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# 271 Note for B A 301 with Professor Gray at PSU

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Date Created: 02/06/15

BA 301 Risk and Return and the Capital Asset Pricing Model Woolridge amp Gray Text Chapter 12 An Important Principle of Finance CAPMThe Trade Off Between Return and Risk Tradeoff between the expected return on an investment and its risk Low risk Treasury Bills have lower expected returns 24 Stocks large price volatility have higher expected returns eg 610 Risk measured by price or return volatility More pricereturn movement greater risk A rational investor requires a higher expected return to accept additional risk Model that describes this tradeoff is the CAPM Risk and Return and the Capital Asset Pricing Model Risk Return Relationship Direct tradeoff between the expected rate of return and risk Tradeoff represented by the diagonal line Expected As the inherent risk increases in Return an investment so does the expected return Risk Risk and Return and the Capital Asset Pricing Model 123 Historic Returns by Asset Class Historically lower risk investments have lower returns and higher risk investments have higher returns Ibbotson and Sinque eld study Return Std Deviation Treasury Bills 38 32 Government Bonds 53 94 Corporate Bonds 58 86 Large Company Stock 107 202 Small Company Stock 125 332 LongTerm Return and Risk of US Securities 19261999 Small Co Common Stocks 126 X 12 10 Common Stocks 113 X g v 8 E 3 6 LT Corp Bonds 56 a X X 0 X LT Gov Bonds 51 4 Treasury Bills 38 2 o 10 20 30 Risk Source Ibbotson Associates 2000 What is Rate of Return Rate of Return Cash Payment Change in PricePrice Paid Buy IBM 90 receive a cash dividend of 4 and sell it one year later at 104 Rate of Return 4 14 90 2 20 Components of Rate of Return Cash PaymentsDividends and Interest taxed as ordinary income ie up to 35 Dividends quarterly payments made on some stocks ownership Interest semiannual payments made on bonds debt Change in Price Capital Gain or Capital Loss Realized you sell your asset and incur gain or loss Unrealized you continue to own your asset If realized the gains or losses are taxed Longterm gains and losses are taxed at a lower rate eg 20 Shortterm gains and losses taxed at a higher rate eg 35 What do we mean by Risk Riskmeasured by the possible range of returns arogid an expected return Measured by a statistic the standard deviation x w a Risk has both negative a positive outcomes returns that are lower I expected or higher than expected Risk and Return and the Capital Asset Pricing Model 122 De nitions Relating to Return and Risk Standard Deviation of Return 039 I Risk on an asset is measured by the variability of returns I Standard deviation is the statistic that is that measures how Wildly or tightly observed stock returns cluster around the average stock return I Greater standard deviation means more uctuations and greater risk Risk and Return and the Capital Asset Pricing Model 122 Definitions Relating to Return and Risk Calculation of Standard Deviation of Return 039 Example The annual returns of stock of XYZ Inc for the last three years was Year 1 8 Year 2 1 Year 3 2 Risk and Return and the Capital Asset Pricing Model 122 De nitions Relating to Return and Risk Calculation of Standard Deviation of Return 62 Step 1 Take the simple average return of the distribution of returns Year Return Average Return 1 8 3 2 1 3 3 2 3 Total 9 Risk and Return and the Capital Asset Pricing Model 122 De nitions Relating to Return and Risk Calculation of Standard Deviation of Return 6 Step 2 Take each individual observed return and subtract the average of the returns Year Return Average Deviation Return of Return 1 8 3 5 2 1 3 4 3 2 3 1 Total 9 Risk and Return and the Capital Asset Pricing Model 122 De nitions Relating to Return and Risk Calculation of Standard Deviation of Return 039 Step 3 Square the resulting difference and add the squares to get the sum of the squares Year Return Average Deviation Squared Return of Return Deviation 1 8 3 5 00025 2 1 3 4 00016 3 2 3 1 00001 Total 9 00042 Risk and Return and the Variance 122 De nitions Relating to Return and Calculation of Standard Deviation of Return 039 Step 4 Divide the sum of the squares by the total number of observations minus 1 the result is the variance of the distribution Variance 0004231 00021 Step 5 The square root of the variance is the standard deviation of the returns Standard Deviation 00021 A 12 458 What Do We Mean by Returns Simple versus Compound Averages of Returns When Analyzing Returns Simple Averages are Never Simple I Many investment managers and advisors use simple averages to portray their historic performance I However simple averages are a misleading way to assess investment returns compound or geometric averages are far more representative of actual investment performance Geometric average is calculated as below Value at the end of the period 1T Value at the beginning of the period Where T is the number of years in the compounding period Simple Averages of Percentages are Never Simple The math underlying investment returns and percentages computes investment gains more favorably than comparable losses Problem is embedded in calculation of simple averages If there is a negative percentage return the calculation of a simple average is biased upwards Simple average returns can hide very poor performance Simple Averages of Percentages are Never Simple Martha s Investment Perferrnanee Simple 3L Cempeunrl uerage Returns Beginning Ending nnual quotIquotear 1Lnl39alue 1Lnl39alue Return 391 10 3 IIIIIII EFn 2 2 Ll 20 Simple uerage Return 1 Cempeund uerane Return 355 Risk and Return Highrisk Stock Expected V R t e um Lowrisk Stock 0vt Bond N Market P0rtf01i0Includes all stocks TBills Corporate Bonds Risk Capital Asset Pricing Model CAPM From the RiskReturn Line we can estimate the expected return on a stock ERi Expected return on stock i ERi equals the Risk Free Rate Rf the stock s Beta 33 times the Market 1 Risk Premium the return I th k t Rm r gt 81 e mar e m1nus p R I c ERi Rf i Rm Rf Sample Averages for Investments Risk Premium Treasury Bills 0 o o 4 Government Bonds 0 o o o o o o 5 100 Corporate Bonds 600 200 Average Common Stock 12 8 Our Questions For Today How do we measure risk of an asset Answer Beta I What s the relatlon 4 between beta and f return 39 Answer It s very positive What is Beta Market IBM Stock Portfolio Return 10 12 10 12 IBM s stock return tends to be the market return multiplied by 12 IBM s beta is 12 What is Beta Market ATampT Stock Portfolio Return 10 8 40 8 ATampTos beta is ATampT s stock return tends to be the market return multiplied by A Quick Quiz on Beta Firm Market up 20 Market down 20 Firm s Beta Intel 30 30 150 GE 15 15 075 Apple 20 20 100 Why is beta a measure of Market Magnification A stock with a beta of 2 will tend to double market movements up or down A stock with a beta of 050 will tend to have movements up or down equal to 12 the market Isn t there more to Risk than Beta Yes Unsystematic or rm speci c risk risk that affects the return of that rm or industry only On average the rm speci c risks average out to be zero if an investor holds a diversi ed portfolio Finance theory assumes that investors are rational and own diversi ed portfolios How to Measure Beta Graph 60 months of returns as done below IBM s Return Slope is Beta SampP500 Return 0 Using Beta to Determine Expected Returns What is a risk premium The amount by which an investment is expected to outperform TBills The Market has averaged 12 a year TBills have averaged 4 a year The market risk premium is 8 An investment s beta determines its risk premium TBill Rate 4 Expected return on Market 8 Market riskpremium 4 AOL has a beta of 16 AOL s riskpremium 16 4 64 AOL s expected return 4 64 104 An investment s beta determines its risk premium TBill Rate 4 Expected return on Market 8 Market riskpremium 4 ATT has a beta of 06 ATT s riskpremium 06 4 24 ATT s expected return 4 24 64 The RiskReturn Line T Bill Rate is 5 Market Risk Premium has averaged 8 Expected Return on the Market ie SampP500 is 8513 Expected Return 5 1 Beta Let s Draw Today s RiskReturn Line Put half your money in T Bills and half in the SampP500 Your portfolio has a beta of 050 Your portfolio has an expected return of 9 Expected Return 1 Beta Let s Draw Today s RiskReturn Line By splitting your money between T Bills and the market portfolio you can obtain any point on the riskreturn line below Expected Return 1 Beta Let s Draw Today s RiskReturn Line By putting all your money in the SampP 500 and borrowing still more and putting that money in the SampP 500 leveraging you can obtain any point on the riskreturn line below Expected Return 1 Beta Let s Draw Today s RiskReturn Line Any point on the riskreturn line can be obtained with the SampP 500 and T Bills Expected Return 1 Beta Evaluating Mutual Fund Performance Using the RiskReturn Line Which fund provided the better performance A or B Average Return 1 Beta Alpha measures performance A positive alpha is g00da negative alpha is not so good 39 39 A h Average Return Posmve p a 4Negative Alpha 1 Beta Alpha measures performance Remember the RiskReturn line is also called the zero talent line so performance below the line is poor Positive Alpha 1 Beta Practice Problem TBills averaged 4 over last few years SampP 500 averaged 14 The XYZ Fund had an average return of 16 and a beta of 14 Find XYZ s alpha The CAPM riskreturn line for a beta of 14 is 4 14 10 18 XYZ s alpha is 1618 2 Alpha measures performance 2 Average Return XYZ Fund 1 Beta Practice Problem TBills averaged 4 over last few years SampP500 averaged 14 The Nittany Lion Fund had an average return of 16 and a beta of 080 Find N ittany Lion s alpha Alpha measures performance Alpha is 4 Good job Average Return 1 Beta

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