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Chapter 12 Financial Return and Risk Concepts © 2000 John Wiley & Sons, Inc.

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2 n Describe the difference between historical and expected rates of return. n Know how to compute arithmetic averages, variances, and standard deviations using return data for a single financial asset. n Know the historical rates of return and risk for different securities.Explain the three forms of market efficiency.Explain how to calculate the expected return on a portfolio of securities. Chapter Outcomes

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3 n Understand how and why the combining of securities into portfolios reduces the overall or portfolio risk. n Explain the difference between systematic and unsystematic risk. n Explain the meaning of beta coefficients and describe how they are calculated. n Describe the capital asset pricing model (CAPM) and discuss how it is used. Chapter Outcomes

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4 Historical Return and Risk for a Single Asset n Return: periodic income and price changes n Can be daily, monthly…but well focus on annual returns n Risk: based on deviations over time around the average return

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5 Returns for Two Stocks Over Time

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6 Arithmetic Average Return n Look backward to see how well weve done: n Average Return (AR) = Sum of returns number of years

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7 An Example YEARSTOCK ASTOCK B 1 6%20% –2 – Sum Sum/6 = AR= 8%20%

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8 Measuring Risk n Deviation = R t - AR n Sum of Deviations (R t - AR) = 0 n To measure risk, we need something else…try squaring the deviations Variance 2 = (R t - AR) 2 n - 1

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9 Since the returns are squared: (R t - AR) 2 The units are squared, too: n Percent squared (% 2 ) n Dollars squared ($ 2 ) n Hard to interpret!

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10 Standard deviation The standard deviation ( ) helps this problem by taking the square root of the variance:

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11 As RETURNRETURN DIFFERENCE FROMDIFFERENCE YRTHE AVERAGESQUARED 16%– 8% = –2%(–2%) 2 = 4% – 8 = 4(4) 2 = – 8 = 0(0) 2 = 0 4–2 – 8 = –10(–10) 2 = – 8 = 10(10) 2 = – 8 = –2(-2) 2 = 4 Sum224% 2 Sum/(6 – 1) = Variance44.8% 2 Standard deviation = 44.8 = 6.7%

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12 Using Average Return and Standard Deviation n If the periodic return are normally distributed n 68% of the returns will fall between AR - and AR + n 95% of the returns will fall between AR - 2 and AR + 2 n 95% of the returns will fall between AR - 3 and AR + 3

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13 For Asset A n If the returns are normal, over time we should see: n 68% of the returns between 1.3% and 14.7% n 95% of the returns between -5.4% and 21.4% n 99% of the returns between -12.1% and 28.1%

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14 Which of these is riskier? Asset AAsset B Avg. Return8% 20% Std. Deviation 6.7% 20%

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15 Another view of risk: Coefficient of Variation = Standard deviation Average return It measures risk per unit of return

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16 Which is riskier? Asset AAsset B Avg. Return8% 20% Std. Deviation 6.7% 20% Coefficient of Variation

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17 Measures of Expected Return and Risk n Looking forward to estimate future performance n Using historical data: ex-post n Estimated or expected outcome: ex-ante

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18 Steps to forecasting Return, Risk n Develop possible future scenarios: –growth, normal, recession n Estimate returns in each scenario: –growth: 20% –normal: 10% –recession: -5% n Estimate the probability or likelihood of each scenario: growth: 0.30 normal: 0.40 recession: 0.30

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19 Expected Return n E(R) = p i. R i n E(R) =.3(20%) +.4(10%) +.3(-5%) = 8.5% n Interpretation: 8.5% is the long-run average outcome if the current three scenarios could be replicated many, many times

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20 Once E(R) is found, we can estimate risk measures: n 2 = p i [ R i - E(R)] 2 =.3( ) 2 +.4( ) 2 +.3( ) 2 = percent squared

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21 n Standard deviation: = 95.25% 2 = 9.76% n Coefficient of Variation = 9.76/8.5 = 1.15

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22 Historical Returns and Risk of Different Assets Two good investment rules to remember: n Risk drives returns n Developed capital markets, such as those in the U.S., are, to a large extent, efficient markets.

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23 Efficient Markets Whats an efficient market? n Many investors/traders n News occurs randomly n Prices adjust quickly to news, reflecting the impact of the news and market expectations

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24 More…. n After adjusting for risk differences, investors cannot consistently earn above-average returns n Expected events dont move prices; only unexpected events (surprises) move prices

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25 Price Reactions in Efficient/Inefficient Markets Overreaction(top) Efficient (mid) Underreaction (bottom) Good news event

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26 Types of Efficient Markets n Strong-form efficient market n Semi-strong form efficient market n Weak-form efficient market

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27 Implications of Efficient Markets n Market price changes show corporate management the reception of announcements by the firm n Investors: consider indexing rather than stock-picking n Invest at your desired level of risk n Diversify your investment portfolio

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28 Portfolio Returns and Risk Portfolio: a combination of assets or investments

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29 Expected Return on A Portfolio: n E(R i ) = expected return on asset i n w i = weight or proportion of asset i in the portfolio E(R p ) = w i. E(R i )

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30 If E(R A ) = 8% and E(R B ) = 20% n More conservative portfolio: E(R p ) =.75 (8%) +.25 (20%) = 11% n More aggressive portfolio: E(R p ) =.25 (8%) +.75 (20%) = 17%

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31 Possibilities of Portfolio Magic The risk of the portfolio may be less than the risk of its component assets

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32 Merging 2 Assets into 1 Portfolio Two risky assets become a low-risk portfolio

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33 The Role of Correlations n Correlation: a measure of how returns of two assets move together over time n Correlation > 0; the returns tend to move in the same direction n Correlation < 0; the returns tend to move in opposite directions

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34 Diversification If correlation between two assets (or between a portfolio and an asset) is low or negative, the resulting portfolio may have lower variance than either asset. Illustrates diversification benefits.

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35 The Two Types of Risk n Diversification shows there are two types of risk: Risk that can be diversified away (diversifiable or unsystematic risk) Risk that cannot be diversified away (undiversifiable or systematic or market risk)

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36 Capital Asset Pricing Model n Focuses on systematic or market risk n An assets risk depend upon whether it makes the portfolio more or less risky n The systematic risk of an asset determines its expected returns

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37 The Market Portfolio n Contains all assets--it represents the market n The total risk of the market portfolio (its variance) is all systematic risk n Unsystematic risk is diversified away

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38 The Market Portfolio and Asset Risk n We can measure an assets risk relative to the market portfolio n Measure to see if the asset is more or less risky than the market n More risky: assets returns are usually higher (lower) than the markets when the market rises (falls) n Less risky: assets returns fluctuate less than the markets over time

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39 Blue = market returns over time Red = asset returns over time More systematic risk than market Less systematic risk than market Return Time 0% AssetMarket Time 0%

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40 Implications of the CAPM n Expected return of an asset depends upon its systematic risk n Systematic risk (beta ) is measured relative to the risk of the market portfolio

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41 Beta example: < 1 n If an assets is 0.5: the assets returns are half as variable, on average, as those of the market portfolio n If the market changes in value by 10%, on average this assets changes value by 10% x 0.5 = 5%

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42 > 1 n If an assets is 1.4: the assets returns are 40 percent more variable, on average, as those of the market portfolio n If the market changes in value by 10%, on average this assets changes value by 10% x 1.4 = 14%

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43 Sample Beta Values FirmBeta AT&T0.75 Coca-Cola1.10 GE1.20 AMR1.30 Amer. Electric Power0.55

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44 Learning Extension 12A Estimating Beta n Beta is derived from the regression line: R i = a + R MKT + e

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45 Ways to estimate Beta n Once data on asset and market returns are obtained for the same time period: n use spreadsheet software n statistical software n financial/statistical calculator n do calculations by hand

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46 Sample Calculation Estimate of beta: n (R MKT R i ) - ( R MKT R i ) n R MKT 2 - ( RMKT) 2

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47 The sample calculation Estimate of beta = n (R MKT R i ) - ( R MKT R i ) n R MKT 2 - ( RMKT) 2 6( ) - (0.72)(1.20) 6(0.1406) - (0.72)(0.72) = 1.90

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48 Security Market Line n CAPM states the expected return/risk tradeoff for an asset is given by the Security Market Line (SML): n E(R i )= RFR + [E(R MKT )- RFR] i

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49 An Example n E(R i )= RFR + [E(R MKT )- RFR] i n If T-bill rate = 4%, expected market return = 8%, and beta = 0.75: n E(R stock )= 4% + (8% - 4%)(0.75) = 7%

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50 Portfolio beta n The beta of a portfolio of assets is a weighted average of its component assets betas n beta portfolio = w i. beta i

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