Risk and return
- 1. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 1 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-1 Chapter 5 Risk and Return Risk and Return © Pearson Education Limited 2004 Fundamentals of Financial Management, 12/e Created by: Gregory A. Kuhlemeyer, Ph.D. Carroll College, Waukesha, WI 5-2 Defining ReturnDefining Return Income received on an investment plus any change in market price, usually expressed as a percent of the beginning market price of the investment. Income received on an investment plus any change in market price, usually expressed as a percent of the beginning market price of the investment. Dt + (Pt - Pt-1 ) Pt-1 R =
- 2. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 2 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-3 Return ExampleReturn Example The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share and shareholders just received a $1 dividend. What return was earned over the past year? The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share and shareholders just received a $1 dividend. What return was earned over the past year? 5-4 Return ExampleReturn Example The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share and shareholders just received a $1 dividend. What return was earned over the past year? The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share and shareholders just received a $1 dividend. What return was earned over the past year? $1.00 + ($9.50 - $10.00 ) $10.00R = = 5%
- 3. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 3 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-5 Defining RiskDefining Risk The variability of returns from those that are expected. The variability of returns from those that are expected. 5-6 Determining Expected Return (Discrete Dist.) Determining Expected Return (Discrete Dist.) R = ΣΣΣΣ ( Ri )( Pi ) R is the expected return for the asset, Ri is the return for the ith possibility, Pi is the probability of that return occurring, n is the total number of possibilities. R = ΣΣΣΣ ( Ri )( Pi ) R is the expected return for the asset, Ri is the return for the ith possibility, Pi is the probability of that return occurring, n is the total number of possibilities. n i=1
- 4. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 4 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-7 How to Determine the Expected Return and Standard Deviation How to Determine the Expected Return and Standard Deviation Stock BW Ri Pi (Ri)(Pi) -.15 .10 -.015 -.03 .20 -.006 .09 .40 .036 .21 .20 .042 .33 .10 .033 Sum 1.00 .090 Stock BW Ri Pi (Ri)(Pi) -.15 .10 -.015 -.03 .20 -.006 .09 .40 .036 .21 .20 .042 .33 .10 .033 Sum 1.00 .090 The expected return, R, for Stock BW is .09 or 9% 5-8 Determining Standard Deviation (Risk Measure) Determining Standard Deviation (Risk Measure) σσσσ = ΣΣΣΣ ( Ri - R )2( Pi ) Standard Deviation, σσσσ, is a statistical measure of the variability of a distribution around its mean. It is the square root of variance. Note, this is for a discrete distribution. σσσσ = ΣΣΣΣ ( Ri - R )2( Pi ) Standard Deviation, σσσσ, is a statistical measure of the variability of a distribution around its mean. It is the square root of variance. Note, this is for a discrete distribution. n i=1
- 5. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 5 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-9 How to Determine the Expected Return and Standard Deviation How to Determine the Expected Return and Standard Deviation Stock BW Ri Pi (Ri)(Pi) (Ri - R )2(Pi) -.15 .10 -.015 .00576 -.03 .20 -.006 .00288 .09 .40 .036 .00000 .21 .20 .042 .00288 .33 .10 .033 .00576 Sum 1.00 .090 .01728 Stock BW Ri Pi (Ri)(Pi) (Ri - R )2(Pi) -.15 .10 -.015 .00576 -.03 .20 -.006 .00288 .09 .40 .036 .00000 .21 .20 .042 .00288 .33 .10 .033 .00576 Sum 1.00 .090 .01728 5-10 Determining Standard Deviation (Risk Measure) Determining Standard Deviation (Risk Measure) σσσσ = ΣΣΣΣ ( Ri - R )2( Pi ) σσσσ = .01728 σσσσ = .1315 or 13.15% σσσσ = ΣΣΣΣ ( Ri - R )2( Pi ) σσσσ = .01728 σσσσ = .1315 or 13.15% n i=1
- 6. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 6 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-11 Coefficient of VariationCoefficient of Variation The ratio of the standard deviation of a distribution to the mean of that distribution. It is a measure of RELATIVE risk. CV = σσσσ / R CV of BW = .1315 / .09 = 1.46 The ratio of the standard deviation of a distribution to the mean of that distribution. It is a measure of RELATIVE risk. CV = σσσσ / R CV of BW = .1315 / .09 = 1.46 5-12 Discrete vs. Continuous Distributions 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 -15% -3% 9% 21% 33% Discrete Continuous 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 -50% -41% -32% -23% -14% -5% 4% 13% 22% 31% 40% 49% 58% 67%
- 7. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 7 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-13 Certainty Equivalent (CE) is the amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same point in time. Certainty Equivalent (CE) is the amount of cash someone would require with certainty at a point in time to make the individual indifferent between that certain amount and an amount expected to be received with risk at the same point in time. Risk AttitudesRisk Attitudes 5-14 Certainty equivalent > Expected value Risk Preference Certainty equivalent = Expected value Risk Indifference Certainty equivalent < Expected value Risk Aversion Most individuals are Risk Averse. Certainty equivalent > Expected value Risk Preference Certainty equivalent = Expected value Risk Indifference Certainty equivalent < Expected value Risk Aversion Most individuals are Risk Averse. Risk AttitudesRisk Attitudes
- 8. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 8 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-15 Risk Attitude Example You have the choice between (1) a guaranteed dollar reward or (2) a coin-flip gamble of $100,000 (50% chance) or $0 (50% chance). The expected value of the gamble is $50,000. Mary requires a guaranteed $25,000, or more, to call off the gamble. Raleigh is just as happy to take $50,000 or take the risky gamble. Shannon requires at least $52,000 to call off the gamble. 5-16 What are the Risk Attitude tendencies of each? Risk Attitude ExampleRisk Attitude Example Mary shows “risk aversion” because her “certainty equivalent” < the expected value of the gamble. Raleigh exhibits “risk indifference” because her “certainty equivalent” equals the expected value of the gamble. Shannon reveals a “risk preference” because her “certainty equivalent” > the expected value of the gamble. Mary shows “risk aversion” because her “certainty equivalent” < the expected value of the gamble. Raleigh exhibits “risk indifference” because her “certainty equivalent” equals the expected value of the gamble. Shannon reveals a “risk preference” because her “certainty equivalent” > the expected value of the gamble.
- 9. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 9 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-17 RP = ΣΣΣΣ ( Wj )( Rj ) RP is the expected return for the portfolio, Wj is the weight (investment proportion) for the jth asset in the portfolio, Rj is the expected return of the jth asset, m is the total number of assets in the portfolio. RP = ΣΣΣΣ ( Wj )( Rj ) RP is the expected return for the portfolio, Wj is the weight (investment proportion) for the jth asset in the portfolio, Rj is the expected return of the jth asset, m is the total number of assets in the portfolio. Determining Portfolio Expected Return Determining Portfolio Expected Return m j=1 5-18 Determining Portfolio Standard Deviation Determining Portfolio Standard Deviation m j=1 m k=1 σσσσP = Σ ΣΣ ΣΣ ΣΣ Σ Wj Wk σσσσjk Wj is the weight (investment proportion) for the jth asset in the portfolio, Wk is the weight (investment proportion) for the kth asset in the portfolio, σσσσjk is the covariance between returns for the jth and kth assets in the portfolio. σσσσP = Σ ΣΣ ΣΣ ΣΣ Σ Wj Wk σσσσjk Wj is the weight (investment proportion) for the jth asset in the portfolio, Wk is the weight (investment proportion) for the kth asset in the portfolio, σσσσjk is the covariance between returns for the jth and kth assets in the portfolio.
- 10. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 10 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-19 Combining securities that are not perfectly, positively correlated reduces risk. Combining securities that are not perfectly, positively correlated reduces risk. Risk and DiversificationRisk and DiversificationINVESTMENTRETURN TIME TIMETIME SECURITY E SECURITY F Combination E and F 5-20 Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole. Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification. Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole. Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification. Total Risk = Systematic Risk + Unsystematic Risk Total Risk = Systematic Risk + Unsystematic Risk Total Risk = Systematic Risk + Unsystematic Risk
- 11. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 11 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-21 Total Risk = Systematic Risk + Unsystematic Risk Total Risk = Systematic Risk + Unsystematic Risk Total Risk Unsystematic risk Systematic risk STDDEVOFPORTFOLIORETURN NUMBER OF SECURITIES IN THE PORTFOLIO Factors such as changes in nation’s economy, tax reform by the Congress, or a change in the world situation. 5-22 Total Risk = Systematic Risk + Unsystematic Risk Total Risk = Systematic Risk + Unsystematic Risk Total Risk Unsystematic risk Systematic risk STDDEVOFPORTFOLIORETURN NUMBER OF SECURITIES IN THE PORTFOLIO Factors unique to a particular company or industry. For example, the death of a key executive or loss of a governmental defense contract.
- 12. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 12 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-23 CAPM is a model that describes the relationship between risk and expected (required) return; in this model, a security’s expected (required) return is the risk-free rate plus a premium based on the systematic risk of the security. CAPM is a model that describes the relationship between risk and expected (required) return; in this model, a security’s expected (required) return is the risk-free rate plus a premium based on the systematic risk of the security. Capital Asset Pricing Model (CAPM) Capital Asset Pricing Model (CAPM) 5-24 1. Capital markets are efficient. 2. Homogeneous investor expectations over a given period. 3. Risk-free asset return is certain (use short- to intermediate-term Treasuries as a proxy). 4. Market portfolio contains only systematic risk (use S&P 500 Index or similar as a proxy). 1. Capital markets are efficient. 2. Homogeneous investor expectations over a given period. 3. Risk-free asset return is certain (use short- to intermediate-term Treasuries as a proxy). 4. Market portfolio contains only systematic risk (use S&P 500 Index or similar as a proxy). CAPM AssumptionsCAPM Assumptions
- 13. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 13 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-25 Characteristic LineCharacteristic Line EXCESS RETURN ON STOCK EXCESS RETURN ON MARKET PORTFOLIO Narrower spread is higher correlation Characteristic Line 5-26 Calculating “Beta” Time Pd. Market My Stock 1 9.6% 12% 2 -15.4% -5% 3 26.7% 19% 4 -.2% 3% 5 20.9% 13% 6 28.3% 14% 7 -5.9% -9% 8 3.3% -1% 9 12.2% 12% 10 10.5% 10% The Market and My Stock returns are “excess returns” and have the riskless rate already subtracted.
- 14. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 14 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-27 Calculating “Beta” Enter the excess market returns as “X” observations of: 9.6%, -15.4%, 26.7%, -0.2%, 20.9%, 28.3%, -5.9%, 3.3%, 12.2%, and 10.5%. Enter the excess stock returns as “Y” observations of: 12%, -5%, 19%, 3%, 13%, 14%, -9%, -1%, 12%, and 10%. 5-28 Calculating “Beta” The regression equation is Y=a+bX. Thus, our characteristic line is Y = 1.4448 + 0.595 X and indicates that our stock has a beta of 0.595.
- 15. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 15 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-29 An index of systematic risk. It measures the sensitivity of a stock’s returns to changes in returns on the market portfolio. The beta for a portfolio is simply a weighted average of the individual stock betas in the portfolio. An index of systematic risk. It measures the sensitivity of a stock’s returns to changes in returns on the market portfolio. The beta for a portfolio is simply a weighted average of the individual stock betas in the portfolio. What is Beta?What is Beta? 5-30 Characteristic Lines and Different Betas Characteristic Lines and Different Betas EXCESS RETURN ON STOCK EXCESS RETURN ON MARKET PORTFOLIO Beta < 1 (defensive) Beta = 1 Beta > 1 (aggressive) Each characteristic line has a different slope.
- 16. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 16 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-31 Rj is the required rate of return for stock j, Rf is the risk-free rate of return, ββββj is the beta of stock j (measures systematic risk of stock j), RM is the expected return for the market portfolio. Rj is the required rate of return for stock j, Rf is the risk-free rate of return, ββββj is the beta of stock j (measures systematic risk of stock j), RM is the expected return for the market portfolio. Security Market LineSecurity Market Line Rj = Rf + ββββj(RM - Rf) 5-32 Security Market LineSecurity Market Line Rj = Rf + ββββj(RM - Rf) ββββM = 1.0 Systematic Risk (Beta) Rf RM RequiredReturn Risk Premium Risk-free Return
- 17. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 17 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-33 Security Market Line (Obtaining information for the model) Security Market Line (Obtaining information for the model) Obtaining Betas Can use historical data if past best represents the expectations of the future Can also utilize services like Value Line, Ibbotson Associates, etc. Obtaining Betas Can use historical data if past best represents the expectations of the future Can also utilize services like Value Line, Ibbotson Associates, etc. 5-34 Adjusted Market return and Risk free rate One may use past for obtaining market return and risk free rate but only if past is a good proxy. Direct estimate of the risk free rate by looking up the current rate of return on an appropriate security. Using forecasts for market return estimated by thesecurity analysts, economists and others who regularly predict such returns. Security Market Line (Obtaining information for the model) Security Market Line (Obtaining information for the model)
- 18. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 18 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-35 Lisa Miller at Basket Wonders is attempting to determine the rate of return required by their stock investors. Lisa is using a 6% Rf and a long-term market expected rate of return of 10%. A stock analyst following the firm has calculated that the firm beta is 1.2. What is the required rate of return on the stock of Basket Wonders? Lisa Miller at Basket Wonders is attempting to determine the rate of return required by their stock investors. Lisa is using a 6% Rf and a long-term market expected rate of return of 10%. A stock analyst following the firm has calculated that the firm beta is 1.2. What is the required rate of return on the stock of Basket Wonders? Determination of the Required Rate of Return Determination of the Required Rate of Return 5-36 RBW = Rf + ββββj(RM - Rf) RBW = 6% + 1.2(10% - 6%) RBW = 10.8% The required rate of return exceeds the market rate of return as BW’s beta exceeds the market beta (1.0). RBW = Rf + ββββj(RM - Rf) RBW = 6% + 1.2(10% - 6%) RBW = 10.8% The required rate of return exceeds the market rate of return as BW’s beta exceeds the market beta (1.0). BWs Required Rate of Return BWs Required Rate of Return
- 19. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 19 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-37 Lisa Miller at BW is also attempting to determine the intrinsic value of the stock. She is using the constant growth model. Lisa estimates that the dividend next period will be $0.50 and that BW will grow at a constant rate of 5.8%. The stock is currently selling for $15. What is the intrinsic value of the stock? Is the stock over or underpriced? Lisa Miller at BW is also attempting to determine the intrinsic value of the stock. She is using the constant growth model. Lisa estimates that the dividend next period will be $0.50 and that BW will grow at a constant rate of 5.8%. The stock is currently selling for $15. What is the intrinsic value of the stock? Is the stock over or underpriced? Determination of the Intrinsic Value of BW Determination of the Intrinsic Value of BW 5-38 The stock is OVERVALUED as the market price ($15) exceeds the intrinsic value ($10). The stock is OVERVALUED as the market price ($15) exceeds the intrinsic value ($10). Determination of the Intrinsic Value of BW Determination of the Intrinsic Value of BW $0.50 10.8% - 5.8% Intrinsic Value = = $10
- 20. Van Horne & Wachowicz, © Pearson Education Limited 2004 V - 20 Fundamentals of Financial Management, 12/e Chapter 5: Risk and Return by Gregory A. Kuhlemeyer, Ph.D., Carroll College, Waukesha, WI 5-39 Security Market LineSecurity Market Line Systematic Risk (Beta) Rf RequiredReturn Direction of Movement Direction of Movement Stock Y (Overpriced) Stock X (Underpriced)