Chapter 12 Financial Return and Risk Concepts © 2011 John Wiley and Sons

2 n Know how to compute arithmetic averages, variances, and standard deviations using return data for a single financial asset. n Understand the sources of risk n Know how to compute expected return and expected variance using scenario analysis. n Know the historical rates of return and risk for different securities. Chapter Outcomes

3 n Understand the concept of market efficiency and explain the three types of efficient markets. n Explain how to calculate the expected return on a portfolio of securities. 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 Understand the importance of ethics in investment-related positions. Chapter Outcomes

4 Historical Return and Risk for a Single Asset n Return: periodic income and price changes n Dollar return = ending price – beginning price + income

5 Historical Return and Risk for a Single Asset n Percentage return = Dollar return/beginning price n Beginning price = $33.63 Ending price = $34.31 Dividend = $0.13 Dollar return = $ =$0.81 Percentage return = $0.81/$33.63 = or 2.4 percent

6 Historical Return and Risk for a Single Asset n Can be daily, monthly or annual returns n Risk: based on deviations over time around the average return

7 Returns for Two Stocks Over Time

8 Arithmetic Average Return n Look backward to see how well we’ve done: n Average Return (AR) = Sum of returns number of periods

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

10 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

11 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!

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

13 A’s 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%

14 Using Average Return and Standard Deviation n If the future will resemble the past and the periodic returns 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 

15 For Asset A 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%

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

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

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

19 Where Does Risk Come From: Risk Sources in Income Statement Revenue Business Risk Purchasing Power Risk Exchange Rate Risk Less: Expenses Equals: Operating Income Less: Interest Expense Financial Risk Interest Rate Risk Equals: Earnings Before Taxes Less: Taxes Tax Risk Equals: Net Income

20 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

21 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

22 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

23 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

24 n Standard deviation:  =  95.25% 2 = 9.76% n Coefficient of Variation = 9.76/8.5 = 1.15

25 Do Investors Really do These Calculations? n Market anticipation of Fed’s actions n Identify consensus; where does our forecast differ? n Simulation and Monte Carlo analysis

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

27 Efficient Markets What’s an efficient market? n Operationally efficient versus informationally efficient n Many investors/traders n News occurs randomly n Prices adjust quickly to news on average reflecting the impact of the news and market expectations

28 More…. n After adjusting for risk differences, investors cannot consistently earn above-average returns n Expected events don’t move prices; only unexpected events (“surprises”) move prices or events which differ from the market’s consensus

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

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

31 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

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

33 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 )

34 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%

35 Possibilities of Portfolio “Magic” The risk of the portfolio may be less than the risk of its component assets

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

37 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

38 Diversification n 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. n Splitting funds among several investments reduces the affect of one asset’s poor performance on the overall portfolio

39 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)

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

41 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

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

43 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%

44 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

45 Beta example:  < 1 n If an asset’s  is 0.5: the asset’s 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%

46  > 1 n If an asset’s  is 1.4: the asset’s 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%

47 Sample Beta Values accessed July 2010 from FirmBeta Caterpillar1.82 Coca-Cola0.59 GE1.68 AMR1.63 Allegheny Energy0.88

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

49 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

50 Sample Calculation Estimate of beta:  n  (R MKT R i ) - (  R MKT )(  R i )  n  R MKT 2 - (  R MKT ) 2

51 The sample calculation Estimate of beta = n  (R MKT R i ) - (  R MKT )(  R i ) n  R MKT 2 - (  R MKT ) 2 6( 34.77) - (3.00)(0.20) 6(38.68) - (3.00)(3.00) = 0.93

52 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

53 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%

54 Portfolio beta n The beta of a portfolio of assets is a weighted average of its component asset’s betas n beta portfolio =  w i. beta i

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