Chapter Risk and Rates of Return Stand-Alone Risk Portfolio Risk Risk and Return: CAPM/SML 8-1 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part What is investment risk? • Two types of investment risk • Investment risk is related to the probability of earning a low or negative actual return • – Stand-alone risk – Portfolio risk The greater the chance of lower than expected, or negative returns, the riskier the investment 8-2 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Probability Distributions • A listing of all possible outcomes, and the probability of each occurrence • Can be shown graphically Firm X Firm Y -70 15 100 Rate of Return (%) Expected Rate of Return 8-3 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Selected Realized Returns, 1926-2010 Source: Based on Ibbotson Stocks, Bonds, Bills, and Inflation: 2011 Classic Yearbook (Chicago: Morningstar, Inc., 2011), p 32 8-4 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Hypothetical Investment Alternatives Economy Recession Prob T-Bills HT Coll 0.1 5.5% -27.0% 27.0% USR MP 6.0% -17.0% Below avg 0.2 5.5% -7.0% 13.0% -14.0% -3.0% Average 0.4 5.5% 15.0% 0.0% Above avg 0.2 5.5% 30.0% -11.0% 41.0% 25.0% Boom 0.1 5.5% 45.0% -21.0% 26.0% 38.0% 3.0% 10.0% 8-5 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Why is the T-bill return independent of the economy? Do T-bills promise a completely risk-free return? • T-bills will return the promised 5.5%, regardless of the economy • No, T-bills not provide a completely risk-free return, as they are still exposed to inflation Although, very little unexpected inflation is likely to occur over such a short period of time • • T-bills are also risky in terms of reinvestment risk T-bills are risk-free in the default sense of the word 8-6 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part How the returns of High Tech and Collections behave in relation to the market? • High Tech: Moves with the economy, and has a positive correlation This is typical • Collections: Is countercyclical with the economy, and has a negative correlation This is unusual 8-7 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Calculating the Expected Return rˆ = Expected rate of return N rˆ = ∑ Piri i=1 rˆ = (0.1)(-27%) + (0.2)(-7%) + (0.4)(15%) + (0.2)(30%) + (0.1)(45%) = 12.4% 8-8 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Summary of Expected Returns Expected Return High Tech Market US Rubber T-bills 5.5% Collections 12.4% 10.5% 9.8% 1.0% High Tech has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk? 8-9 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Calculating Standard Deviation σ = Standard deviation σ = Variance = σ2 σ= N ˆ ( r − r ) Pi ∑ i=1 8-10 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Calculating Betas • Well-diversified investors are primarily concerned with how a stock is expected to move relative to the market in the future • Without a crystal ball to predict the future, analysts are forced to rely on historical data A typical approach to estimate beta is to run a regression of the security’s past returns against the past returns of the market • The slope of the regression line is defined as the beta coefficient for the security 8-36 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Illustrating the Calculation of Beta _ ri 20 15 Year 10 rM ri 15% -5 12 18% -10 16 -5 -5 -10 10 15 20 rM Regression line: r^i = -2.59 + 1.44 r^M 8-37 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Beta Coefficients for High Tech, Collections, and T-Bills HT: b = 1.32 ri 40 20 T-bills: b = -20 20 40 rM Coll: b = -0.87 -20 8-38 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Comparing Expected Returns and Beta Coefficients Security High Tech Market US Rubber T-Bills Collections Expected Return 12.4% 10.5 9.8 5.5 1.0 Beta 1.32 1.00 0.88 0.00 -0.87 Riskier securities have higher returns, so the rank order is OK 8-39 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part The Security Market Line (SML): Calculating Required Rates of Return SML: ri = rRF + (rM – rRF)bi ri = rRF + (RPM)bi • Assume the yield curve is flat and that rRF = 5.5% and RPM = rM − rRF = 10.5% − 5.5% = 5.0% 8-40 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part What is the market risk premium? • Additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk • Its size depends on the perceived risk of the stock market and investors’ degree of risk aversion • Varies from year to year, but most estimates suggest that it ranges between 4% and 8% per year 8-41 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Calculating Required Rates of Return 8-42 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Expected vs Required Returns rˆ r High Tech Market US Rubber T-bills Collections 12.4% 12.1% 10.5 10.5 9.8 9.9 5.5 5.5 1.0 1.15 Undervalued (rˆ > r) Fairly valued (rˆ = r) (rˆ < r) Overvalued Fairly valued Overvalued (rˆ = r) (rˆ < r) 8-43 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Illustrating the Security Market Line SML: ri = 5.5% + (5.0%)bi ri (%) SML HT rM = 10.5 -1 rRF = 5.5 Coll T-bills USR Risk, bi 8-44 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part An Example: Equally-Weighted Two-Stock Portfolio • Create a portfolio with 50% invested in High Tech and 50% invested in Collections • The beta of a portfolio is the weighted average of each of the stock’s betas bP = wHTbHT + wCollbColl bP = 0.5(1.32) + 0.5(-0.87) bP = 0.225 8-45 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Calculating Portfolio Required Returns • The required return of a portfolio is the weighted average of each of the stock’s required returns rP = wHTrHT + wCollrColl rP = 0.5(12.10%) + 0.5(1.15%) rP = 6.625% • Or, using the portfolio’s beta, CAPM can be used to solve for expected return rP = rRF + (RPM)bP rP = 5.5% + (5.0%)(0.225) rP = 6.625% 8-46 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Factors That Change the SML • What if investors raise inflation expectations by 3%, what would happen to the SML? ri (%) SML2 SML1 ΔI = 3% 13.5 10.5 8.5 5.5 Risk, bi 0.5 1.0 1.5 8-47 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Factors That Change the SML • What if investors’ risk aversion increased, causing the market risk premium to increase by 3%, what would happen to the SML? ri (%) SML2 ΔRPM = 3% SML1 13.5 10.5 5.5 Risk, bi 0.5 1.0 1.5 8-48 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Verifying the CAPM Empirically • • The CAPM has not been verified completely • Some argue that there are additional risk factors, other than the market risk premium, that must be considered Statistical tests have problems that make verification almost impossible 8-49 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part More Thoughts on the CAPM • Investors seem to be concerned with both market risk and total risk Therefore, the SML may not produce a correct estimate of ri ri = rRF + (rM – rRF)bi + ??? • CAPM/SML concepts are based upon expectations, but betas are calculated using historical data A company’s historical data may not reflect investors’ expectations about future riskiness 8-50 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part [...]... -bills σ T -bills 2 σHT = 20% σColl = 13.2% σM = 15.2% σUSR = 18.8% 1/2 8-11 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Comparing Standard Deviations Prob T-bills USR HT 0 5.5 9.8 12.4 Rate of Return (%) 8-12 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated,... distribution of returns 8-13 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Comparing Risk and Return Security T-bills High Tech Collections* US Rubber* Market Expected Return, rˆ 5.5% 12.4 1.0 9.8 10.5 Risk, σ 0.0% 20.0 13.2 18.8 15.2 *Seems out of place 8-14 © 2013 Cengage Learning All Rights Reserved... 8-15 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Illustrating the CV as a Measure of Relative Risk Prob A B 0 Rate of Return (%) σA = σB , but A is riskier because of a larger probability of losses In other words, the same amount of risk (as measured by σ) for smaller returns 8-16 © 2013 Cengage. .. distribution for the portfolio returns be constructed 8-19 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Calculating Portfolio Expected Return rˆp is a weighted average : N rˆp = ∑ wirˆi i=1 rˆp = 0.5(12.4%) + 0.5(1.0%) = 6.7% 8-20 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied,... 6.7% 8-21 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Calculating Portfolio Standard Deviation and CV  0.10 (0.0 - 6.7)   2  + 0.20 (3.0 - 6.7)  σp = + 0.40 (7.5 - 6.7)2    + 0.20 (9.5 - 6.7)2    2 + 0.10 (12.0 - 6.7)  2 1 2 = 3.4% 3.4% CVp = = 0.51 6.7% 8-22 © 2013 Cengage Learning... stocks 8-23 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part General Comments about Risk • • σ ≈ 35% for an average stock • Combining stocks in a portfolio generally lowers risk Most stocks are positively (though not perfectly) correlated with the market (i.e., ρ between 0 and 1) 8-24 © 2013 Cengage Learning... Negatively Correlated Stocks (ρ = -1.0) 8-25 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Returns Distribution for Two Perfectly Positively Correlated Stocks (ρ = 1.0) Stock M’ Stock M Portfolio MM’ 25 25 25 15 15 15 0 0 0 -10 -10 -10 8-26 © 2013 Cengage Learning All Rights Reserved May not be... (after about 40 stocks), and for large stock portfolios, σp tends to converge to ≈ 20% 8-28 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Illustrating Diversification Effects of a Stock Portfolio 8-29 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to... welldiversified portfolio 8-32 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Beta • Measures a stock’s market risk, and shows a stock’s volatility relative to the market • Indicates how risky a stock is if the stock is held in a well-diversified portfolio 8-33 © 2013 Cengage Learning All Rights Reserved... -10 8-26 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Partial Correlation, ρ = +0.35 8-27 © 2013 Cengage Learning All Rights Reserved May not be scanned, copied, or duplicated, or posted to a publicly accessible website, in whole or in part Creating a Portfolio: Beginning with One Stock and Adding