financial_Rissk_Rettun_CAPM_PPT (1).pptx

riskreturn

1. CHAPTER 7 RISK, RETURN, AND THE CAPITAL ASSET PRICING MODEL Copyright © 2017 by Nelson Education Ltd. 7- 1

2. 7-1 Investment Returns Measure the financial results of an investment with the scale and timing effect May be historical or prospective (anticipated) Can be expressed in: Dollar terms Percentage terms Copyright © 2017 by Nelson Education Ltd. 7- 2

3. Investment Returns: An Example Dollar return: Percentage return: $Received – $Invested $1,100 – $1,000 = $100 $Return/$Invested $100/$1,000 = 0.10 = 10% Copyright © 2017 by Nelson Education Ltd. 7- 3

4. Copyright © 2017 by Nelson Education Ltd. 7- 4 Holding Period Returns examples

5. Holding Period Returns examples Copyright © 2017 by Nelson Education Ltd. 7- 5

6. 7-2 Stand-Alone Risk Typically, investment returns are not known with certainty. An asset’s stand-alone risk pertains to the probability of earning a return on one asset less than that expected. The greater the chance of a return far below the expected return, the greater the risk. Copyright © 2017 by Nelson Education Ltd. 7- 6

7. Probability Distributions Probability distributions are used to describe the certainty of returns by listing all possible returns and their probabilities. Graphically, the tighter (i.e., more peaked) the probability distribution, the more likely it is that the actual returns will be close to the expected value. The tighter the probability distribution, the lower the risk assigned to a stock. Copyright © 2017 by Nelson Education Ltd. 7- 7

8. Graphical Presentation of Probability Distributions Copyright © 2017 by Nelson Education Ltd. 7- 8

9. Quantitative Characteristics of a Probability Distribution Expected return: The weighted average of outcomes Standard deviation: A measure of the tightness of a probability distribution giving an idea of how far above or below the expected value the actual value is likely to be Copyright © 2017 by Nelson Education Ltd. 7- 9

10. Copyright © 2017 by Nelson Education Ltd. 7- 10

11. Expected Return Calculation r = expected rate of return ۸ r M = 0.3(100%) + 0.4(15%) + 0.3( – 70%) = 15% ^ n ∑ r = ^ i=1 r i P i ۸ r B = 0.3(40%) + 0.4(15%) + 0.3( – 10%) = 15% Copyright © 2017 by Nelson Education Ltd. 7- 11 (7-1)

12. Copyright © 2017 by Nelson Education Ltd. 7- 12

13. Measuring Stand-Alone Risk: Standard Deviation (SD) o f Returns σ = Standard deviation σ = √ Variance = √ σ 2 n ∑ i=1 = √ (r i – r) 2 P i ^ Copyright © 2017 by Nelson Education Ltd. 7- 13 (7-2, 7-3)

14. Calculating Standard Deviations  M = [(100 – 15) 2 (0.3) + (15 – 15) 2 (0.4) + (-70 – 15) 2 (0.3)] 1/2 = 65.84%  B = [(40 – 15) 2 (0.3) + (15 – 15) 2 (0.4) + ( – 10 – 15) 2 (0.3)] 1/2 = 19.36% Copyright © 2017 by Nelson Education Ltd. 7- 14

15. Using Historical Data to Measure Risk Copyright © 2017 by Nelson Education Ltd. 7- 15 Copyright © 2016 by Nelson Education Ltd.

16. Measuring Stand-Alone Risk: Coefficient of Variation (CV) CV = Standard deviation / expected return CV M = 65.84%/15% = 4.39 CV B = 19.36%/15% = 1.29 CV shows the risk per unit of return and captures the effects of both risk and return. A better measure than using SD for comparison Copyright © 2017 by Nelson Education Ltd. 7- 16 (7-6)

17. Risk Aversion and Required Return A risk-averse investor will consider risky assets or portfolios only if they provide compensation for risk via a risk premium. Risk premium is the excess return on the risky asset that is the difference between expected return on risky assets and the return on risk-free assets. Copyright © 2017 by Nelson Education Ltd. 7- 17

18. 7-3 Risk i n a Portfolio Context Investors often hold portfolios, not an asset of only one kind. A particular asset going up or down is important, but what matters the most is the return on the portfolio and its risk. Therefore, risk/return of an asset should be analyzed in terms of how that asset affects the overall risk/return of the portfolio in which it is held. Copyright © 2017 by Nelson Education Ltd. 7- 18

19. Portfolio Returns The expected return on a portfolio is the weighted average of the expected returns on the individual assets forming the basket, with the weights being the fraction of the total portfolio invested in each asset. Copyright © 2017 by Nelson Education Ltd. 7- 19 (7-7)

20. An Example of Calculating Portfolio Returns Stocks X and Y, each with investments of $25,000, form a portfolio of $50,000. Their expected returns are 11% and 7%, respectively. The rate of return on the portfolio is a weighted average of the returns on X and Y in the portfolio: Copyright © 2017 by Nelson Education Ltd. 7- 20

21. Unlike returns, σ P is generally not the weighted average of the standard deviations of the individual assets in the basket. Portfolio SD = σ P = √ σ P 2 Portfolio Risk, σ P The variance of the rate of return on the two risky assets portfolio is where  XY is the correlation coefficient between the returns on X and Y . Copyright © 2017 by Nelson Education Ltd. 7- 21

22. Correlation Coefficient, Measures the tendency of two variables to move together The estimate of correlation from a sample of historical data is often called “R.” ρ Copyright © 2017 by Nelson Education Ltd. 7- 22

23. Copyright © 2017 by Nelson Education Ltd. 7- 23 Copyright © 2016 by Nelson Education Ltd.

24. An Example of Calculating Portfolio Risk Two independent assets (i.e., ρ AB = 0) A and B with w A = 0.75, and w B = 1 – w A = 0.25 form a portfolio. Their standard deviations are σ A = 4%, and σ B = 10%. SDP = √0.001525 = 0.039 = 3.9% Copyright © 2017 by Nelson Education Ltd. 7- 24

25. Two-Asset Portfolios with Various Correlations – 1.0 < ρ < +1.0 The smaller the correlation, the greater the risk reduction potential. If ρ = –1.0, complete risk reduction is possible. If ρ = +1.0, no risk reduction is possible.  = -1.0  = 0.2  = 1.0 E(R P ) σ P Copyright © 2017 by Nelson Education Ltd. 7- 25

26. Efficient Portfolios Portfolio is a collection of assets. In a mean-variance (۸R – σ ) space, a set of portfolios maximizes expected return at each level of portfolio risk. Equally, a set of portfolios minimizes risk for each expected return. Investors choose along the efficient set for the best mix of risk and return with their own risk attitudes. Copyright © 2017 by Nelson Education Ltd. 7- 26

27. The Efficient Set for Two Assets Copyright © 2017 by Nelson Education Ltd. 7- 27

28. Diversification Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns. This reduction in risk arises because worse-than-expected returns from one asset are offset by better-than-expected returns from another. However, there is a minimum level of risk that cannot be diversified away, and that is the systematic portion. Copyright © 2017 by Nelson Education Ltd. 7- 28

29. Diversifiable Risk vs. Market Risk The risk (variance) of an individual asset’s return can be broken down into: Market risk: Economy-wide random events that affect almost all assets to a certain degree Diversifiable risk: Random events that affect a single security or small groups of securities The effect of diversification: Unsystematic risk will significantly diminish in large portfolios. Systematic risk cannot be eliminated by diversification since it affects all assets in any large portfolio. Copyright © 2017 by Nelson Education Ltd. 7- 29

30. Portfolio Risk as a Function of t he Number of Assets in t he Portfolio In a large portfolio (N ≥ 40), 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. A large part of the risk of any individual asset can be removed.  P Diversifiable Risk; Unsystematic Risk; Company-specific Risk n Nondiversifiable risk; Systematic Risk; Market Risk Portfolio Risk Copyright © 2017 by Nelson Education Ltd. 7- 30

31. Relevant Risk of Individual Asset to a Portfolio Researchers have shown that the best measure of the risk of an asset in a large portfolio is the beta ( b ) of the asset. Beta measures the responsiveness of an asset to movements in the market portfolio. In principle, a market portfolio includes all risky assets. Clearly, the estimate of beta will depend upon the choice of a proxy for the market portfolio. Copyright © 2017 by Nelson Education Ltd. 7- 31 (7-10)

32. Individual Stock Beta, β i The tendency of a stock to move up and down with the market is reflected in its beta coefficient. Estimate beta by running a regression between the asset’s return and the market return. The slope of the regression line (i.e., characteristic line) is equal to beta, showing how a stock moves in response to a movement in the general market. Copyright © 2017 by Nelson Education Ltd. 7- 32

33. Beta Coefficients Average-risk stock( β = 1): Returns tend to move up and down, on average, with the market, as measured by some index, such as the S&P/TSX Composite Index. Risky stock ( β > 1): Returns are more volatile than the market. Safe stock ( β < 1): Returns are less volatile than the market. Betas are usually positive. Choose a lower beta stock in a well-diversified portfolio. Theoretically, it is possible for a stock to have a negative beta. Copyright © 2017 by Nelson Education Ltd. 7- 33

34. Portfolio Betas The beta of a portfolio is a weighted average of its individual securities’ betas: Portfolio betas can be explained in the same way as individual stock betas. Adding a low-beta stock would reduce the risk of the portfolio. Copyright © 2017 by Nelson Education Ltd. 7- 34

35. 7-4 The Relationship between Risk and Rates of Return CAPM Graph: SML Expected return b 1 r RF E(R M ) Copyright © 2017 by Nelson Education Ltd. 7- 35

36. Capital Asset Pricing Model (CAPM) CAPM relates a risky asset’s risk premium to its market risk by stating that the expected return on a security is positively related to the security’s beta. The CAPM formula: E( r i ) = r RF + β i × [ r M – r RF ] = r RF + β i × RP M Interpretation: Expected return on an individual asset = risk-free rate + risk premium = risk-free rate + (beta of the asset × market risk premium) Assume β i = 0, then the expected return is risk-free rate r RF . Assume β i = 1, then E( R i ) = (R M ). Copyright © 2017 by Nelson Education Ltd. 7- 36 (7-15)

37. SML: A Numerical Example Given: β i = 1.5, r RF = 3%, r M = 10% r i = 3% + 1.5 × (10% - 3%) = 13.5% β 1.5 13.5% 3% Copyright © 2017 by Nelson Education Ltd. 7- 37

38. Identifying undervalued overvalued assets Copyright © 2017 by Nelson Education Ltd. 7- 38

39. Identifying undervalued overvalued assets Copyright © 2017 by Nelson Education Ltd. 7- 39