FNCE2000 Lecture 8 Risk & Return (Revised) PDF

WARNING This material has been reproduced and communicated to you by or on behalf of Curtin University in accordance with section 113P of the Copyright Act 1968 (the Act) The material in this communic...

WARNING This material has been reproduced and communicated to you by or on behalf of Curtin University in accordance with section 113P of the Copyright Act 1968 (the Act) The material in this communication may be subject to copyright under the Act. Any further reproduction or communication of this material by you may be the subject of copyright protection under the Act. Do not remove this notice. Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Chapters 10 and 11 Capital Markets and the Pricing of Risk Optimal Portfolio Choice and the Capital Asset Pricing Model Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Learning Objectives 1. Compute the realized return and variance for an investment. 2. Compute the expected return, variance, and standard deviation (or volatility) of returns. 3. Compute the expected return on the portfolio and variance of the portfolio given a portfolio of stocks. 4. Use the Capital Asset Pricing Model to calculate the expected return for a risky security. Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  10.3 Historical Returns of Stocks and Bonds Computing Historical Returns - Realized Return – The gain or loss from the investment that occurs over a particular time period. – The return has 2 components.  Income component of the return (receive some cash directly).  Capital gain/capital loss (value of the asset). 𝐷𝑖 𝑣 𝑡 +1 +𝑃 𝑡 +1 𝐷𝑖𝑣 𝑡 +1 𝑃 𝑡 +1 − 𝑃𝑡 𝑅𝑡 + 1= − 1= + 𝑃𝑡 𝑃𝑡 𝑃𝑡 Where: Pt = share price at beginning of period Pt+1 = share price at end of period Dt+1 = dividend received at end of period Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Example 1 t t+1 Pt = $10 (bought stock for) Pt+ 1 = $11 (Sold stock for) D t+1= Dividend = $0.50 = 5% + 10% = 15% Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Alternative Example 10.2 What were the realized annual returns for NRG stock in 2012 and in 2014? Price Dividend Date ($) ($) Return 12/31/20 ( 𝑃 𝑡 +1 + 𝐷𝑖𝑣𝑡 +1 ) (61.44+ 0.26) 11 58.69 − 1= − 1=5.13 % 𝑃𝑡 58.69 12/31/20 12 61.44 0.26 5.13% ( 𝑃 𝑡 +1 + 𝐷𝑖𝑣𝑡 +1 ) ( 48.5 +0.26 ) 12/31/20 𝑃𝑡 − 1= 63.94 − 1=− 23.74 % 13 63.94 0.26 4.49% 12/31/20 14 48.5 0.26 -23.74% 12/31/20 15 54.88 0.29 13.75% 12/31/20 16 53.31 -2.86% Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Table 10.2 Realized Return for the S&P 500, Microsoft, and Treasury Bills, 2002–2014 Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Average Annual Return 1 1 T R  R1  R2    RT    Rt T T t 1 – Where Rt is the realized return of a security in year t, for the years 1 through T Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  The Variance and Volatility of Returns The variance measures the average squared difference between the actual/realised returns and the average return. The bigger the variance is, the more the actual returns tend to differ from the average return. The larger the variance (or standard deviation) is, the greater the range of returns. 1 T 2 = Var (R )  T  1  R t 1 t  R Variance Estimate Using Realized Returns SD(R) = σ = Standard Deviation = the square root of the variance Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  The Variance and Volatility of Returns - example Realised return Average return Deviation Squared deviation (Rt) () Year 1 0.12 0.05 0.07 0.0049 Year 2 0.09 0.05 0.04 0.0016 Year 3 -0.07 0.05 -0.12 0.0144 Year 4 0.06 0.05 0.01 0.0001 Total 0.0210 [ … +] = 0.007 SD(R) = σ = SD(R) = σ = SD(R) = σ = The standard deviation is 8.367% Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Table 10.4 Volatility of U.S. Small Stocks, Large Stocks (S&P 500), Corporate Bonds, and Treasury Bills, 1926– 2014 Notice that the standard deviation for the small shares (σ = 38.8%) is more than 12 times larger than the Treasury bill (σ = 3.1%). On average, bearing risk is awarded. The greater the reward (return), the greater the risk (standard deviation,σ) Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  10.4 The Historical Trade-Off Between Risk and Return Excess Returns/Risk Premium  The difference between the average return for an investment and the average return for T-Bills (risk-free investment).  Government can always raise taxes to pay its bills, this debt is virtually free of any default risk over its life. The rate of return on the government bonds a risk-free return and we use it as a benchmark. Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  10.2 Common Measures of Risk and Return - Expected Return Expected Return – Calculated as a weighted average of the possible returns, where the weights correspond to the probabilities. – The return on a risky asset expected in the future. Investor can expect to earn this return from the share, on average. Expected Return  E  R    R PR  R Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Expected Return Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Variance and Standard Deviation Variance – The expected squared deviation from the mean 2 2 σ 2=¿Var (R)  E  R  E  R       R PR  R  E  R   Standard Deviation – The square root of the variance σ=¿ SD( R)  Var ( R) Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Textbook Example 10.1 2 2 Var (R )  E  R  E  R      R PR  R  E  R     Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  11.1 The Expected Return of a Portfolio Expected return for a portfolio is the weighted average return: E  RP   E   i xi Ri    Ex R  i i i   x E R  i i i – Portfolio Weights: The fraction of the total investment in the portfolio held in each individual investment in the portfolio. The portfolio weights must add up to 1.00 or 100%. Value of investment i xi  Total value of portfolio Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Textbook Example 11.2 Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Determining Covariance and Correlation To find the risk of a portfolio, one must know the degree to which the stocks’ returns move together. Covariance – The expected product of the deviations of two returns from their means – Covariance between Returns Ri and Rj Cov(Ri ,R j )  E[(Ri  E[ Ri ]) (R j  E[ R j ])] – Estimate of the Covariance from Historical Data 1 Cov(Ri ,R j )   (Ri ,t  Ri ) (R j ,t  R j )  1 the two returns tend to move together.  If the covarianceTis positive, t  If the covariance is negative, the two returns tend to move in opposite directions. Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Determining Covariance and Correlation (cont'd) Correlation coefficient – A measure of the common risk shared by stocks that does not depend on their volatility Cov (Ri ,R j ) rearranging Corr (Ri ,R j )  SD (Ri ) SD (R j ) ,) – The correlation between two stocks will always be between –1 and +1. Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Table 11.2 Computing the Covariance and Correlation between Pairs of Stocks 0.0558 =0.0112 1 6−1 Cov(Ri ,R j )  T  1  t (Ri ,t  Ri ) (R j ,t  R j ) Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Computing a Portfolio’s Variance and Volatility The Variance of a Two-Stock Portfolio σ 2𝑝 =¿Var (RP )  x12Var (R1 )  x22Var (R2 )  2 x1 x2Cov(R1 ,R2 ) ,) The effect of correlation The variance of the portfolio differ depending on the correlation. The lower the correlation, the lower the risk (standard deviation) we can obtain. The reduction in risk becomes greater as the correlation decreases. Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Textbook Example 11.6 Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Textbook Example 11.6 (cont'd) Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  10.6 Diversification in Stock Portfolios Total risk, as measured by return variance or standard deviation, is made up of: Firm-Specific (non-systematic risk) versus Systematic Risk – Firm Specific News: fluctuations of a stock’s return that are due to company- or industry- specific news.  Good or bad news about an individual company. E.g. introduction of a strong competitor, oil strike by a company. – Market-Wide News: fluctuation of a stock’s return that are due to market-wide news representing common risk.  News that affects all stocks due to the risk inherent to the economy in general. e.g. interest rates, inflation, economic growth, commodity prices Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  10.6 Diversification in Stock Portfolios (cont'd) Firm-Specific Versus Systematic Risk – When many stocks are combined in a large portfolio, the firm-specific risks for each stock will average out and be diversified. Firm-specific risk will be eliminated through diversification. – The systematic risk, however, will affect all firms and will not be diversified. Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Figure 11.2 Volatility of an Equally Weighted Portfolio Versus the Number of Stocks Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  10.7 Measuring Systematic Risk (cont'd) Efficient Portfolio – A portfolio that contains only systematic risk. There is no way to reduce the volatility of the portfolio without lowering its expected return. Market Portfolio – An efficient portfolio that contains all shares and securities in the market  The S&P 500 is often used as a proxy for the market portfolio. Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  10.7 Measuring Systematic Risk (cont'd) Measurement of systematic risk: Beta (β) – It measures the systematic risk of a security in comparison to the market as a whole. – Beta differs from volatility. Volatility measures total risk (systematic plus unsystematic risk), while beta is a measure of only systematic risk. 𝐶𝑜𝑣 ( 𝑅𝑖 , 𝑅 𝑀𝑘𝑡 ) 𝛽𝑖= 𝑉𝑎𝑟 ( 𝑅 𝑀𝑘𝑡 ) Interpreting Beta (β) – A security’s beta is related to how sensitive its underlying revenues and cash flows are to general economic conditions. Stocks in cyclical industries are likely to be more sensitive to systematic risk and have higher betas than stocks in less sensitive industries. Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Table 10.6 Betas with Respect to the S&P 500 for Individual Stocks (based on monthly data for 2010–2015) Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Capital Asset Pricing Model The CAPM is an equilibrium model of the relationship between risk and return that characterizes a security’s expected return based on its beta. E  R   Risk-Free Interest Rate  Risk Premium  rf    (E  RMkt   rf ) Market risk premium Expected return/cost of capital Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.  Example - CAPM Suppose the risk-free rate is 5%, the market risk premium is 7%, and a particular share has a beta of 1.2. Based on the CAPM, what is the expected return on this share? What would the expected return if the beta were to double? Copyright ©2017 Pearson Education, Ltd. All rights reserved. Copyright © 2020 Pearson Education Ltd. All Rights Reserved.