There is no universally agreed-upon definition of risk.
The measures of risk that we discuss are variance and standard deviation.
Variance - A measure of volatility. Average value of squared deviations from mean.
Standard Deviation - The standard deviation is the standard statistical measure of the spread of a sample (the square root of the variance). It is the measure of total risk that we use most of the time.
13.
Capital Asset Pricing Model R = r f + B ( r m - r f ) CAPM Security Market Line (SML) RP = Risk Premium
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Security Market Line Expected Return BETA r f Risk Free Return = Market Return = r m 1.0 Security Market Line (SML)
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The Formula for Beta Covariance with the market Variance of the market
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Beta Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market. Beta - Sensitivity of a stock’s return to the return on the market portfolio.
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Beta and CL 1. Market risk is measured by beta, the sensitivity to market changes. 2. The slope of the characteristic line is beta beta Expected return Expected market return 10% 10% - +
10%
+10% stock Copyright 1996 by The McGraw-Hill Companies, Inc -10%
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Estimating with regression Security Returns Return on market % R i = i + i R m + e i Slope = i Characteristic Line
The SML shows the relationship between return and risk.
CAPM uses Beta as the measure for risk.
Beta is the slope of the Characteristic Line (CL).
Other methods - Regression Analysis - can be employed to determine the slope of the CL and thus Beta.
20.
Measuring Betas Hewlett Packard Beta Slope determined from 60 months of prices and plotting the line of best fit. Price data - Jan 78 - Dec 82 Market return (%) Hewlett-Packard return (%) R 2 = .53 B = 1.35
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Measuring Betas Hewlett Packard Beta Slope determined from 60 months of prices and plotting the line of best fit. Price data - Jan 93 - Dec 97 Market return (%) Hewlett-Packard return (%) R 2 = .35 B = 1.69
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Measuring Betas A T & T Beta Slope determined from 60 months of prices and plotting the line of best fit. Price data - Jan 78 - Dec 82 Market return (%) A T & T (%) R 2 = .28 B = 0.21
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Measuring Betas A T & T Beta Slope determined from 60 months of prices and plotting the line of best fit. Price data - Jan 93 - Dec 97 Market return (%) R 2 = ..17 B = .90 A T & T (%)
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Using the SML to Estimate the Risk-Adjusted Discount Rate for Projects
An all-equity firm should accept a project whose IRR exceeds the cost of equity capital and reject projects whose IRRs fall short of the cost of capital.
Project IRR Firm’s risk (beta) 5% Good project Bad project 30% 2.5 A B C
It is frequently argued that one can better estimate a firm’s beta by involving the whole industry.
If you believe that the operations of the firm are similar to the operations of the rest of the industry, you should use the industry beta.
If you believe that the operations of the firm are fundamentally different from the operations of the rest of the industry, you should use the firm’s beta.
Don’t forget about adjustments for financial leverage ( more details coming later in the course ).
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Example: Pinnacle West Corp R asset = r f + β ( r m - r f ) = .045 + .24(.08) = .064 or 6.4% (7.5% for Pinnacle’s beta = .38) Assumes riskfree rate of 4.5% and market risk premium of 8%
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Other Methods of Estimating Cost of Equity Capital
The EP Method
r = EPS / Stock Price
The Constant Growth (Gordon) Model
r = DIV 1 / P 0 + g
compute g from earnings, dividend, or cash flow growth or use the sustainable growth estimate
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