第十一章-套利定价理论

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,2020年5月29日星期五,#,11 十一月 2024,第十一章 套利定价理论,Arbitrage Pricing Theory,Arbitrage-arises if an investor can construct a zero investment portfolio with a sure profit.,Since no investment is required,an investor can create large positions to secure large levels of profit.,In efficient markets,profitable arbitrage opportunities will quickly disappear.,11.1 Factor Models:Announcements,Surprises,and Expected Returns,The return on any security consists of two parts.,First the expected returns,Second is the unexpected or risky returns.,A way to write the return on a stock in the coming month is:,11.1 Factor Models:Announcements,Surprises,and Expected Returns,Any announcement can be broken down into two parts,the anticipated or expected part and the surprise or innovation:,Announcement=Expected part+Surprise.,The expected part of any announcement is part of the information the market uses to form the expectation,R,of the return on the stock.,The surprise is the news that influences the unanticipated return on the stock,U,.,11.2 Risk:Systematic and Unsystematic,A,systematic risk,is any risk that affects a large number of assets,each to a greater or lesser degree.,An,unsystematic risk,is a risk that specifically affects a single asset or small group of assets.,Unsystematic risk can be diversified away.,Examples of systematic risk include uncertainty about general economic conditions,such as GNP,interest rates or inflation.,On the other hand,announcements specific to a company,such as a gold mining company striking gold,are examples of unsystematic risk.,11.2 Risk:Systematic and Unsystematic,Systematic Risk;,m,Nonsystematic Risk;,n,Total risk;,U,We can break down the risk,U,of holding a stock into two components:systematic risk and unsystematic risk:,11.3 Systematic Risk and Betas,The beta coefficient,b,tells us the response of the stocks return to a systematic risk.,In the CAPM,b,measured the responsiveness of a securitys return to a specific risk factor,the return on the market portfolio.,We shall now consider many types of systematic risk.,11.3 Systematic Risk and Betas,For example,suppose we have identified three systematic risks on which we want to focus:,Inflation,GDP,growth,The dollar-euro spot exchange rate,S,($,),Our model is:,Systematic Risk and Betas:Example,Suppose we have made the following estimates:,b,I,=-2.30,b,GDP,=1.50,b,S,=0.50.,Finally,the firm was able to attract a“superstar”CEO and this unanticipated development contributes 1%to the return.,Systematic Risk and Betas:Example,We must decide what surprises took place in the systematic factors.,If it was the case that the inflation rate was expected to be by 3%,but in fact was 8%during the time period,then,F,I,=Surprise in the inflation rate,=actual expected,=8%-3%,=5%,Systematic Risk and Betas:Example,If it was the case that the rate of,GDP,growth was expected to be 4%,but in fact was 1%,then,F,GDP,=Surprise in the rate of,GDP,growth,=actual expected,=1%-4%,=-3%,Systematic Risk and Betas:Example,If it was the case that dollar-euro spot exchange rate,S,($,),was expected to increase by 10%,but in fact remained stable during the time period,then,F,S,=Surprise in the exchange rate,=actual expected,=0%-10%,=-10%,Systematic Risk and Betas:Example,Finally,if it was the case that the expected return on the stock was 8%,then,11.4 Portfolios and Factor Models,Now let us consider what happens to portfolios of stocks when each of the stocks follows a one-factor model.,We will create portfolios from a list of,N,stocks and will capture the systematic risk with a 1-factor model.,The,i,th,stock in the list have returns:,Relationship Between the Return on the Common Factor&Excess Return,Excess return,The return on the factor,F,If we assume that there is no unsystematic risk,then,e,i,=0,Relationship Between the Return on the Common Factor&Excess Return,Excess return,The return on the factor,F,If we assume that there is no unsystematic risk,then,e,i,=0,Relationship Between the Return on the Common Factor&Excess Return,Excess return,The return on the factor,F,Different securities will have different betas,Portfolios and Diversification,We know that the portfolio return is the weighted average of the returns on the individual assets in the portfolio:,Portfolios and Diversification,The return on,any,portfolio is determined by three sets of parameters:,In a large portfolio,the third row of this equation disappears as the unsystematic risk is diversified away.,The weighed average of expected returns.,The weighted average of the betas times the factor.,The weighted average of the unsystematic risks.,Portfolios and Diversification,So the return on a,diversified,portfolio is determined by two sets of parameters:,The weighed average of expected returns.,The weighted average of the betas times the factor,F.,In a large portfolio,the only source of uncertainty is the portfolios sensitivity to the factor.,11.5 Betas and Expected Returns,The retur