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1、Chapter 6,MARKET EQUILIBRIUM: Capital Asset Pricing Model (CAPM) And Arbitrage Pricing Theory (APT),CAPM & APT,1,市场均衡：资本资产定价模型和套利定价模型,Outline,Introduction The efficiency of the market portfolio Derivation of the CAPM (Capital asset pricing model) Properties of the CAPM Use of the CAPM for valuation
2、Extensions of the CAPM Empirical tests of the CAPM The arbitrage pricing theory (APT) Empirical tests of the APT,A.INTRODUCTION,CAPM: A great innovation in the field of finance invented by William Sharpe (1963 1964) and John Lintner (1965 1969),William F. Sharpe 威廉. 夏普,CAPM：The equilibrium rates of
3、return on all risky assets are function of their covariance with the market portfolio. 所有风险资产均衡收益率是它们与市场证券组合之间的协方差的函数。,A.INTRODUCTION,A second important equilibrium asset pricing model（均衡定价模型） APT（arbitrage pricing theory）(Ross 1976) ：套利定价理论也是一均衡定价模型。一种风险资产的收益率是影响资产收益的各种共同因素的线性组合。,2011/10/14,CAPM &
4、APT,4,斯蒂芬罗斯（Stephen A. Ross）,A.INTRODUCTION,Assumptions 1. Investors are risk-averse individuals who maximize the expected utility of their wealth. 2. Investors are price takers and have homogeneous expectations about asset returns that have a joint normal distribution. 3. There exists a risk-free a
5、sset such that investors may borrow or lend unlimited amount of fund at a risk-free rate.,假设： 投资者是风险回避者，他们期望期末财富的期望效用最大化。 投资者是价格接受者（price takers），且他们对具有联合正态分布的资产收益具有同质期望（homogeneous expectations）。 存在无风险资产，使投资者能以无风险利率不受限制地借或贷。,CAPM & APT,5,A.INTRODUCTION,4. The quantities of assets are fixed. Also, a
6、ll assets are marketable and perfectly divisible. 5. Asset markets are frictionless, and information is costless and simultaneously available to all investors. 6. There are no market imperfections such as taxes, regulations, or restrictions on short selling. (All investors have homogeneous beliefs,
7、they make decisions based on an identical opportunity set).,资产的数量固定，所有资产是可交易且完全可分的。 市场是无摩擦的，信息是无成本的，所有投资者均可同时获得信息。 市场是完善的，没有税收、管制，对卖空没有限制。,CAPM & APT,6,B. THE EFFICIENCY OF THE MARKET PORTFOLIO,CAPM的证明要求：在均衡时，市场证券组合必须是有效证券组合。它必须位于图6.1中最小方差有效集的上半部。 一种保证市场证券组合有效性的方法是：只要投资者有一致的期望，他们都将接受相同的最小方差机会集（见Fama
8、，1976，Chapter 8）。即便没有无风险资产，无论他们个人风险的容忍度如何，他们都将选择有效的证券组合。,In equilibrium the market portfolio must be an efficient portfolio and it must lie on the upper half of the minimum variance opportunity set. In theory, (a)when all individuals have homogenous expectations, the market portfolio must be efficie
9、nt. (b)Thus the efficiency of the market portfolio and the capital asset pricing model are inseparable. (c)It is not possible to test the validity of one without the other.,Eugene F. Fama,当所有投资者投资有效证券组合的比例为正时，则市场证券组合是有效的，这是因为： （1）市场证券组合是所有个人持有证券之和。 （2）所有个人持有的证券是有效的。,C. DERIVATION OF THE CAPM（推导CAPM）
10、,前提：市场证券组合M是有效的。 图6.2表示M期望收益与标准差，Rf、I连接无风险资产和市场证券组合的直线是资本市场线。 在均衡时，市场证券组合中每一种证券的投资比例即为其市场价值，即， 每一种证券在市场证券组合中的均衡投资比例为（The equilibrium proportion of each asset in the market portfolio must be）：,（6.1）,Market value of the individual asset,wi =,Market value of all assets,设投资到风险资产I的投资比例为a%，(1-a)%投资于M， 此时形
11、成的证券组合的期望收益和标准差为 (A portfolio consisting of a% invested in a risky asset i and (1-a)% in the market portfolio will have the following mean and standard deviation): 其中： ：风险资产I的方差， ：市场证券组合M的方差。 ：风险资产I和市场证券组合的协方差。,（6.2）,（6.3）,（6.4）,（6.5）,The change in the mean and standard deviation with respect to the
12、 percentage of the portfolio, a, invested in asset i is determined as follows:,C.DERIVATION OF THE CAPM,In equilibrium the market portfolio already has value weight, wi percent, invested in the risky asset i. Therefore the percentage a in the above equations is the excess demand(超额需求) for an individ
13、ual risky asset. But we know that in equilibrium the excess demand for any asset must be zero. Prices will adjust until all assets are held by someone. Therefore if Eqs (6.4) and (6.5) are evaluated where excess demand, a, equals zero, then we can determine the equilibrium price relationships at poi
14、nt M in Fig 6.2. This will provide the equilibrium price of risk.,CAPM & APT,14,（6.6）,（6.7）,因此，均衡时，在市场证券组合M处，风险收益权衡曲线的斜率为（The slope of the risk-return trade-off evaluated at point M, in market equilibrium, is） ： （6.8）,回忆方程（5.34）中，资本市场线的斜率为：,由风险资产和市场证券组合构成的证券组合的机会集IMI 在M点的斜率等于资本市场线RfM的斜率。 The final i
15、nsight is to realize that the slope of the opportunity set IMI provided by the relationship between the risky asset and the market portfolio at point M must also be equal to the slope of the capital market line, RfM.,（6.9）,（6.9）式称为资本资产定价模型（capital asset pricing model）CAPM。 见图6.3，图中直线又称为证券市场线（SML）（se
16、curity market line）,CAPM的含义,The required rate of return on any asset E(Ri) is equal to the risk-free-rate of return plus a risk premium. 股票i的期望回报=无风险利率+风险溢价（酬金） The risk premium is the price of risk multiplied by the quantity of risk. 风险溢价=风险价格股票i所含的风险量。 The price of risk is the slope of the line, the difference between the expected rate of return on the market portfolio and the risk-free-rate of return.,称第i种股票的风险量（the quantity of risk）为： （1）如果资产i是无风险资产（risk-free asset），贝塔
