Practical Financial Management, 7e by William Lasher

Chapter 9 Risk and ReturnWhy 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 2The 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 wayRelate that measurement to a return 3Portfolio TheoryModern 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 investmentMajor impact on practical investing activities

4The Return on an InvestmentThe rate of return allows an investment's return to be compared with other investmentsOne-Year InvestmentsThe return on a debt investment isk = interest paid / loan amountThe return on a stock investment is k = [D1 + (P1 P0)] / P05The Expected Return The expected return on stock is the return investors feel is most likely to occur based on current informationAnticipated return based on the dividends expected as well as the future expected price6The Required ReturnThe required return on a stock is the minimum rate at which investors will purchase or hold a stock based on their perceptions of its risk7RiskA Preliminary Definition A preliminary definition of investment risk is the probability that return will be less than expected

Feelings About RiskMost people have negative feelings about bearing risk: Risk AversionMost people see a trade-off between risk and returnHigher risk investments must offer higher expected returns to be acceptable 8Review of the Concept of a Random VariableIn statistics, a random variable is the outcome of a chance process and has a probability distributionDiscrete variables can take only specific variablesContinuous variables can take any value within a specified range 9Review of the Concept of a Random VariableThe Mean or Expected ValueThe most likely outcome for the random variableFor symmetrical probability distributions, the mean is the center of the distribution.Statistically it is the weighted average of all possible outcomes

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Review of the Concept of a Random VariableVariance and Standard DeviationVariability relates to how far a typical observation of the variable is likely to deviate from the meanThe standard deviation gives an indication of how far from the mean a typical observation is likely to fall11Review of the Concept of a Random VariableVariance and Standard DeviationVariance 12

Variance is the average squared deviation from the meanStandard deviation Concept Connection Example 9-1 Discrete Probability Distributions131.00000.062540.250030.375020.250010.06250P(X)XThe mean of this distribution is 2, since it is a symmetrical distribution.If you toss a coin four times, what is the chance of getting x heads?Figure 9-1 Discrete Probability Distribution14

Concept Connection Example 9-2 Calculating the Mean of a Discrete Distribution15

Concept Connection Example 9-3 Variance and Standard Deviation16

Review of the Concept of a Random Variable The Coefficient of VariationA relative measure of variation the ratio of the standard deviation of a distribution to its meanCV = Standard Deviation Mean17

Review of the Concept of a Random VariableContinuous Random VariableCan take on any numerical value within some rangeThe probability of an actual outcome involves falling within a range of values rather than being an exact amount

18Figure 9-2 Probability Distribution for a Continuous Random Variable19

The Return on a Stock Investment as a Random VariableReturn 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 value20Figure 9-3 Probability Distribution of the Return on an Investment in Stock X21

Figure 9-4 Probability Distributions With Large and Small Variances22

Risk Redefined as VariabilityIn portfolio theory, risk is variability as measured by variance or standard deviationA risky stock has a high probability of earning a return that differs significantly from the mean of the distributionA low-risk stock is more likely to earn a return similar to the expected returnIn practical terms risk is the probability that return will be less than expected23

Figure 9-5 Investment Risk Viewed as Variability of Return Over Time 24Both stocks have the same expected return, the high risk stock has a greater variability in return over time.Risk AversionRisk 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

25Figure 9-6 Risk Aversion26

Concept Connection Example 9-4 Evaluating Stand-Alone Risk27Harold 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

High tech firms are high-risk - new ideas can be very successful or fail completelyHarold has made a discrete estimate of the probability distribution of returns for each stock:Concept Connection Example 9-4 Evaluating Stand-Alone Risk 28Evaluate Harold's options in terms of the statistical concepts of risk and return.

Concept Connection Example 9-4 Evaluating Stand-Alone Risk 29First calculate the expected return for each stock.Next calculate the variance and standard deviation of the return on each stock:

Concept Connection Example 9-4 Evaluating Stand-Alone Risk 30

Concept Connection Example 9-4 Evaluating Stand-Alone Risk 31Finally, calculate the coefficient of variation for each stocks return.

Example 9-4 DiscussionWhich stock should Harold choose Astro is better on expected return but Evanston wins on riskConsiderWorst cases and Best casesHow variable is each return around its meanDoes a picture (next slide) help?Which would you chooseIs it likely that Harolds choice would be influenced by his age and/or wealth?

Concept Connection Example 9-4 Evaluating Stand-Alone Risk 33Continuous approximations of the two distributions are plotted as follows:

Decomposing RiskSystematic and Unsystematic RiskMovement in Return as RiskTotal up and down movement in a stock's return is the total risk inherent in the stock

Separate Movement/Risk into Two PartsMarket (systematic) risk Business-specific (unsystematic) risk

34Defining Market and Business-Specific RiskRisk is Movement in Return

Components of Risk Market RiskMovement caused by things that influence all stocks: political news, inflation, interest rates, war, etc.

Business-Specific Risk Movement caused by things that influence particular firms and/or industries: labor unrest, weather, technology, key executives

Total Risk = Market Risk + Business-Specific Risk

35PortfoliosA portfolio is the collection of investment assets held by an investorPortfolios have their own risks and returnsA portfolios return is simply the weighted average of the returns of the stocks in itEasy to calculateA portfolios risk is the standard deviation of the probability distribution of its returnDepends on risks of stocks in portfolio, but...Very complex and difficult to calculate/measure36PortfoliosGoal of the Investor/Portfolio Owner is to capture the high average returns of stocks while avoiding as much of their risk as possibleDone by constructing diversified portfolios

Investors are concerned only with how stocks impact portfolio performance, not with stand-alone risk

37DiversificationHow Portfolio Risk Is Affected When Stocks Are AddedDiversification - adding different (diverse) stocks to a portfolioBusiness-Specific Risk and DiversificationBusiness Specific risk: Random eventsGood and Bad effects wash out in large portfolioBusiness-Specific Risk is said to be Diversified Away in a well-diversified portfolio Portfolio Theory assumes it is gone

38Diversifying to Reduce Market (Systematic) RiskMarket risk is caused by events that affect all stocksReduced but not eliminated by diversifying with stocks that do not move together Not perfectly positively correlated with the marketMarket risk in a portfolio depends on the timing of variations in individual returns (next slide)39Figure 9-7 Risk In and Out of a Portfolio40

Portfolio Theory and the Small InvestorThe Importance of Market RiskModern portfolio theory assumes business risk is diversified awayLarge, diversified portfolio

For the small investor with a limited portfolio the theorys results may not apply

41Measuring Market RiskThe Concept of BetaMarket risk is crucial Its all thats left because Business-Specific risk is diversified awayThe theory needs a way to measure market risk for individual stocksIn the financial world, a stocks Beta is a widely accepted measure of its riskBeta measures the variation in a stocks return that accompanies variation in the market's return42Measuring Market RiskThe Concept of BetaDeveloping BetaDetermine the historical relationship between a stock's return and the return on the market Regress stocks return against return on an index such as the S&P 500

Projecting Returns with BetaKnowing a stock's Beta enables us to estimate changes in its return given changes in the market's return43Figure 9-8 The Determination of Beta44

Concept Connection Example 9-6 Projecting Returns with BetaConroys beta is 1.8. Its 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 Conroys new return likely to be?

Solution:Beta represents the past average change in Conroys return relative to changes in the markets return.

The new return can be estimated as kConroy = 14% - 7.2% = 6.8%

Measuring Market RiskThe Concept of BetaBetas are developed from historical dataNot accurate if a fundamental change in the firm or business environment has occurredBeta > 1.0 -- the stock moves more than the marketBeta < 1.0 -- the stock moves less than the marketBeta < 0 -- the stock moves against the market

Beta for a PortfolioThe weighted average of the betas of the individual stocks within the portfolio Weighted by $ invested46Using Beta The Capital Asset Pricing Model CAPM)CAPM attempts to explain how stock prices are setCAPM's ApproachPeople won't invest in a stock unless its expected return is at least equal to their required return for that stockCAPM attempts to quantify how required returns are determinedThe stocks value (price) is estimated based on CAPMs required return for that stock47Using Beta The Capital Asset Pricing Model (CAPM)Rates of Return, The Risk-Free Rate and Risk Premiums The current return on the market is kMThe risk-free rate (kRF) no chance of receiving less than expectedInvesting in any other asset is risky Investors require a risk premium of additional return over kRF when there is risk48The CAPMs Security Market Line (SML)The SML proposes that required rates of return are determined by:49The Market Risk Premium is (kM kRF)The Risk Premium for Stock XThe beta for Stock X times the market risk premium In the CAPM a stocks risk premium is determined only by the stock's market risk as measured by its beta

Figure 9-9 The Security Market Line50

The Security Market Line (SML)Valuation Using Risk-ReturnUse the SML to calculate a required rate of return for a stockUse that return in the Gordon model to calculate a price

51Concept Connection Example 9-10Valuing (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 twice as much as the average stock in response to political and economic changes. What should Kelvin sell for today?Concept Connection Example 9-10Valuing (Pricing) a Stock with CAPMThe required rate of return using the SML is:kKelvin = 6 + (10 6)2.0 = 14%

Substituting this along with the 7% growth rate into the Gordon model yields the estimated price:

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 managements goal is generally to maximize stock priceConcept Connection Example 9-11 Strategic Decisions Based on CAPM55 A new venture promises to increase Kelvins 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 managements objective is to maximize stock price, should Kelvin undertake the project ?

Solution: The new required rate of return will be: kKelvin = 6 + (10 6)2.3 = 15.2%Substituting this and 9% growth in the Gordon model yields:

Hence it seems the project will increase the stocks price helping to achieve managements goals.

The SML Adjusting to ChangesA change in the risk-free rateChanges in the risk-free rate cause parallel shifts in the SMLA change in risk aversionAttitudes toward risk are reflected in the slope of the SML (kM kRF) Changes cause rotations of the SML around its vertical intercept at kRF56Figure 9-10 A Shift in the Security Market Line to Accommodate an Increase in the Risk-Free Rate57

Figure 9-11 A Rotation of the Security Market Line to Accommodate an Increase in Risk Aversion58

The Validity and Acceptance of the CAPM and its SMLCAPM is an abstraction of reality designed to help make predictionsIts simplicity has probably enhanced its popularity

CAPM is not universally acceptedRelevance and usefulness is the subject of an ongoing debate59