the present value of each share often called the intrinsic value of the share equals the dividend divided by the appropriate discount rate. A summary of the report of the security analysts app
5、ears in Table 9.2.,股票的需求与均衡价格DEMAND FOR STOCKS AND EQUILIBRIUM PRICES,股票的需求与均衡价格DEMAND FOR STOCKS AND EQUILIBRIUM PRICES,Using these data and assumptions Sigma easily generates the efficient frontier shown in Figure 9.1 and computes the optimal portfolio proportions corresponding to the tangency por
6、tfolio. These proportions, combined with the total investment budget, yield the funds buy orders. With a budget of $220 million, Sigma wants a position in BU of $220,000,000 X 0.8070 =$177,540,000, or $177,540,000/39 =4,552,308 shares, and a position in TD of $220,000,000 X 0.1930= $42,460,000, whic
7、h corresponds to 1,088,718 shares.,股票的需求与均衡价格DEMAND FOR STOCKS AND EQUILIBRIUM PRICES,股票的需求与均衡价格DEMAND FOR STOCKS AND EQUILIBRIUM PRICES,The expected rates of return that Sigma used to derive its demand for shares of BU and TD were computed from the forecast of year-end stock prices and the current
8、prices. If, say, a share of BU could be purchased at a lower price, Sigmas forecast of the rate of return on BU would be higher. Conversely, if BU shares were selling at a higher price, expected returns would be lower. A new expected return would result in a different optimal portfolio and a differe
9、nt demand for shares.,股票的需求与均衡价格DEMAND FOR STOCKS AND EQUILIBRIUM PRICES,股票的需求与均衡价格DEMAND FOR STOCKS AND EQUILIBRIUM PRICES,股票的需求与均衡价格DEMAND FOR STOCKS AND EQUILIBRIUM PRICES,Sigmas demand curve for BU stock is given by the Desired Shares column in Table 9.3 and is plotted in Figure 9.2. Notice that
10、 the demand curve for the stock slopes downward. When BUs stock price falls, Sigma will desire more shares for two reasons: (1) an income effect - at a lower price Sigma can purchase more shares with the same budget, and (2) a substitution effect - the increased expected return at the lower price wi
11、ll make BU shares more attractive relative to TD shares. Notice that one can desire a negative number of shares, that is, a short position. If the stock price is high enough, its expected return will be so low that the desire to sell will overwhelm diversification motives and investors will want to
12、take a short position. Figure 9.2 shows that when the price exceeds $44, Sigma wants a short position in BU.,股票的需求与均衡价格DEMAND FOR STOCKS AND EQUILIBRIUM PRICES,股票的需求与均衡价格DEMAND FOR STOCKS AND EQUILIBRIUM PRICES,The demand curve for BU shares assumes that the price and therefore expected return of TD
13、 remain constant. A similar demand curve can be constructed for TD shares given a price for BU shares. As before, we would generate the demand for TD shares by revising Table 9.2 for various current prices of TD, leaving the price of BU unchanged. We use the revised expected returns to calculate the
14、 optimal portfolio for each possible price of TD, ultimately obtaining the demand curve shown in Figure 9.3.,资本资产定价模型是现代金融学的奠基石(风险与期望收益均衡模型) It is the equilibrium model that underlies all modern financial theory. 由诸多简单假定原理来建立 Derived using principles of diversification with simplified assumptions. 马
15、克维茨, 威廉夏普,林特纳和简莫辛研究和发展了资本资产定价模型。 Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development.,资本资产定价模型 Capital Asset Pricing Model (CAPM),个体投资者是价格的接受者 Individual investors are price takers 单周期投资期限 Single-period investment horizon 投资限制在金融资产的交易 Investments are limited to traded
16、 financial assets 无税负和交易成本 No taxes, and transaction costs,假设Assumptions,投资者是理性的均值-方差完善者 Investors are rational mean-variance optimizers 同质期望 Homogeneous expectations 给定一系列证券的价格和无风险利率，所有投资者的证券收益的期望收益率与协方差矩阵相等，从而产生了有效率边界和一个独一无二的最优风险资产组合。这一假定也被称为 同质期望。 Given a set of security prices and the risk-free interest rate, all investors use the same expected returns and covariance matrix of sec
