VIEWS: 96 PAGES: 86 CATEGORY: Accounting POSTED ON: 4/25/2011
Required Rate of Return RISK How to measure risk (variance, standard deviation, beta) How to reduce risk (diversification) How to price risk (security market line, CAPM) For a Treasury security, what is the required rate of return? Required rate of = return For a Treasury security, what is the required rate of return? Required Risk-free rate of = rate of return return Since Treasury’s are essentially free of default risk, the rate of return on a Treasury security is considered the “risk-free” rate of return. For a corporate stock or bond, what is the required rate of return? Required rate of = return For a corporate stock or bond, what is the required rate of return? Required Risk-free rate of = rate of return return For a corporate stock or bond, what is the required rate of return? Required Risk-free rate of = rate of Risk + Premium return return How large of a risk premium should we require to buy a corporate security? Returns Expected Return - the return that an investor expects to earn on an asset, given its price, growth potential, etc. Required Return - the return that an investor requires on an asset given its risk. Expected Return State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession .20 4% -10% Normal .50 10% 14% Boom .30 14% 30% For each firm, the expected return on the stock is just a weighted average: Expected Return State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession .20 4% -10% Normal .50 10% 14% Boom .30 14% 30% For each firm, the expected return on the stock is just a weighted average: k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn Expected Return State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession .20 4% -10% Normal .50 10% 14% Boom .30 14% 30% k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn k (OU) = .2 (4%) + .5 (10%) + .3 (14%) = 10% Expected Return State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession .20 4% -10% Normal .50 10% 14% Boom .30 14% 30% k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn k (OI) = .2 (-10%)+ .5 (14%) + .3 (30%) = 14% Based only on your expected return calculations, which stock would you prefer? Have you considered RISK? What is Risk? The possibility that an actual return will differ from our expected return. Uncertainty in the distribution of possible outcomes. What is Risk? Uncertainty in the distribution of possible outcomes. Company A 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 4 8 12 return What is Risk? Uncertainty in the distribution of possible outcomes. Company A Company B 0.5 0.2 0.45 0.18 0.4 0.16 0.35 0.14 0.3 0.12 0.25 0.1 0.2 0.08 0.15 0.06 0.1 0.04 0.05 0.02 0 4 8 12 0 -10 -5 0 5 10 15 20 25 30 return return How do we Measure Risk? Toget a general idea of a stock’s price variability, we could look at the stock’s price range over the past year. How do we Measure Risk? A more scientific approach is to examine the stock’s STANDARD DEVIATION of returns. Standard deviation is a measure of the dispersion of possible outcomes. The greater the standard deviation, the greater the uncertainty, and therefore , the greater the RISK. Standard Deviation s = S (ki - k) n 2 P(ki) i=1 s S n 2 = (ki - k) P(ki) i=1 Orlando Utility, Inc. s n S n 2 = (ki - k) P(ki) i=1 i=1 Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 s S n 2 = (ki - k) P(ki) i=1 Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 (10% - 10%)2 (.5) = 0 s S n 2 = (ki - k) P(ki) i=1 Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 (10% - 10%)2 (.5) = 0 (14% - 10%)2 (.3) = 4.8 s S n 2 = (ki - k) P(ki) i=1 Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 (10% - 10%)2 (.5) = 0 (14% - 10%)2 (.3) = 4.8 Variance = 12 s S n 2 = (ki - k) P(ki) i=1 Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 (10% - 10%)2 (.5) = 0 (14% - 10%)2 (.3) = 4.8 Variance = 12 Stand. dev. = 12 = 3.46% s S n 2 = (ki - k) P(ki) i=1 Orlando Technology, Inc. s S n 2 = (ki - k) P(ki) i=1 Orlando Technology, Inc. (-10% - 14%)2 (.2) = 115.2 s S n 2 = (ki - k) P(ki) i=1 Orlando Technology, Inc. (-10% - 14%)2 (.2) = 115.2 (14% - 14%)2 (.5) = 0 s S n 2 = (ki - k) P(ki) i=1 Orlando Technology, Inc. (-10% - 14%)2 (.2) = 115.2 (14% - 14%)2 (.5) = 0 (30% - 14%)2 (.3) = 76.8 s S n 2 = (ki - k) P(ki) i=1 Orlando Technology, Inc. (-10% - 14%)2 (.2) = 115.2 (14% - 14%)2 (.5) = 0 (30% - 14%)2 (.3) = 76.8 Variance = 192 s S n 2 = (ki - k) P(ki) i=1 Orlando Technology, Inc. (-10% - 14%)2 (.2) = 115.2 (14% - 14%)2 (.5) = 0 (30% - 14%)2 (.3) = 76.8 Variance = 192 Stand. dev. = 192 = 13.86% Which stock would you prefer? How would you decide? Which stock would you prefer? How would you decide? Summary Orlando Orlando Utility Technology Expected Return 10% 14% Standard Deviation 3.46% 13.86% It depends on your tolerance for risk! It depends on your tolerance for risk! Return Risk Remember there’s a tradeoff between risk and return. Portfolios Combining several securities in a portfolio can actually reduce overall risk. How does this work? Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated). rate of return time Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated). rate kA of return time Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated). rate kA of return kB time Suppose we have stock A and stock B. The returns on these stocks do not tend to move together over time (they are not perfectly correlated). rate kA of return kp kB time What has happened to the variability of returns for the portfolio? rate kA of return kp kB time Diversification Investing in more than one security to reduce risk. If two stocks are perfectly positively correlated, diversification has no effect on risk. If two stocks are perfectly negatively correlated, the portfolio is perfectly diversified. Ifyou owned a share of every stock traded on the NYSE and NASDAQ, would you be diversified? YES! Would you have eliminated all of your risk? NO! Common stock portfolios still have risk. (Remember the October 1987 stock market “crash?”) Some risk can be diversified away and some can not. Market Risk is also called Non diversifiable risk. This type of risk can not be diversified away. Firm-Specific risk is also called diversifiable risk. This type of risk can be reduced through diversification. Market Risk Unexpected changes in interest rates. Unexpected changes in cash flows due to tax rate changes, foreign competition, and the overall business cycle. Firm-Specific Risk A company’s labor force goes on strike. A company’s top management dies in a plane crash. A huge oil tank bursts and floods a company’s production area. As you add stocks to your portfolio, firm-specific risk is reduced. As you add stocks to your portfolio, firm-specific risk is reduced. portfolio risk number of stocks As you add stocks to your portfolio, firm-specific risk is reduced. portfolio risk Market risk number of stocks As you add stocks to your portfolio, firm-specific risk is reduced. portfolio risk Firm- specific risk Market risk number of stocks Do some firms have more market risk than others? Yes. For example: Interest rate changes affect all firms, but which would be more affected: a) Retail food chain b) Commercial bank Do some firms have more market risk than others? Yes. For example: Interest rate changes affect all firms, but which would be more affected: a) Retail food chain b) Commercial bank Note As we know, the market compensates investors for accepting risk - but only for market risk. Firm-specific risk can and should be diversified away. So - we need to be able to measure market risk. This is why we have BETA. Beta: a measure of market risk. Specifically, it is a measure of how an individual stock’s returns vary with market returns. It’s a measure of the “sensitivity” of an individual stock’s returns to changes in the market. The market’s beta is 1 A firm that has a beta = 1 has average market risk. The stock is no more or less volatile than the market. A firm with a beta > 1 is more volatile than the market (ex: computer firms). A firm with a beta < 1 is less volatile than the market (ex: utilities). Calculating Beta XYZ Co. returns 15 10 5 S&P 500 returns -15 -10 -5 -5 5 10 15 -10 -15 Calculating Beta XYZ Co. returns 15 .. . .. . . 10 . . . . .. . . .. . . 5 S&P 500 .. . . returns -15 -10 .. . 5 -5 -5 . 10 15 .. . . . . . . -10 .. . . . . . . -15 Calculating Beta Beta = slope XYZ Co. returns = 1.20 15 .. . .. . . 10 . . . . .. . . .. . . 5 S&P 500 .. . . returns -15 -10 .. . 5 -5 -5 . 10 15 .. . . . . . . -10 .. . . . . . . -15 Summary: We know how to measure risk, using standard deviation for overall risk and beta for market risk. We know how to reduce overall risk to only market risk through diversification. We need to know how to price risk so we will know how much extra return we should require for accepting extra risk. What is the Required Rate of Return? Thereturn on an investment required by an investor given the investment’s risk. Required rate of = return Required Risk-free rate of = rate of + return return Required Risk-free rate of = rate of Risk + Premium return return Required Risk-free rate of = rate of Risk + Premium return return Market Risk Required Risk-free rate of = rate of Risk + Premium return return Market Firm-specific Risk Risk Required Risk-free rate of = rate of Risk + Premium return return Market Firm-specific Risk Risk can be diversified away Required rate of Let’s try to graph this return relationship! Beta Required rate of return 12% . Risk-free rate of return (6%) 1 Beta Required rate of security return market line 12% . (SML) Risk-free rate of return (6%) 1 Beta This linear relationship between risk and required return is known as the Capital Asset Pricing Model (CAPM). Required SML rate of Is there a riskless return (zero beta) security? 12% . Risk-free rate of return (6%) 0 1 Beta Required SML rate of Is there a riskless return (zero beta) security? 12% . Treasury securities are as close to riskless Risk-free rate of as possible. return (6%) 0 1 Beta Required SML rate of Where does the S&P 500 return fall on the SML? 12% . Risk-free rate of return (6%) 0 1 Beta Required SML rate of Where does the S&P 500 return fall on the SML? 12% . The S&P 500 is a good Risk-free approximation rate of for the market return (6%) 0 1 Beta Required SML rate of return Utility Stocks 12% . Risk-free rate of return (6%) 0 1 Beta Required High-tech SML rate of stocks return 12% . Risk-free rate of return (6%) 0 1 Beta The CAPM equation: kj = krf + b j (km - krf) where: kj = the Required Return on security j, krf = the risk-free rate of interest, b j = the beta of security j, and km = the return on the market index. Example: Suppose the Treasury bond rate is 6%, the average return on the S&P 500 index is 12%, and Walt Disney has a beta of 1.2. According to the CAPM, what should be the required rate of return on Disney stock? kj = krf + b (km - krf) kj = .06 + 1.2 (.12 - .06) kj = .132 = 13.2% According to the CAPM, Disney stock should be priced to give a 13.2% return. Required SML rate of Theoretically, every return security should lie on the SML 12% . Risk-free rate of return (6%) 0 1 Beta Required SML rate of Theoretically, every return security should lie on the SML 12% . If every stock is on the SML, investors are being fully Risk-free compensated for risk. rate of return (6%) 0 1 Beta Required SML rate of If a security is above return the SML, it is underpriced. 12% . Risk-free rate of return (6%) 0 1 Beta Required SML rate of If a security is above return the SML, it is underpriced. 12% . If a security is below the SML, it Risk-free is overpriced. rate of return (6%) 0 Beta 1 Practice Problem: Find the intrinsic value of a common stock with the following information: ROE = 20% 50% retention of earnings Beta = 1.4 recent dividend = $4.30 Treasury bond yield = 7.5% Return on the S&P 500 = 12% Market price for common stock = $100 Should you buy the stock?