资本资产定价

1、CHAPTERNINETHE CAPITAL ASSET PRICING MODEL资本资产定价模型1The CAPM describes the relationship between risk and equilibrium expected return in an efficient market context. The security market line, SML(证券市场线), of the CAPM, defines that the excess return on any asset over the risk free rate is proportional t

2、o the excess return on the market portfolio. The main goal of this chapter is to introduce the capital asset pricing model (CAPM) develeped by William Sharpe, which introduce the notion that portfolios risk can be decomposed into systematic and specific risk. 29.1 OutlineStocks valuation and their f

3、air pricesDefinition of stocks priceConstant growth modelStocks without a dividend Securities prices correspond to their risk股票的估价与其公允价格股票价格的定义固定增长模型不发放股息的股票相对于风险的证券价格. Stocks valuation and .股票估价与均衡价格its equilibrium price31. Stocks Valuation and Their Fair PricesStock prices can be defined as the su

4、m of the present value of each future cash inflow (dividend): (9.1)The value of the stock at time 0 is often called the intrinsic value（内在价值）.4Constant Growth ModelIf the stream of dividends is expected to growth at a constant rate, g, it will apply to the constant growth model(固定增长模型), which is pro

5、posed by Myron Gordon. (9.2)5SupposeA company just paid a dividend of $0.6 per share to its shareholder, and the dividend is expected to grow at a constant 5% in the coming years.The required rate of return on its stock is 8%. The estimated dividend paid in the next year is then D1 = $0.61.05= $0.63

6、. The intrinsic value of the stock at present is:6Stocks price without a dividendStocks of some start-up firms that have never paid a dividend would provide capital appreciation(资本升值) for their rapid growth. Their values also can be expressed as the present value of a stream of cash flows. 7In gener

7、al stocks are fairly priced and in equilibrium .If a stock was found underpriced, well-informed investors would buy shares of this stock and sell shares of high-priced stock immediately, these actions would bid up the price to its fair value. 82. Securities Prices Correspond to Their Risk In free fi

8、nancial markets, interest rates and/or returns on securities are determined by the force of supply and demand. 9Figure 9.110%RBRAE(R)Dollars7%5%D1D2S1S1Market ADollarsD1Market BDemand for fund declined would lead to an equilibrium interest rate or return drop. 10Since financial markets are interdepe

9、ndent. Two markets will realise a new equilibrium.And theoretically, when market is in equilibrium, the market price of an asset must equal its intrinsic value: P=V.119.2OutlineCAPM的假设条件市场投资组合资本资产定价模型贝塔系数证券市场线股票市场的均衡条件股票均衡价格的变化Assumptions of the CAPMThe market portfolioThe capital asset pricing mode

10、lThe beta coefficientsThe security market lineStock market equilibrium conditionsChanges in equilibrium stock prices. 资本资产定价模型 . The Capital Asset Pricing Model121. Assumptions of the Capital Asset Pricing ModelCAPM is based upon several assumptions:Investors are rational and risk averse（投资者是理性的且厌恶风

11、险）. All investors have homogenous expectations (beliefs) about asset returns（所有投资者对资产收益率的期望值是相同的）. There exists a risk-free asset, and investors may borrow or lend unlimited amounts of this asset at a constant rate: the risk-free rate. （存在一种无风险资产，投资者可以以固定不变的无风险利率无限量地借或贷这种资产）13Asset returns are stoch

12、astic and follow a normal distribution（资产收益率是服从正态分布的随机变量）.All assets are perfectly divisible and priced in a perfectly competitive market（所有资产都是完全可分割的并且在完全竞争市场中定价）. 14There are no market imperfections such as taxes, regulations, or restrictions on short selling（不存在如税收、管制或限制卖空之类的市场缺陷）.Capital markets

13、 are completely frictionless and information is costless and simultaneously available to all investors（资本市场完全没有摩擦，信息没有成本并且同时提供给所有投资者）.15Under these assumptions, all investors will hold the market portfolio (M), which includes all traded assets. Investors need to be compensated in two ways: time valu

14、e of money（资金的时间价值）represented by the risk-free rate（无风险收益率）, Rf associated investment risk（相关的投资风险）calculated by taking a risk measure (beta) that compares the returns of the asset to the market over a period of time and the market premium (RMRf). 162. The Market Portfolio（市场投资组合） The market portfo

15、lio M is a portfolio consisting of all risky assets (for simplicity, all the stocks) traded in the market. An average portfolio tends to move up and down in step with the general market, as measured by some index such as the Dow Jones Industrials Average（道琼斯工业平均指数） or S&P 500（标准普尔500指数）. 173. The Ca

16、pital Asset Pricing Model The capital asset pricing model (CAPM) is developed on the basis of the Markowitz model. 简单回顾第八章内容18Figure 9.2 Capital Market Line All investors will hold M as their optimal risky portfolio. Any point on the CML stands for a portfolio including risk-free assets and the risk

17、y portfolio M.E(R)MRfABP2P119The equilibrium return that investors require in general is presented as the CML equation: (9.3)The slope of the CML is referred to as equilibrium market price of risk(风险的均衡市场价格).20With CAMP theoretical framework, Sharpe breaks up the riskiness of each security into two

18、components systematic (the market related) risk specific risk. All specific risk or unique risk can be diversified away, the remaining systematic risk of a single stock is measured using beta.21SupposeAn average investor intends to increase her position in the market portfolio by a tiny fraction, ,

19、financed by borrowing at the risk-free rate Rf. Then, E(RP) = E(RM)RfSince is very small, 2 will be illegible. Therefore, P2 = 22M22Combining these results, the reward to additional risk is:23Suppose that the investor invest the increment in stock A only Then E(RP) = E(RA)RfAgain we ignore the term

20、involving 2 . P2 = 2Cov(RA,RM) Then the reward to additional risk is:24In equilibrium must hold.Otherwise investors will start buying or selling stock A and as a result will bid up or down its price and the yields drop or rise. Rearrange the equation we can found the fair risk premium of stock, A: (

21、9.4)25Sharpe uses A to denote the ratio of Cov(RA,RM)/M2, which measures the contribution of stock As variability to the market variability. That is: (9.5)Equation (9.4) can be rewritten as264. The Beta CoefficientsThe beta coefficient measures the volatility of the individual asset relative to the

22、volatility of the market (9.6)Define M=1. If i1, then the stock i is more risky than the market . A stock with a beta of 0.5 would rise by 5% if the market rose by 10%, and fall by 5% if the market fell by 10%.27Table 9.1Selected beta coefficients as company by Value Line28A portfolios beta is a wei

23、ghted average of its individual securities betas with fractions of total fund invested in securities being the weights:P = w11 + w22 + wnn (9.7)29For exampleStockAmount InvestedPercent of investmentBetaA$200 20%0.8B$300 30%1C$500 50%1.4A portfolio is comprised of the stocks as listed in above table

24、with their betas, then the beta of portfolio is0.20.8 + 0.31+ 0.51.4 = 1.16305. The Security Market LineIn an equilibrium condition, CAPM specifies the relationship between risk and rate of return on a stock: Ri = Rf +i (RMRf) (9.8)Equation 9.8 is known as the expected return-beta relationship of th

25、e CAPM, which is also called the Security Market Line (SML)(证券市场线）. 31Figure 9.3Security market line RMLowHighRisk Premium on a safe stockRLowRMRfRHighRisk Premium on M SMLMAll points on this line are stocks with fair returns for given levels of risk.32How can we tell if a stock is overpriced or und

26、erpriced? Suppose the return on stock A is 10% and the beta of A is 1.02; Predicted by CAPM, the required return on stock A should be RA = Rf +A (RMRf) = 4% + 1.02 (7%-4%)= 7.06%.0246810121400.511.522.53BACOverpricedSMLUnderpriced33The relationship between securitys risk and return (SML) in equilibr

27、ium conditions is important, suggesting that the rate of return on an individual asset depends on the risk-free rate and the compensation for taking on additional systematic risk. (单个证券的收益率取决于无风险收益率和对承担增加的系统性风险的补偿）346. Stock Market Equilibrium Conditions1) A stocks expected rate of return must equal

28、 its required rate of return:2) The actual market price of the stock must equal its intrinsic value:35An exampleSuppose the risk-free rate of return is 4%, the return on a market portfolio is 10%, and Stock i has a beta of 1.2, then Ri = Rf + (RM Rf)i=11.2%, is the rate of return an investor will re

29、quired on Stock i.36Now the investor analyzes the stocks expected dividend for the next period is $1 and its share price is expected to grow at 5% next year. The current price of the stock i, P0, is $20. The expected rate of return is, less than its required rate of return projected by the CAPM mode

30、l.37Thus this investor would want to sell the stock, pushing the price of the stock falling until it reaches the market equilibrium price, $16.13, at which the expected rate of return is equal to the required rate of return at 11.2%:387. Changes in Equilibrium Stock PricesIf the conditions on the market and on the stock A are changed as shown in Table 9.3, whats your estimate for the stocks price?39Table 9.3Changes in conditions on the market and on the stock AVariables CurrentexpectationNewinfo