Practical financial managment 7e LASHER chapter 9

Chapter Risk and Return Why Study Risk and Return? Is there a way to invest in stocks to take advantage of the high returns while minimizing the risks? Investing in portfolios enables investors to manage and control risk while receiving high returns – A portfolio is a collection of financial assets The General Relationship Between Risk and Return Risk – The meaning in everyday language: The probability of losing some or all of the money invested Understanding the risk-return relationship involves: – Define risk in a measurable way – Relate that measurement to a return Portfolio Theory—Modern Thinking about Risk and Return Portfolio theory defines investment risk in a measurable way and relates it to the expected level of return from an investment – Major impact on practical investing activities The Return on an Investment The rate of return allows an investment's return to be compared with other investments One-Year Investments – The return on a debt investment is k = interest paid / loan amount – The return on a stock investment is k = [D1 + (P1 – P0)] / P0 The Expected Return The expected return on stock is the return investors feel is most likely to occur based on current information – Anticipated return based on the dividends expected as well as the future expected price The Required Return The required return on a stock is the minimum rate at which investors will purchase or hold a stock based on their perceptions of its risk Risk—A Preliminary Definition A preliminary definition of investment risk is the probability that return will be less than expected Feelings About Risk – Most people have negative feelings about bearing risk: Risk Aversion – Most people see a trade-off between risk and return – Higher risk investments must offer higher expected returns to be acceptable Review of the Concept of a Random Variable In statistics, a random variable is the outcome of a chance process and has a probability distribution – Discrete variables can take only specific variables – Continuous variables can take any value within a specified range Review of the Concept of a Random Variable The Mean or Expected Value – The most likely outcome for the random variable For symmetrical probability distributions, the mean is the center of the distribution Statistically it is the weighted average of all possible outcomes n X = ∑ XiP ( Xi ) i=1 10 Concept Connection Example 9-6 Projecting Returns with Beta Conroy’s beta is 1.8 It’s stock returns 14% The market is declining, and experts estimate the return on an average stock will fall by 4% from 12% to 8% What is Conroy’s new return likely to be? Solution: Beta represents the past average change in Conroy’s return relative to changes in the market’s return bConroy = The new return can be estimated as ∆k Conroy ∆k M ∆k kConroy = 14% - 7.2% = Conroy 6.8% or 1.8 = = 7.2% ∆k Conroy 4% Measuring Market Risk The Concept of Beta Betas are developed from historical data – Not accurate if a fundamental change in the firm or business environment has occurred – Beta > 1.0 the stock moves more than the market – Beta < 1.0 the stock moves less than the market – Beta < the stock moves against the market Beta for a Portfolio – The weighted average of the betas of the individual stocks within the portfolio Weighted by $ invested 46 Using Beta The Capital Asset Pricing Model CAPM) CAPM attempts to explain how stock prices are set CAPM's Approach – People won't invest in a stock unless its expected return is at least equal to their required return for that stock – – CAPM attempts to quantify how required returns are determined The stock’s value (price) is estimated based on CAPM’s required return for that stock 47 Using Beta The Capital Asset Pricing Model (CAPM) Rates of Return, The Risk-Free Rate and Risk Premiums – The current return on the market is kM – The risk-free rate (kRF) – no chance of receiving less than expected Investing in any other asset is risky – Investors require a “risk premium” of additional return over k RF when there is risk 48 The CAPM’s Security Market Line (SML) The SML proposes that required rates of return are determined by: k X = k RF + ( k M − k RF ) b X 14243 Market Risk Premium 4 43 Stock X's Risk Premium The Market Risk Premium is (kM – kRF) The Risk Premium for Stock X The beta for Stock X times the market risk premium In the CAPM a stock’s risk premium is determined only by the stock's market risk as measured by its beta 49 Figure 9-9 The Security Market Line 50 The Security Market Line (SML) Valuation Using Risk-Return – Use the SML to calculate a required rate of return for a stock – Use that return in the Gordon model to calculate a price 51 Concept Connection Example 9-10 Valuing (Pricing) a Stock with CAPM Kelvin paid an annual dividend of $1.50 recently, and is expected to grow at 7% indefinitely T- bills yield 6%, an average stock yields 10% Kelvin is a volatile stock Its return moves about stock in response to political and economic changes What should Kelvin sell for today? twice as much as the average Concept Connection Example 9-10 Valuing (Pricing) a Stock with CAPM The required rate of return using the SML is: kKelvin = + (10 – 6)2.0 = 14% Substituting this along with the 7% growth rate into the Gordon model yields the estimated price : P0 = D0 ( + g ) k−g = $1.5 ( 1.07 ) 14 − 07 = $22.93 The Security Market Line (SML) The Impact of Management Decisions on Stock Prices Management decisions can influence a stock's beta as well as future growth rates An SML approach to valuation may be relevant for policy decisions Recall that management’s goal is generally to maximize stock price Concept Connection Example 9-11 Strategic Decisions Based on CAPM A new venture promises to increase Kelvin’s growth rate from 7% to 9% However, it will make the firm more risky, so its beta may increase from 2.0 to 2.3 The current stock price is $22.90 If management’s objective is to maximize stock price, should Kelvin undertake the project ? Solution: The new required rate of return will be: kKelvin = + (10 – 6)2.3 = 15.2% Substituting this and 9% growth in the Gordon model yields: ( ) ( ) D0 +the g stock’s $1.5 Hence it seems the project will increase price1.09 helping to achieve management’s goals P0 = k−g = 152 − 09 = $26.37 55 The SML – Adjusting to Changes A change in the risk-free rate – Changes in the risk-free rate cause parallel shifts in the SML A change in risk aversion – Attitudes toward risk are reflected in the slope of the SML (kM – kRF) Changes cause rotations of the SML around its vertical intercept at k RF 56 Figure 9-10 A Shift in the Security Market Line to Accommodate an Increase in the Risk-Free Rate 57 Figure 9-11 A Rotation of the Security Market Line to Accommodate an Increase in Risk Aversion 58 The Validity and Acceptance of the CAPM and its SML CAPM is an abstraction of reality designed to help make predictions – Its simplicity has probably enhanced its popularity CAPM is not universally accepted – Relevance and usefulness is the subject of an ongoing debate 59 [...]... Example 9- 4 Evaluating Stand-Alone Risk Evaluate Harold's options in terms of the statistical concepts of risk and return 28 Concept Connection Example 9- 4 Evaluating Stand-Alone Risk First calculate the expected return for each stock Next calculate the variance and standard deviation of the return on each stock: 29 Concept Connection Example 9- 4 Evaluating Stand-Alone Risk 30 Concept Connection Example 9- 4... Figure 9- 2 Probability Distribution for a Continuous Random Variable 19 The Return on a Stock Investment as a Random Variable Return is influenced by stock price and dividends Return is a continuous random variable The mean of the distribution of returns is the expected return The variance and standard deviation show how likely an actual return will be some distance from the expected value 20 Figure 9- 3...  i=1  n 12 Concept Connection Example 9- 1 Discrete Probability Distributions X P(X) 0 0.0625 1 0.2500 2 0.3750 3 0.2500 4 0.0625 The mean of this distribution is 2, since it is a symmetrical distribution 1.0000 If you toss a coin four times, what is the chance of getting x heads? 13 Figure 9- 1 Discrete Probability Distribution 14 Concept Connection Example 9- 2 Calculating the Mean of a Discrete Distribution... 23 Figure 9- 5 Investment Risk Viewed as Variability of Return Over Time Both stocks have the same expected return, the high risk stock has a greater variability in return over time 24 Risk Aversion Risk aversion means investors prefer lower risk when expected returns are equal When expected returns are not equal the choice of investment depends on the investor's tolerance for risk 25 Figure 9- 6 Risk... 21 Figure 9- 4 Probability Distributions With Large and Small Variances 22 Risk Redefined as Variability In portfolio theory, risk is variability as measured by variance or standard deviation A risky stock has a high probability of earning a return that differs significantly from the mean of the distribution A low-risk stock is more likely to earn a return similar to the expected return In practical. .. stock’s return 31 Example 9- 4 Discussion Which stock should Harold choose – Astro is better on expected return but Evanston wins on risk Consider – Worst cases and Best cases – How variable is each return around its mean – Does a picture (next slide) help? – Which would you choose Is it likely that Harold’s choice would be influenced by his age and/or wealth? Concept Connection Example 9- 4 Evaluating Stand-Alone... times, what is the chance of getting x heads? 13 Figure 9- 1 Discrete Probability Distribution 14 Concept Connection Example 9- 2 Calculating the Mean of a Discrete Distribution 15 Concept Connection Example 9- 3 Variance and Standard Deviation 16 Review of the Concept of a Random Variable The Coefficient of Variation – A relative measure of variation — the ratio of the standard deviation of a distribution... risk when expected returns are equal When expected returns are not equal the choice of investment depends on the investor's tolerance for risk 25 Figure 9- 6 Risk Aversion 26 Concept Connection Example 9- 4 Evaluating Stand-Alone Risk Harold will invest in one of two companies: Evanston Water Inc (a public utility) Astro Tech Corp (a high-tech company) Public utilities are low-risk - regulated monopolies ... getting x heads? 13 Figure 9- 1 Discrete Probability Distribution 14 Concept Connection Example 9- 2 Calculating the Mean of a Discrete Distribution 15 Concept Connection Example 9- 3 Variance and Standard... and standard deviation of the return on each stock: 29 Concept Connection Example 9- 4 Evaluating Stand-Alone Risk 30 Concept Connection Example 9- 4 Evaluating Stand-Alone Risk Finally, calculate... will be some distance from the expected value 20 Figure 9- 3 Probability Distribution of the Return on an Investment in Stock X 21 Figure 9- 4 Probability Distributions With Large and Small Variances