【正文】 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 ine 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 . 股票的需求與均衡價(jià)格 DEMAND FOR STOCKS AND EQUILIBRIUM PRICES 95 股票的需求與均衡價(jià)格 DEMAND FOR STOCKS AND EQUILIBRIUM PRICES 96 Using these data and assumptions Sigma easily generates the efficient frontier shown in Figure and putes the optimal portfolio proportions corresponding to the tangency portfolio. These proportions, bined 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 =$177,540,000, or $177,540,000/39 =4,552,308 shares, and a position in TD of $220,000,000 X = $42,460,000, which corresponds to 1,088,718 shares. 股票的需求與均衡價(jià)格 DEMAND FOR STOCKS AND EQUILIBRIUM PRICES 97 股票的需求與均衡價(jià)格 DEMAND FOR STOCKS AND EQUILIBRIUM PRICES 98 The expected rates of return that Sigma used to derive its demand for shares of BU and TD were puted from the forecast of yearend 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. 股票的需求與均衡價(jià)格 DEMAND FOR STOCKS AND EQUILIBRIUM PRICES 99 股票的需求與均衡價(jià)格 DEMAND FOR STOCKS AND EQUILIBRIUM PRICES 910 股票的需求與均衡價(jià)格 DEMAND FOR STOCKS AND EQUILIBRIUM PRICES Sigma’s demand curve for BU stock is given by the Desired Shares column in Table and is plotted in Figure . 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 ine 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 shows that when the price exceeds $44, Sigma wants a short position in BU. 911 股票的需求與均衡價(jià)格 DEMAND FOR STOCKS AND EQUILIBRIUM PRICES 912 股票的需求與均衡價(jià)格 DEMAND FOR STOCKS AND EQUILIBRIUM PRICES The demand curve for BU shares assumes that the price and therefore expected return of TD 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 for various current prices of TD, leaving the price of BU unchanged. We use the revised expected returns to calculate the optimal portfolio for each possible price of TD, ultimately obtaining the demand curve shown in Figure . 913 資本資產(chǎn)定價(jià)模型是現(xiàn)代金融學(xué)的奠基石 (風(fēng)險(xiǎn)與期望收益均衡模型 ) It is the equilibrium model that underlies all modern financial theory. 由諸多簡(jiǎn)單假定原理來(lái)建立 Derived using principles of diversification with simplified assumptions. 馬克維茨 , 威廉 這一假定也被稱為 同質(zhì)期望。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(gè)體證券的風(fēng)險(xiǎn)溢價(jià)是市場(chǎng)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(gè)證券的風(fēng)險(xiǎn)溢價(jià)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(gè)人投資者的資產(chǎn)組合加總起來(lái)時(shí)，借與貸將互相抵消（這是因?yàn)槊總€(gè)借入者都有一個(gè)相應(yīng)的貸出者與之對(duì)應(yīng)），加總的風(fēng)險(xiǎn)資產(chǎn)組合價(jià)值等于整個(gè)經(jīng)濟(jì)中全部財(cái)富的價(jià)值，這就是市場(chǎng)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(gè)相同的時(shí)期內(nèi)計(jì)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(huì)達(dá)到相同的最優(yōu)風(fēng)險(xiǎn)資產(chǎn)組合。 這意味著投資者之間的凈借入與凈貸 出的總和為零 。為此，我們按第 8章討論過(guò)的方法將 n階協(xié)方差矩陣各項(xiàng)按照從行到列的順序分別乘以各證券在市場(chǎng)資產(chǎn)組合中的權(quán)重?？偟馁Y產(chǎn)組合收益為 rM＋ δ(rMrf)，將其期望值與最初期望值 E(rM)比較，期望收益的增加額為 單個(gè)證券的收益和風(fēng)險(xiǎn) Expected Return and Risk on Individual Securities 934 單個(gè)證券的收益和風(fēng)險(xiǎn) Expected Return and Risk on Individual Securities 935 單個(gè)證券的收益和風(fēng)險(xiǎn) Expected Return and Risk on Individual Securities 為了度量新資產(chǎn)組合的風(fēng)險(xiǎn)，我們重新計(jì)算資產(chǎn)組合的方差。這一比率稱作貝塔（ beta），以 β表示，這樣， 96式可以寫(xiě)作為： The ratio Cov(rGM， rM)/ σ2M measures the contribution of GM stock to the variance of the market portfolio as a fraction of the total variance of the market portfolio. The ratio is called beta and is denoted by β. Using this measure, we can restate equation as 945 單個(gè)證券的收益和風(fēng)險(xiǎn) Expected Return and Risk on Individual Securities 上式即是 CAPM模型的最普通形式 ─ 期望收益 貝塔關(guān)系 ,