chapter 6 (risk and return)

chapter 6 (risk and return) - Chapter 6 Objectives Chapter...

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Unformatted text preview: Chapter 6: Objectives Chapter How to measure risk How measure (variance, standard deviation, beta) (variance, How to reduce risk How reduce (diversification) (diversification) How to price risk How price risk (security market line, Capital Asset Pricing Model) Pricing Returns Returns Expected Return - the return that an investor expects to earn on an asset, given its price, growth potential, etc. given Required Return - the return that an investor requires on an asset given its risk and market interest rates. its risk and For a Treasury security, what is the required rate of return? the Required rate of rate return return Risk-free rate of rate return return = Since Treasuries are essentially free of Since default risk, the rate of return on a default the Treasury security is considered the “risk-free” rate of return. For a corporate stock or bond, corporate what is the required rate of return? what Required Required rate of rate return return Risk-free rate of rate return return Risk premium = + How large of a risk premium should we How risk require to buy a corporate security? Expected Return State of Probability Return State Economy (P) Orl. Utility Orl. Tech Orl. Economy Recession .20 4% -10% Normal .50 10% 14% Boom .30 14% 30% For each firm, the expected return on the For stock is just a weighted average: weighted k = P(k1)*k1 + P(k2)*k2 + ...+ P(kn)*kn P(k Expected Return Expected State of Probability Return Economy (P) Orl. Utility Orl. Tech Orl. Economy 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% .2 Expected Return Expected State of Probability Return Economy (P) Orl. Utility Orl. Tech Orl. Economy 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% .2 What is Risk? What The possibility that an actual return The actual will differ from our expected return. expected Uncertainty in the distribution of Uncertainty possible outcomes. possible What is Risk? What Uncertainty in the distribution of Uncertainty possible outcomes. possible 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 0.2 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 -10 -5 0 5 10 15 20 25 30 Company B return return How do We Measure Risk? How A more scientific approach is to more examine the stock’s standard deviation of returns. deviation Standard deviation is a measure of Standard the dispersion of possible outcomes. dispersion The greater the standard deviation, The the greater the uncertainty, and, therefore, the greater the risk. therefore, Standard Deviation Standard σ = Σ n (ki - k) P(ki) 2 i=1 σ= Σ (ki - k) i=1 n 2 P(ki) Orlando Utility, Inc. ( 4% - 10%)2 (.2) = 7.2 4% (10% - 10%)2 (.5) = 0 (14% - 10%)2 (.3) = 4.8 4.8 Variance = 12 Stand. dev. = 12 = 3.46% Stand. 3.46% σ= Σ (ki - k) i=1 n 2 P(ki) Orlando Technology, Inc. (-10% - 14%)2 (.2) = 115.2 (-10% (14% - 14%)2 (.5) = 0 (30% - 14%)2 (.3) = 76.8 Variance = 192 Stand. dev. = 192 = 13.86% Stand. 13.86% Summary Orlando Orlando Utility Utility Expected Return Standard Deviation 10% 10% 3.46% 3.46% Orlando Technology 14% 13.86% Which stock would you prefer? Which It depends on your tolerance for risk! It Return Risk Remember, there’s a tradeoff between risk and return. risk Portfolios Portfolios Combining several securities Combining in a portfolio can actually portfolio reduce overall risk. reduce 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). kA rate of return kB time What has happened to the variability of returns for the portfolio? kA rate of return kp kB time Diversification Diversification Investing in more than one security Investing more to reduce risk. reduce If two stocks are perfectly positively If positively correlated, diversification has no correlated diversification effect on risk. effect If two stocks are perfectly negatively If negatively correlated, the portfolio is perfectly correlated the perfectly diversified. diversified. If you owned a share of every stock If traded on the NYSE and NASDAQ, would you be diversified? would YES! YES! Would you have eliminated all of Would your risk? your NO! Common stock portfolios still NO! have risk. Some risk can be diversified away and some cannot. away Market risk (systematic risk) is nondiversifiable. This type of risk cannot be diversified away. cannot Company-unique risk (unsystematic risk) is diversifiable. This type of risk risk) diversifiable This can be reduced through diversification. diversification. Market Risk Market Unexpected changes in interest Unexpected rates. rates. Unexpected changes in cash flows Unexpected due to tax rate changes, foreign competition, and the overall business cycle. business Company-unique Risk Company-unique A company’s labor force goes on company’s strike. strike. A company’s top management dies company’s in a plane crash. in A huge oil tank bursts and floods a huge company’s production area. company’s As you add stocks to your portfolio, company-unique risk is reduced. company-unique portfolio risk companyunique risk Market risk number of stocks Do some firms have more Do market risk than others? market Yes. For example: Yes Interest rate changes affect all firms, but Interest which would be more affected: more a) Retail food chain b) Commercial bank b) Commercial Note As we know, the market compensates As investors for accepting risk - but only for market risk. Companymarket unique risk can and should be unique diversified away. diversified So - we need to be able to measure So measure market risk. market This is why we have Beta. Beta. Beta: a measure of market risk. Specifically, beta is a measure of how Specifically, an individual stock’s returns vary with market returns. with It’s a measure of the “sensitivity” of It’s “sensitivity” an individual stock’s returns to changes in the market. changes The market’s beta is 1 The A firm that has a beta = 1 has average firm beta market risk. The stock is no more or less market The volatile than the market. volatile A firm with a beta > 1 is more volatile than firm beta more the market. (ex: technology firms) A firm with a beta < 1 is less volatile than firm beta less the market. the (ex: utilities) (ex: Calculating Beta Calculating XYZ Co. returns 15 .. . Beta = slope = 1.20 S&P 500 returns -15 .. . . 10 . . . . .. . . . . 5. . .. . . .. . 5 . -10 -5 -5 10 .. . . . . . . -10 .. . . . . . -15 . 15 Summary: Summary: We know how to measure risk, using measure standard deviation for overall risk standard and beta for market risk. beta We know how to reduce overall risk We reduce to only market risk through diversification. diversification We need to know how to price risk so We price we will know how much extra return we should require for accepting extra risk. risk. What is the Required Rate of Return? Return? The return on an investment The required by an investor given required market interest rates and the investment’s risk. risk Required rate of return = Risk-free rate of return + Risk premium market risk companyunique risk can be diversified away Required Required rate of rate return return 12% . security market line (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). Capital Required Required rate of rate return return Is there a riskless (zero beta) security? SML 12% . Risk-free rate of return (6%) Treasury securities are as close to riskless as possible. 0 1 Beta Required Required rate of rate return return Where does the S&P 500 fall on the SML? SML 12% . Risk-free rate of return (6%) The S&P 500 is a good approximation for the market Beta 0 1 Required Required rate of rate return return SML Utility Stocks 12% . Risk-free rate of return (6%) 0 1 Beta Required Required rate of rate return return High-tech stocks SML 12% . Risk-free rate of return (6%) 0 1 Beta The CAPM equation: kj = krf + β j (km - krrff ) where: where: kj = the required return on security j, j, krf = the risk-free rate of interest, β j = the beta of security j, and km = the return on the market index. Example: Example: Suppose the Treasury bond rate is Suppose 6%, the average return on the 6% S&P 500 index is 12%, and Walt 12% Disney has a beta of 1.2. 1.2 According to the CAPM, what According CAPM what should be the required rate of return on Disney stock? return kj = krf + β (km - krrff ) kj = .06 + 1.2 (.12 - .06) kj = .132 = 13.2% 13.2% According to the CAPM, Disney According stock should be priced to give a 13.2% return. 13.2% Required Required rate of rate return return Theoretically, every security should lie on the SML SML 12% Risk-free rate of return (6%) If every stock is on the SML, investors are being fully compensated for risk. . 0 1 Beta Required Required rate of rate return return If a security is above the SML, it is underpriced. SML 12% Risk-free rate of return (6%) If a security is below the SML, it is overpriced. . 0 1 Beta Simple Return Calculations $50 t $60 t+1 Pt+1 - Pt Pt Pt+1 Pt = 60 - 50 50 60 50 = 20% -1 = -1 = 20% -1 ...
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This note was uploaded on 11/13/2009 for the course FIN 3000 taught by Professor Coraci during the Spring '08 term at CUNY Baruch.

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