#### Transcript Chapter 8

Risk and Return Chapter 8 © 2003 South-Western/Thomson Learning Why Study Risk and Return? Returns to equity investments (stock) have historically been much higher than the return to debt investments Equity returns average 9% or 10% while debt returns average about 3% • Inflation also averaged about 3% during the same time period Returns on equity investments are much more volatile than the returns on debt instruments in the short-run 2 Why Study Risk and Return? Since equity earns a much higher return but with higher risk, it would be nice if we could invest and earn a high return but reduce the risk associated with such investments Investing in portfolios of securities can help manage risk • A portfolio is a collection of financial assets by investors We wish to capture the high average returns of equity investing while limiting the associated risk as much as possible 3 The General Relationship Between Risk and Return Risk in finance is defined as the probability of losing some or all of the money invested in a deal Generally investments that offer higher returns involve higher risks Suppose you could invest in a stock that would either return you 15% or a loss of everything (100%) Also, suppose the chance of losing everything is 1% and the chance of earning 15% is 99% The risk associated with this investment is the 1% chance of losing everything 4 The General Relationship Between Risk and Return Investors more or less expect to receive a positive return but they realize that there is risk associated with these investments and the chance that they can lose their money Stocks offering a higher likely return also have higher probabilities of total loss It is difficult to determine how much risk is associated with a given level of return Need to define risk in a measurable way • The definition has to include all the probabilities of loss Have to relate that measurement to return 5 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 Has had major impact on practical investing activities 6 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 • A return is what the investor receives divided by what is invested The return on a stock investment is • K = D1 + (P1 – P0) P0 7 Returns, Expected and Required The expected return on a stock is the return investors feel is most likely to occur based on currently available information Anticipated return based on the dividends expected as well as the future expected price No rational person makes any investment without some expectation of return 8 Returns, Expected and Required 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 People will only invest in an asset if they believe the expected return is at least equal to the required return • Different people have different levels of both expected and required return • Significant investment in a stock occurs only if the expected return exceeds the required return for a substantial number of investors 9 Risk—A Preliminary Definition A preliminary definition of investment risk is the probability that return will be less than expected This definition includes both positive and negative returns that are lower than expected Feelings About Risk Most people have negative feelings about bearing risk Risk averse investors prefer lower risk when expected returns are equal Most people see a trade-off between risk and return However risk isn't to be avoided, but higher risk investments must offer a higher expect return to encourage investment 10 Portfolio Theory 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 11 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 X = XiP Xi n i=1 12 Portfolio Theory Variance and Standard Deviation Variability relates to how far a typical observation of the variable is likely to deviate from the mean • There's is a great deal of difference in variability around the mean for different distributions • Telephone poles don't vary much in height from pole to pole— actual pole heights are closely clustered around the mean • Office buildings do vary a great deal in terms of height— widely dispersed around the mean • The standard deviation gives an indication of how far from the mean a typical observation is likely to fall 13 Portfolio Theory Variance and Standard Deviation Variance Formula 2 Var X Xi X P Xi i=1 2 x n • Variance is the average squared deviation from the mean Standard deviation formula SDX 2 x Xi X P Xi i=1 n 14 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 to its mean • CV = Standard Deviation Mean • For example, if the CV = 0.5, then the typical variation is 50% the size of the mean, or ½ Continuous Random Variable Can take on any numerical value within some range We talk about the probability of an actual outcome being within a range of values rather than being an exact amount 15 The Return on a Stock Investment as a Random Variable In financial theory, the return on a stock investment is considered a random variable Return is influenced by the future price of the stock and the expected dividends • There is an element of uncertainty in both of these variables Return is a continuous random variable with a low value of -100% but no limit to the high value The mean of the distribution of returns is the stock's expected return The variance and standard deviation show how likely it is that an actual return will be some distance from the expected value Actual return in a distribution with a large variance is likely to be different from the mean 16 Risk Redefined as Variability In financial theory risk is defined as variability in return A risky stock has a high probability of earning a return that significantly differs from the mean of the distribution While a low-risk stock is more like to earn a return similar to the expected return In practical terms risk is the probability that return will be less than expected 17 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 18 Decomposing Risk—Systematic (Market) and Unsystematic (Business-Specific) Risk Fundamental truth of the investment world The returns on securities tend to move up and down together • Not exactly together or proportionately Events and Conditions Causing Movement in Returns Some things influence all stocks (market risk) • Political news, inflation, interest rates, war, etc. Some things influence only specific companies (businessspecific risk) • Earnings reports, unexpected death of key executive, etc. Some things affect all companies within an industry • A labor dispute, shortage of a raw material 19 Decomposing Risk—Systematic (Market) and Unsystematic (Business-Specific) Risk Movement in Return as Risk The total movement in a stock's return is the total risk inherent in the stock Separating Movement/Risk into Two Parts A stock's risk can be separated into systematic or market risk and unsystematic or business-specific risk 20 Portfolios A portfolio is an investor's total stock holding Risk and Return for a Portfolio Each stock in a portfolio has its own expected return and its own risk Portfolios have their own risks and returns • The return on a portfolio is a weighted average of the returns of the individual stocks in the portfolio • The risk is the variance or standard deviation of the probability distribution of the portfolio's return • Not the same as the weighted average of the standard deviations or variances of the individual stocks within the portfolio 21 Portfolios The Goal of the Investor/Portfolio Owner Goal of investors: to capture the high average returns of equities while avoiding as much risk as possible • Generally done by constructing diversified portfolios to minimize portfolio risk for a given return Investors are concerned with how stocks impact portfolio performance, not with the stocks' stand-alone characteristics 22 Diversification—How Portfolio Risk Is Affected When Stocks Are Added Diversification means adding different (diverse) stocks to a portfolio Can reduce (but not eliminate) risk in a portfolio Business-Specific Risk and Diversification Business-specific risk is a series of essentially random events that push the returns of individual stocks up or down • Their effects simply cancel when added together over a substantial number of stocks • Is essentially random and can be diversified away • For this to work, the stocks within the portfolio must be from fundamentally different industries 23 Diversification—How Portfolio Risk Is Affected When Stocks Are Added Systematic (Market) Risk and Diversification If the returns of all stocks move up and down more or less together, it's not possible to reduce risk completely • Systematic risk can be reduced but never entirely eliminated The Portfolio If we have a portfolio that is as diversified as the market, its return will move in tandem with the market The Impact on Portfolio Risk of Adding New Stocks If we add a stock to the portfolio which has returns perfectly positively correlated with the portfolio, it will generally add risk to the diversified portfolio If we add a stock that is perfectly negatively correlated with the portfolio, it will decrease the risk of the portfolio 24 Diversification—How Portfolio Risk Is Affected When Stocks Are Added The Risk of the New Additions By Themselves and in Portfolios Stocks with equal stand-alone risk can have opposite risk impacts on a portfolio because of the timing of the variation in their returns A stock's risk in a portfolio sense is its market risk Choosing Stocks to Diversify for Market Risk How do we diversify to reduce market risk in a portfolio • Theoretically it's simple: just add stocks that move counter cyclically with the market • Unfortunately it's difficult to find stocks that move in that direction • However numerous stocks exist that have returns that are less than positively correlated with the market • Adding these stocks to the portfolio will generally reduce risk somewhat, but will not eliminate it 25 Diversification—How Portfolio Risk Is Affected When Stocks Are Added The Importance of Market Risk Modern portfolio theory is based on the assumption that investors focus on portfolios rather than on individual stocks • How stocks affect portfolios depends only on market risk For the small investor with a limited portfolio, these concepts do not apply 26 Measuring Market Risk—The Concept of Beta Market risk is a crucial concept in investing, so we need a way to measure it for individual stocks A stock's beta measures its market risk It measures the variation of a stock's return which accompanies the market's variation in return Developing Beta Beta is developed by determining the historical relationship between a stock's return and the return on a market index, such as the S&P500 • The stock's characteristic line reflects the average relationship between its return and the market • Beta is the slope of the characteristic line Projecting Returns with Beta Knowing a stock's beta enables us to estimate changes in its 27 return given changes in the market's return Measuring Market Risk—The Concept of Beta Betas are developed from historical data Small investors should remember that beta doesn't measure total risk A beta > (<) 1.0 implies the stock moves more (less) than the market Beta < 0 means the stock tends to move against the market May not be accurate if a fundamental change in the business environment occurs Stocks in gold mining companies are a real-world example of negative beta stocks Beta for a Portfolio Beta for a portfolio is the weighted average of the betas of the individual stocks within the portfolio 28 Using Beta—The Capital Asset Pricing Model (CAPM) The CAPM helps us determine how stock prices are set in the market Developed in 1950s and 1960s by Harry Markowitz and William Sharpe The CAPM's Approach People won't invest unless a stock's expected return is at least equal to their required return The CAPM attempts to explain how investors' required returns are determined 29 Using Beta—The Capital Asset Pricing Model (CAPM) Rates of Return, The Risk-Free Rate and Risk Premiums The risk-free rate (kRF) is a rate for which there is no chance of receiving less than what is expected • Returns on federally insured bank accounts and short-term Treasury debt are examples of risk-free investments Investing in any other investment is a risky venture; thus investors will require a return greater than the risk-free rate • Investors want to be compensated for the extra risk taken via a rate known as the risk premium (KRP) • The CAPM purports to explain how the risk premium in required rates of return are formed • The Security Market Line (SML) is the heart of the CAPM 30 The Security Market Line (SML) The SML proposes that required rates of return are determined by: k X kRF kM k RF b X Market Risk Premium Stock X's Risk Premium The Market Risk Premium • Is a reflection of the investment community's level of risk aversion • It is the risk premium for an investment in the market as a whole The Risk Premium for Stock X • The beta for Stock X times the risk premium of the market • Says that the risk premium for a stock is determined only by the stock's relationship with the market as measured by beta 31 The Security Market Line (SML) The SML as a Portrayal of the Securities Market The standard equation of a straight line is • y = mx + b • Where: y is the vertical axis variable; x is the horizontal axis variable; m is the slope of the line and b is the y intercept The SML can be viewed as a straight line: k X k RF k M k RF b X y= b+ m x • The slope of the SML plotted in risk-return space reflects the general level of risk aversion • The vertical intercept of the SML represents investment in short-term government securities 32 The Security Market Line (SML) The SML as a Line of Market Equilibrium If, for every stock, its expected return equals its required return, the SML represents equilibrium Suppose that a stock's expected return now becomes less than its required return • Investors would no longer desire that stock and owners of the stock would sell while potential buyers would no longer be interested • The stock price would drop because supply would exceed demand • Since the stock price is dropping, its expected return is increasing, driving it back toward equilibrium • The SML represents a condition of stable equilibrium 33 The Security Market Line (SML) Valuation Using Risk-Return Concepts The SML allows us to calculate the minimum required rate of return for a stock This return can then be used in the Gordon model to determine an intrinsic value for a stock The Impact of Management Decisions on Stock Prices Since managers can influence a stock's beta and future growth rates, management's decisions impact the price of the stock 34 The Security Market Line Adjustments to Changing Market Conditions The response to a change in the risk-free rate • If all else remains the same, a change in the risk-free rate causes a parallel shift in the SML • The slope of the SML remains the same which means KM must increase by the amount of the change in kRF The response to a change in risk aversion • Changes in attitudes toward risk are reflected by rotations of the SML around its vertical intercept 35 The Validity and Acceptance of the CAPM and SML CAPM is an abstraction of reality designed to help make predictions Its simplicity has lead to its popularity • It relates risk and return in an easy-to-understand concept However, CAPM is not universally accepted Continuing debate exists as to its relevance and usefulness • Fama and French found no historical relationship between the returns on stocks and their betas 36