【正文】 給定一系列證券的價格和無風(fēng)險利率，所有投資者的證券收益的期望收益率與協(xié)方差矩陣相等，從而產(chǎn)生了有效率邊界和一個獨(dú)一無二的最優(yōu)風(fēng)險資產(chǎn)組合。這一假定也被稱為 同質(zhì)期望。 Given a set of security prices and the riskfree interest rate, all investors use the same expected returns and covariance matrix of security returns to generate the efficient frontier and the unique optimal risky portfolio. This assumption is often referred to as homogeneous expectations. 對投資者來說信息是無成本的和有效的 Information is costless and available to all investors 假設(shè) Assumptions (cont’d) 916 全部投資者將持有相同的風(fēng)險資產(chǎn) 市場組合 All investors will hold the same portfolio for risky assets – market portfolio. 市場組合含有全部股票和每只股票在市場資產(chǎn)組合所占的比例等于它的市值占所有股票的市值 Market portfolio contains all securities and the proportion of each security is its market value as a percentage of total market value. 均衡條件 Resulting Equilibrium Conditions 917 市場的風(fēng)險溢價取決于全部市場參與者的平均風(fēng)險厭惡 Risk premium on the market depends on the average risk aversion of all market participants 均衡條件 Resulting Equilibrium Conditions (cont.) 式中 σ2 M為市場資產(chǎn)組合的方差； A 為投資者風(fēng)險厭惡的平均水平。請注意由于市場資產(chǎn)組合是最優(yōu)資產(chǎn)組合，即風(fēng)險有效地分散于資產(chǎn)組合中的所有股票， σ2 M也 就是這個市場的系統(tǒng)風(fēng)險。 918 個體證券的風(fēng)險溢價是市場協(xié)方差的函數(shù) Risk premium on an individual security is a function of its covariance with the market 貝塔是用來測度股票與一起變動情況下證券收益的變動程度的。貝塔的正式定義如下： Beta measures the extent to which returns on the stock and the market move together. Formally, beta is defined as 均衡條件 Resulting Equilibrium Conditions (cont.) 919 個體證券的風(fēng)險溢價是市場協(xié)方差的函數(shù)Risk premium on an individual security is a function of its covariance with the market 單個證券的風(fēng)險溢價等于： The risk premium on individual securities is 均衡條件 Resulting Equilibrium Conditions (cont.) 920 當(dāng)我們把所有個人投資者的資產(chǎn)組合加總起來時，借與貸將互相抵消（這是因為每個借入者都有一個相應(yīng)的貸出者與之對應(yīng)），加總的風(fēng)險資產(chǎn)組合價值等于整個經(jīng)濟(jì)中全部財富的價值，這就是市場資產(chǎn)組合。每只股票在這個資產(chǎn)組合中的比例等于股票的市值占所有股票市場價值的比例。 資本資產(chǎn)定價模型認(rèn)為每個投資者均有優(yōu)化其資產(chǎn)組合的傾向，最終所有個人的資產(chǎn)組合會趨于一致，每種資產(chǎn)的權(quán)重等于它們在市場資產(chǎn)組合中所占的比例。 The portfolios of all individual investors, lending and borrowing will cancel out (since each lender has a corresponding borrower), and the value of the aggregate risky portfolio will equal the entire wealth of the economy. This is the market portfolio, M. The proportion of each stock in this portfolio equals the market value of the stock (price per share times number of shares out standing) divided by the sum of the market values of all The CAPM implies that as individuals attempt to optimize their personal portfolios, they each arrive at the same port folio, with weights on each asset equal to those of the market portfolio. 市場資產(chǎn)組合 The Market Portfolio 921 依據(jù)前文給定的假定條件，不難看出所有的投資者均傾向于持有同樣的風(fēng)險資產(chǎn) 組合。如果所有的投資者都將馬克維茨分析(假定 5)應(yīng)用于同樣廣泛的證券 (假定 3)，在一個相同的時期內(nèi)計劃他們的投資 (假定 2)，并且投資順序內(nèi)容也相同的話 (假定 6),那么他們必然會達(dá)到相同的最優(yōu)風(fēng)險資產(chǎn)組合。正如下圖所示 . Given the assumptions of the previous section, it is easy to see that all investors will desire to hold identical risky portfolios. If all investors use identical Markowitz analysis (Assumption 5) applied to the same universe of securities (Assumption 3) for the same time horizon (Assumption 2) and use the same input list (Assumption 6), they all must arrive at the same determination of the optimal risky portfolio, the portfolio on the efficient frontier identified by the tangency line from Tbills to that frontier, as in following figure. 市場資產(chǎn)組合 The Market Portfolio 922 資本市場線 Capital Market Line E(r) E(rM) rf M 資本市場線 CML ?m ? 923 M = 市場組合 Market portfolio rf = 無風(fēng)險率 Risk free rate E(rM) rf = 市場風(fēng)險溢價 Market risk premium E(rM) rf = 風(fēng)險市場價格 Market price of risk = CAPM斜率 Slope of the CAPM M ? 市場風(fēng)險溢價和斜率 Slope and Market Risk Premium 924 市場資產(chǎn)組合的均衡風(fēng)險溢價， E(rM)rf，與投資者群體的平均風(fēng)險厭惡程度和市場資產(chǎn)組合的風(fēng)險 σ 2M是成比例的。 The equilibrium risk premium on the market portfolio, E(rM)rf, will be proportional to the average degree of risk aversion of the investor population and the risk of the market portfolio. Now we can explain this result. 市場資產(chǎn)組合的風(fēng)險溢價 The Risk Premium of the Market Portfolio 925 在簡化了的 CAPM模型經(jīng)濟(jì)中 ， 無風(fēng)險投資包括投資者之間的借入與貸出 。 任何借 入頭寸必須同時有債權(quán)人的貸出頭寸作為抵償 。 這意味著投資者之間的凈借入與凈貸 出的總和為零 。 那么在風(fēng)險資產(chǎn)組合上的投資比例總的來說是 100%， 或 y = 1。 設(shè) y＝ 1， 代入 91式經(jīng)整理 ， 我們發(fā)現(xiàn)市場資產(chǎn)組合的風(fēng)險溢價與風(fēng)險厭惡的平均水平有關(guān)： In the simplified CAPM economy, riskfree investments involve borrowing and lending among investors. Any borrowing position must be offset by the lending position of the creditor. This means that borrowing and lending across all investors must be zero, and in consequence the average position in the risky portfolio is 100%, or y=1. Setting y=1 in equation and rearranging, we find that the risk premium on the market portfolio is related to its variance by the average degree of risk aversion: 市場資產(chǎn)組合的風(fēng)險溢價 The Risk Premium of the Market Portfolio 926 單個證券的風(fēng)險益價是單個證券對市場組合風(fēng)險的貢獻(xiàn)函數(shù) The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio. 單個證券的風(fēng)險益價是構(gòu)成市場組合資產(chǎn)收益協(xié)方差的函數(shù) An