Note 11 Portfolio Return and Risk, and the Capital Asset Pricing Model Outline Risk Aversion Portfolio Returns and Risk Portfolio and Diversification Systematic Risk: Beta (β) The Capital Asset Pricing Model and the Security Market Line The Security Market Line and Securities Pricing The Security Market Line and Capital Budgeting 2 1
Risk Aversion It is generally believed that investors prefer an investment with a higher expected return (to an investment with a lower return) and an investment with lower risk (to an investment with higher risk). Such an investment attitude is called risk aversion. Risk aversion is an attitude to avoid risk unless a sufficient amount of compensation (in return) is provided. 3 Exercise: Expected Return and Variance Investment in Single Assets Example) Calculate the expected returns, variances, and standard deviations of A and B. State of economy Probability of state Return on asset A Return on asset B Expansion 0.40 30% -5% Recession 0.60-10% 25% 1.00 To a risk-averse investor, which investment is better? 4 2
Exercise: Expected Return and Variance Investment in Single Assets For A, E(r A ) = (0.4)(0.3) + (0.6)(-0.1) = 0.06 Var(r A ) = (0.4)(0.3 0.06) 2 + (0.6)(-0.1 0.06) 2 = 0.0384 S.D.(r A ) = [0.0384] 1/2 = 0.196 For B, E(r A ) = (0.4)(-0.05) + (0.6)(0.25) = 0.13 Var(r A ) = (0.4)(-0.05 0.13) 2 + (0.6)(0.25 0.13) 2 = 0.0216 S.D.(r A ) = [0.0216] 1/2 = 0.147 5 Comparison between Stock A and Stock B Stock A Stock B E(r) 0.06 0.13 0.196 0.147 6 3
Comparison between Stock A and Stock B E(r) B (14.7%, 13%) A (19.6%, 6%) (Risk) 7 Portfolios A portfolio is a collection of assets An asset s risk and return are important in how they affect the risk and return of the portfolio The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets 8 4
Portfolio Returns Portfolio return is the weighted average of the return from each component asset of the portfolio, where the weights are the percentage of money invested in each asset. Thus, if a portfolio consists of two securities, A and B, and A s contribution to the portfolio is 40% while B s is 60%, then the portfolio s return is: r portfolio = (0.4)*(r A ) + (0.6)*(r B ) 9 Example: Expected Return and Variance Investment in a Portfolio Consider the case where you invest 50% of your money in Asset A and 50% in B (Let s call the new investment portfolio AB). State Probability A B Expans..4 30% -5% Recess..6-10% 25% Portfolio AB 12.5% 7.5% when expansion, r AB = (0.5)(0.3) + (0.5)(-0.05) = 0.125 when recession, r AB = (0.5)(-0.1) + (0.5)(0.25) = 0.075 10 5
Exercise: Expected Return and Variance Investment in a Portfolio What is the expected return and standard deviation for the portfolio? (hint: we just treat the portfolio as if it were another stock) State Probability Port. AB Boom.4 12.5% Bust.6 7.5% E(r P ) = (0.4)(0.125) + (0.6)(0.075) = 0.095 Var(r P ) = (0.4)(0.125 0.095) 2 + (0.6)(0.075 0.095) 2 = 0.0006 S.D.(r P ) = [0.0006] 1/2 = 0.0245 11 Comparison between Stock A, Stock B, and Portfolio Stock A Stock B Portfolio E(r) 0.06 0.13 0.095 0.196 0.147 0.0245 12 6
Comparison between Portfolio and Individual Stocks E(r) B (14.7%, 13%) P (2.5%, 9.5%) A (19.6%, 6%) (Risk) 13 Portfolio Risk: One Plus One is Not Two 0.05 0.04 0.03 0.02 0.01 0-0.01-0.02-0.03 Stock A returns Stock B returns 0.05 0.04 0.03 0.02 0.01 0-0.01-0.02-0.03 0.04 0.03 0.02 0.01 0-0.01-0.02-0.03 Portfolio returns: 50% A and 50% B -0.04-0.05 14 7
Portfolio Size and Risk 15 But Why? Risk (Portfolio standard deviation) Risk of Portfolio Number of stocks in portfolio 16 8
Total Risk and Its Components The standard deviation of returns is a measure of total risk Total Risk is the sum of Systematic Risk and Unsystematic Risk Two Components of Total Risk (1) Systematic Risk: Risk due to market wide, macroeconomic factors (also called market risk, systematic risk, non-diversifiable risk) (2) Unsystematic Risk: Risk due to firm specific factors (also called unique risk, firm-specific risk, diversifiable risk) 17 Example: Market wide information event 18 9
19 Example: Firm-specific information event 20 10
Disappointed by Boehringer s contract termination, Hanmi shares plummeted 24 percent during two trading sessions on Sept. 30 and Oct. 4, after the firm s stock price spiked nearly 5 percent on a disclosure made on Sept. 29 that it had clinched a 1 trillion won deal with Genentech, a member of Roche Group. 21 Portfolio Diversification You can eliminate the risk component due to firm-specific factors by including sufficiently large number of securities in your portfolio but the risk component due to the market wide factors still remain. Risk Total risk Unsystematic Risk, Firm-Specific Risk Systematic risk, Market Risk Portfolio Size 22 11
The Principle of 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 For well-diversified portfolios, unsystematic risk is very small and, consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk 23 Systematic Risk Principle There is a reward for bearing risk There is not a reward for bearing risk unnecessarily Unsystematic risk easily avoidable The expected return on a risky asset depends only on that asset s systematic risk since unsystematic risk can be diversified away 24 12
Measuring Systematic Risk How do we measure systematic risk? We use the beta coefficient ( ) to measure systematic risk How is beta measured? For Security A, The denominator in the above expression is the covariance between an individual security (e.g.: Security A above) and the market as a whole (market portfolio). The numerator is the variance of the market portfolio 25 What does tell us? (beta) measures the sensitivity (systematic movement) of stock A's return to the market movement. A beta of 1 implies the asset has the same systematic risk as the overall market A beta < 1 implies the asset has less systematic risk than the overall market A beta > 1 implies the asset has more systematic risk than the overall market 26 13
Beta Values: Examples (U.S.) Kraft Food: 0.06 Merck & Co.: 0.38 Exxon Mobil: 0.86 Microsoft: 1.17 Harley-Davidson: 1.58 The Goldman Sachs Group: 1.59 Abercrombie & Fitch: 1.9 MGM Resorts International: 2.48 27 Some Beta Examples: Korea Exchange (Monthly Data Used, 2008-2017) TS Corp. (Food & Bev.): Hyundai Steel (Steel): Samsung Electronics (Elec.): Nexen Tire (Mftg.-Auto): SK E&S (Utility - Gas) : 28 14
Total versus Systematic Risk Consider the following information: Standard Deviation Beta Security C 20% 1.25 Security K 30% 0.95 Which security has more total risk? Which security has more systematic risk? Which security should have the higher expected return? 29 Beta and the Risk Premium Remember : risk premium = expected return risk-free rate The higher the beta, the greater the risk premium Can we define the relationship between the risk premium and beta so that we can estimate the expected return? YES! 30 15
Capital Asset Pricing Model (CAPM) Stock returns show very systematic relationship with the market returns. E(r i ) r f = i [E(r m ) r f ] By moving r f to the L.H.S., we get E(r i ) = r f + i [E(r m ) r f ] E(r i ) Expected return on an individual security or portfolio r f Risk-free rate E(r M ) The average expected return on the whole market I The systematic risk of the individual security or portfolio In other words, the expected return of a stock is the sum of the risk-free rate and the market risk premium multiplied by the stock s beta. (beta) measures the sensitivity of stock i's return to the market risk premium (market movement). 31 Factors Affecting Expected Return Pure time value of money measured by the risk-free rate Reward for bearing systematic risk measured by the market risk premium Amount of systematic risk measured by beta E(r i ) = r f + i [E(r m ) r f ] 32 16
The Security Market Line (SML) Graphical illustration of the CAPM E(r) E(r i ) = r f + [E(r m ) r f ] i E(r M ) SML E(r M ) r F r f M 33 Example - CAPM Consider the betas for each of the assets given earlier. If the risk-free rate is 4.5% and the market risk premium is 8.5%, what is the expected return for each? Security Beta Expected Return DKNI 3.69 4.5 + 3.69(8.5) = 35.865% UBM.64 4.5 +.64(8.5) = 9.940% AAR 1.64 4.5 + 1.64(8.5) = 18.440% QTRI 1.79 4.5 + 1.79(8.5) = 19.715% 34 17
Capital Asset Pricing Model Developed by researchers including W. Sharpe * (1964) and J. Linter (1965). The CAPM provides us with a precise prediction of the relation between the risk of an asset and its expected return. The model also provides a benchmark required rate of return for evaluating possible investments. * Nobel economics prize winner in 1990 35 CAPM Application: Real Cases Risk-free rate (91-Day CD, End of July. 2017) = 1.65% Market risk premium (Based on Rating) = 7.03% Hyundai Steel Beta = 1.54 E(R HDS ) = Samsung Elec. = 0.89 E(R SSE ) = TS Corporate ( 대한제당 ) = 0.17 E(R TS ) = 18
An Important Lesson from the SML The security market line tells us the reward for bearing risk in financial markets. At an absolute minimum, any new investment our firm undertakes must offer an expected return that is no worse than what the financial markets offer for the same risk. If not, what will happen? Simply investors can always invest for themselves in the financial markets. This lesson has important meaning for capital budgeting. 37 19