第十章 收益和风险 CAPM

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1. Chapter Outline10.1 Individual Securities 10.2 Expected Return, Variance, and Covariance 10.3 The Return and Risk for Portfolios 10.4 The Efficient Set for Two Assets 10.5 The Efficient Set for Many Securities 10.6 Diversification: An Example 10.7 Riskless Borrowing and Lending 10.8 Market Equilibrium 10.9 Relationship between Risk and Expected Return (CAPM) 10.10 Summary and Conclusions
2. 10.1 Individual SecuritiesThe characteristics of individual securities that are of interest are the: Expected Return Variance and Standard Deviation Covariance and Correlation
3. 10.2 Expected Return, Variance, and Covariance Consider the following two risky asset world. There is a 1/3 chance of each state of the economy and the only assets are a stock fund and a bond fund.
4. 10.2 Expected Return, Variance, and Covariance
5. 10.2 Expected Return, Variance, and Covariance
6. 10.2 Expected Return, Variance, and Covariance
7. 10.2 Expected Return, Variance, and Covariance
8. 10.2 Expected Return, Variance, and Covariance
9. 10.2 Expected Return, Variance, and Covariance
10. 10.2 Expected Return, Variance, and Covariance
11. 10.2 Expected Return, Variance, and Covariance
12. 10.3 The Return and Risk for PortfoliosNote that stocks have a higher expected return than bonds and higher risk. Let us turn now to the risk-return tradeoff of a portfolio that is 50% invested in bonds and 50% invested in stocks.
13. 10.3 The Return and Risk for PortfoliosThe rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio:
14. 10.3 The Return and Risk for PortfoliosThe rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio:
15. 10.3 The Return and Risk for PortfoliosThe rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio:
16. 10.3 The Return and Risk for PortfoliosThe expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio.
17. 10.3 The Return and Risk for PortfoliosThe variance of the rate of return on the two risky assets portfolio is where BS is the correlation coefficient between the returns on the stock and bond funds.
18. 10.3 The Return and Risk for PortfoliosObserve the decrease in risk that diversification offers. An equally weighted portfolio (50% in stocks and 50% in bonds) has less risk than stocks or bonds held in isolation.
19. 10.4 The Efficient Set for Two AssetsWe can consider other portfolio weights besides 50% in stocks and 50% in bonds …100% bonds100% stocks
20. 10.4 The Efficient Set for Two AssetsWe can consider other portfolio weights besides 50% in stocks and 50% in bonds …100% bonds100% stocks
21. 10.4 The Efficient Set for Two Assets100% stocks100% bondsNote that some portfolios are “better” than others. They have higher returns for the same level of risk or less. These compromise the efficient frontier.
22. Two-Security Portfolios with Various Correlations 100% bondsreturn100% stocks = 0.2 = 1.0 = -1.0
23. Portfolio Risk/Return Two Securities: Correlation EffectsRelationship depends on correlation coefficient -1.0 < r < +1.0 The smaller the correlation, the greater the risk reduction potential If r = +1.0, no risk reduction is possible
24. Portfolio Risk as a Function of the Number of Stocks in the PortfolioNondiversifiable risk; Systematic Risk; Market RiskDiversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique RisknIn a large portfolio the variance terms are effectively diversified away, but the covariance terms are not. Thus diversification can eliminate some, but not all of the risk of individual securities.Portfolio risk
25. 10.5 The Efficient Set for Many SecuritiesConsider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios.returnPIndividual Assets
26. 10.5 The Efficient Set for Many SecuritiesGiven the opportunity set we can identify the minimum variance portfolio.returnPminimum variance portfolioIndividual Assets
27. 10.5 The Efficient Set for Many SecuritiesThe section of the opportunity set above the minimum variance portfolio is the efficient frontier.returnPminimum variance portfolioefficient frontierIndividual Assets
28. Optimal Risky Portfolio with a Risk-Free Asset In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills100% bonds100% stocksrfreturn
29. 10.7 Riskless Borrowing and LendingNow investors can allocate their money across the T-bills and a balanced mutual fund100% bonds100% stocksrfreturnBalanced fundCML
30. 10.7 Riskless Borrowing and Lending With a risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope returnPefficient frontierrfCML
31. 10.8 Market Equilibrium With the capital allocation line identified, all investors choose a point along the line—some combination of the risk-free asset and the market portfolio M. In a world with homogeneous expectations, M is the same for all investors.returnPefficient frontierrfMCML
32. The Separation Property The Separation Property states that the market portfolio, M, is the same for all investors—they can separate their risk aversion from their choice of the market portfolio.returnPefficient frontierrfMCML
33. The Separation Property Investor risk aversion is revealed in their choice of where to stay along the capital allocation line—not in their choice of the line.returnPefficient frontierrfMCML
34. Market EquilibriumJust where the investor chooses along the Capital Asset Line depends on his risk tolerance. The big point though is that all investors have the same CML.100% bonds100% stocksrfreturnBalanced fundCML
35. Market EquilibriumAll investors have the same CML because they all have the same optimal risky portfolio given the risk-free rate. 100% bonds100% stocksrfreturnOptimal Risky PorfolioCML
36. The Separation Property The separation property implies that portfolio choice can be separated into two tasks: (1) determine the optimal risky portfolio, and (2) selecting a point on the CML. 100% bonds100% stocksrfreturnOptimal Risky PorfolioCML
37. Optimal Risky Portfolio with a Risk-Free Asset By the way, the optimal risky portfolio depends on the risk-free rate as well as the risky assets.100% bonds100% stocksreturnFirst Optimal Risky PortfolioSecond Optimal Risky PortfolioCML0CML1
38. Definition of Risk When Investors Hold the Market PortfolioResearchers have shown that the best measure of the risk of a security in a large portfolio is the beta (b)of the security. Beta measures the responsiveness of a security to movements in the market portfolio.
39. Estimating b with regressionSecurity ReturnsReturn on market %Ri = a i + biRm + eiSlope = biCharacteristic Line
40. Estimates of b for Selected StocksStockBetaBank of America1.55Borland International2.35Travelers, Inc.1.65Du Pont1.00Kimberly-Clark Corp.0.90Microsoft1.05Green Mountain Power0.55Homestake Mining0.20Oracle, Inc.0.49
41. The Formula for BetaClearly, your estimate of beta will depend upon your choice of a proxy for the market portfolio.
42. 10.9 Relationship between Risk and Expected Return (CAPM)Expected Return on the Market: Expected return on an individual security: Market Risk PremiumThis applies to individual securities held within well-diversified portfolios.
43. Expected Return on an Individual SecurityThis formula is called the Capital Asset Pricing Model (CAPM)Assume bi = 0, then the expected return is RF. Assume bi = 1, thenExpected return on a security=Risk-free rate+Beta of the security×Market risk premium
44. Relationship Between Risk & Expected ReturnExpected returnb1.0
45. Relationship Between Risk & Expected ReturnExpected returnb1.5
46. 10.10 Summary and ConclusionsThis chapter sets forth the principles of modern portfolio theory. The expected return and variance on a portfolio of two securities A and B are given byBy varying wA, one can trace out the efficient set of portfolios. We graphed the efficient set for the two-asset case as a curve, pointing out that the degree of curvature reflects the diversification effect: the lower the correlation between the two securities, the greater the diversification. The same general shape holds in a world of many assets.
47. 10.10 Summary and ConclusionsThe efficient set of risky assets can be combined with riskless borrowing and lending. In this case, a rational investor will always choose to hold the portfolio of risky securities represented by the market portfolio.Then with borrowing or lending, the investor selects a point along the CML.returnPefficient frontierrfMCML
48. 10.10 Summary and ConclusionsThe contribution of a security to the risk of a well-diversified portfolio is proportional to the covariance of the security's return with the market’s return. This contribution is called the beta.The CAPM states that the expected return on a security is positively related to the security’s beta: