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 Riskfree 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 “riskfree” 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 Riskfree 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 Companyunique 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 Companyunique Risk Companyunique 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, companyunique risk is reduced. companyunique
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 = Riskfree 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) Riskfree 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% . Riskfree 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% . Riskfree 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% . Riskfree rate of return (6%) 0 1 Beta Required Required rate of rate return return Hightech stocks SML 12% . Riskfree 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 riskfree 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% Riskfree 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% Riskfree 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 ...
View
Full
Document
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.
 Spring '08
 CORACI

Click to edit the document details