第9章 资本资产定价模型 The Capital Asset pricing model
9-1 第9章 资本资产定价模型 The Capital Asset Pricing Model
资木资产定价模型 Capital Asset Pricing Model(CAPM) 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 9-2
9-2 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)
股票的需求与均衡价格 DEMAND FOR STOCKS AND EQUILIBRIUM PRICES The supply and demand for shares determine equilibrium prices and expected rates of return Imagine a simple world with only two corporations: Bottom 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% BU TD Price per share $) 39.00 39.00 Shares outstanding 5,000,000 4,000,000 Market value($ millions C 156 9-3
9-3 The supply and demand for shares determine equilibrium prices and expected rates of return. Imagine a simple world with only two corporations: Bottom 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
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 has 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 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 appears in Table 9.2
9-4 Sigma Fund is a new actively managed mutual fund that has 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 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 appears 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 BU TD Expected annual dividend (S/share) 6.40 380 iscount rate=Required return(%) Expected end-of-year price(S/share) Current price 039 Expected return(%): Capital gain 64326 2.56 2.56 Dividend yield 9.74 Total expected retum for the year 7.18 Standard deviation of rate of return 40% Correlation coefficient between rates of return on bu and TD 20 9-5
9-5 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 portfolio. These proportions, combined with the total investment budget, yield the fund's buy orders. With a budget of $220 million, Sigma wants a position in BU of $220,000,000X08070=$177,540,000,or $177,540,000/39=4,552,308 shares, and a position in td of$220,000,000X0.1930=$42,460,000, which corresponds to 1,088, 718 shares 9-6
9-6 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 portfolio. These proportions, combined with the total investment budget, yield the fund’s 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, which 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 45 40 Optimal Portfolio √B=80.70% Wm=1930% Mean=16.69% Standard deviation= 33.27% Efficient frontier of risky assets 8 2 5 10 Optimal portfolio 40 100 Standard deviation (%)
9-7 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 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 expmortfollo and a different demand for shares cted return would result in a different optimal p 9-8
9-8 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 prices. If, say, a share of BU could be purchased at a lower price, Sigma’s 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 different 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 Current Price Capital Gain Dividend Yield Expected Return BU Optimal Desired BU ( Proportion Shares 450 111 1422 3.1 4113 2010582 425 588 1506 9.18 3192 1652482 40 1600 1600 7013856053 667 1707 2373 5490247 1429 1829 3257 10947686125 9-9
9-9 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 Sigma's 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 the demand curve for the stock slopes downward. When bU s 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 will 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 take a short position Figure 9. 2 shows that when the price exceeds $44, Sigma wants a short position in BU 9-10
9-10 股票的需求与均衡价格 DEMAND FOR STOCKS AND EQUILIBRIUM PRICES Sigma’s 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 the demand curve for the stock slopes downward. When BU’s 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 will 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 take a short position. Figure 9.2 shows that when the price exceeds $44, Sigma wants a short position in BU