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Chapter 8 1

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Based on annual returns from 1926-2004 Avg. ReturnStd Dev. Small Stocks17.5%33.1% Large Co. Stocks12.4%20.3% L-T Corp Bonds6.2%8.6% L-T Govt. Bonds5.8%9.3% U.S. T-Bills3.8%3.1% 2

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Risk: The Big Picture Expected Return Stand Alone Risk Portfolio Return and Risk Risk Diversification Market Risk Beta CAPM/Security Market Line Equation (SML) 3

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Risk is an uncertain outcome or chance of an adverse outcome. Concerned with the riskiness of cash flows from financial assets. Stand Alone Risk: Single Asset relevant risk measure is the total risk of expected cash flows measured by standard deviation. 4

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Portfolio Context: A group of assets. Total risk consists of: Diversifiable Risk (company-specific, unsystematic) Market Risk (non-diversifiable, systematic) Small group of assets with Diversifiable Risk remaining: interested in portfolio standard deviation. correlation ( or r) between asset returns which affects portfolio standard deviation 5

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Well-diversified Portfolio Large Portfolio (10-15 assets) eliminates diversifiable risk for the most part. Interested in Market Risk which is the risk that cannot be diversified away. The relevant risk measure is Beta which measures the riskiness of an individual asset in relation to the market portfolio. 6

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HPR = (End of Period Price - Beginning Price + Dividends)/Beginning Price HPR = Capital Gains Yield + Dividend Yield HPR = (P1-P0)/P0 + D/P0 Example: Bought at $50, Receive $3 in dividends, current price is $54 HPR = (54-50+3)/50 =.14 or 14% CGY = 4/50 = 8%, DY = 3/50 = 6% 7

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Expected Rate of Return given a probability distribution of possible returns(r i ): E(r) n E(r) = P i r i i=1 Realized or Average Return on Historical Data: - n r = 1/n r i i=1 8

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Relevant Risk Measure for single asset Variance = 2 = ( r i - E(r)) 2 P i Standard Deviation = Square Root of Variance Historical Variance = 2 = 1/n (r i – r AVG ) 2 Sample Variance = s 2 = 1/(n-1) (r i – r AVG ) 2 9

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Most investors are Risk Averse, meaning they don’t like risk and demand a higher return for bearing more risk. The Coefficient of Variation (CV) scales risk per unit of expected return. CV = /E(r) CV is a measure of relative risk, where standard deviation measures absolute risk. 12

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MAD Inc. E(r) = 33.5% = 34.0% CV = 34%/33.5% CV = 1.015 Contrary Co. E(r) = 7.5% = 8.5% CV = 8.5%/7.5% CV = 1.133 13

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E(r p ) = w i E(r i ) = weighted average of the expected return of each asset in the portfolio In our example, MAD E(r) = 33.5% and CON E(r) = 7.5% What is the expected return of a portfolio consisting of 60% MAD and 40% CON? E(r p ) = w i E(r i ) =.6(33.5%) +.4(7.5%) = 23.1% 14

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Looking at a 2-asset portfolio for simplicity, the riskiness of a portfolio is determined by the relationship between the returns of each asset over different states of nature or over time. This relationship is measured by the correlation coefficient( r ): -1<= r < =+1 All else constant: Lower r = less portfolio risk 15

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Each MAD-CON r i =.6(MAD)+.4(CON); E(R p ) = 23.1% 16

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As more and more assets are added to a portfolio, risk measured by decreases. However, we could put every conceivable asset in the world into our portfolio and still have risk remaining. (See Fig. 8-8, pg. 265) This remaining risk is called Market Risk and is measured by Beta. 18

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Beta(b) measures how the return of an individual asset (or even a portfolio) varies with the market. b = 1.0 : same risk as the market b < 1.0 : less risky than the market b > 1.0 : more risky than the market Beta is the slope of the regression line (y = a + bx) between a stock’s return(y) and the market return(x) over time, b from simple linear regression. Sources for stock betas: ValueLine Investment Survey (at BEL), Yahoo Finance, MSN Money, Standard & Poors 19

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The story is the same as Chapter 6: a stock’s required rate of return = nominal risk-free rate + the stock’s risk premium. The main assumption is investors hold well diversified portfolios = only concerned with market risk. A stock’s risk premium = measure of market risk X market risk premium. 20

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RP M = market risk premium = r M - r RF RP i = stock risk premium = (RP M )b i r i = r RF + (r M - r RF )b i = r RF + (RP M )b i 21

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What is Intel’s required return if its B = 1.2 (from ValueLine Investment Survey), the current 3-mo. T-bill rate is 5%, and the historical US market risk premium of 8.6% is expected? 22

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The beta of a portfolio of stocks is equal to the weighted average of their individual betas: b p = w i b i Example: What is the portfolio beta for a portfolio consisting of 25% Home Depot with b = 1.0, 40% Hewlett-Packard with b = 1.35, and 35% Disney with b = 1.25. What is this portfolio’s required (expected) return if the risk-free rate is 5% and the market expected return is 14%? 23

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AT&T currently sells for $36.50. Should we add AT&T with an expected price and dividend in a year of $39.54 & $1.42 and a b = 1.2 to our portfolio? To make our decision find AT&T’s expected return using the holding period return formula and compare to AT&T’s SML return. Recall that r RF = 5% and r M = 14% 24

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A graphical representation of the CAPM/SML equation. Gives required (expected) returns for investments with different betas. Y axis = expected return, X axis = beta Intercept = risk-free rate = 3-month T-bill rate (B = 0) Slope of SML = market risk premium For the following SML graph, let’s use a 3-month T- bill rate of 5% and assume investors require a market return of 14%. Graph r = 5% + B(14%-5%) Market risk premium = 14% - 5% = 9% 26

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What happens if inflation increases? What happens if investors become more risk averse about the stock market? Check out the following graphs with our base SML = 5% + (14%-5%)b 28

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There are two functions in Excel that will find the X coefficient (beta). The functions are LINEST and SLOPE. The format is =LINEST(y range,x range) The above format is the same for SLOPE. Remember the stock’s returns is the y range, and the market’s returns is the x range. 31

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CHAPTER 8 Risk and Rates of Return

CHAPTER 8 Risk and Rates of Return

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