Presentation on theme: "Expected Returns Expected returns are based on the probabilities of possible outcomes In this context, “expected” means “average” if the process is repeated."— Presentation transcript:
1 Expected ReturnsExpected returns are based on the probabilities of possible outcomesIn this context, “expected” means “average” if the process is repeated many timesThe “expected” return does not even have to be a possible returnUse the following example to illustrate the mathematical nature of expected returns:Consider a game where you toss a fair coin: If it is Heads then student A pays student B $1. If it is Tails then student B pays student A $1. Most students will remember from their statistics that the expected value is $0 (=.5(1) + .5(-1)). That means that if the game is played over and over then each student should expect to break-even. However, if the game is only played once, then one student will win $1 and one will lose $1.
2 Example: Expected Returns Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns?State Probability C TBoomNormalRecession ???RC = .3(.15) + .5(.10) + .2(.02) = .099 = 9.9%RT = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7%What is the probability of a recession? 0.2If the risk-free rate is 6.15%, what is the risk premium?Stock C: 9.9 – 6.15 = 3.75%Stock T: 17.7 – 6.15 = 11.55%
3 Portfolios A portfolio is a collection of assets An asset’s risk and return are important to how the stock affects the risk and return of the portfolioThe risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets
4 Example: Portfolio Weights Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security?$2,000 of DCLK$3,000 of KO$4,000 of INTC$6,000 of KEIShow the students that the sum of the weights = 1DCLK: 2/15 = .133KO: 3/15 = .2INTC: 4/15 = .267KEI: 6/15 = .4
5 Portfolio Expected Returns The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolioYou can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities
6 Example: Expected Portfolio Returns Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio?DCLK: 19.65%KO: 8.96%INTC: 9.67%KEI: 8.13%E(RP) = .133(19.65) + .2(8.96) (9.67) + .4(8.13) = 10.24%
7 Portfolio VarianceCompute the portfolio return for each state: RP = w1R1 + w2R2 + … + wmRmCompute the expected portfolio return using the same formula as for an individual assetCompute the portfolio variance and standard deviation using the same formulas as for an individual assetThe instructor’s manual provides information on how to compute the portfolio variance using the correlation or covariance between assets.
8 Expected versus Unexpected Returns Realized returns are generally not equal to expected returnsThere is the expected component and the unexpected componentAt any point in time, the unexpected return can be either positive or negativeOver time, the average of the unexpected component is zero
9 Announcements and News Announcements and news contain both an expected component and a surprise componentIt is the surprise component that affects a stock’s price and therefore its returnThis is very obvious when we watch how stock prices move when an unexpected announcement is made, or earnings are different from anticipated
10 Efficient MarketsEfficient markets are a result of investors trading on the unexpected portion of announcementsThe easier it is to trade on surprises, the more efficient markets should beEfficient markets involve random price changes because we cannot predict surprises
11 Systematic Risk Risk factors that affect a large number of assets Also known as non-diversifiable risk or market riskIncludes such things as changes in GDP, inflation, interest rates, etc.
12 Unsystematic Risk Risk factors that affect a limited number of assets Also known as unique risk and asset-specific riskIncludes such things as labor strikes, part shortages, etc.
13 Returns Total Return = expected return + unexpected return Unexpected return = systematic portion + unsystematic portionTherefore, total return can be expressed as follows:Total Return = expected return + systematic portion + unsystematic portion
14 DiversificationPortfolio diversification is the investment in several different asset classes or sectorsDiversification is not just holding a lot of assetsFor example, if you own 50 Internet stocks, then you are not diversifiedHowever, if you own 50 stocks that span 20 different industries, then you are diversifiedVideo Note: “Portfolio Management” looks at the value of diversification using Tower Records
16 The Principle of Diversification Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returnsThis reduction in risk arises because worse-than-expected returns from one asset are offset by better-than-expected returns from another assetHowever, there is a minimum level of risk that cannot be diversified away - that is the systematic portion
18 Diversifiable RiskThe risk that can be eliminated by combining assets into a portfolioOften considered the same as unsystematic, unique, or asset-specific riskIf we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away
19 Total Risk Total risk = systematic risk + unsystematic risk The standard deviation of returns is a measure of total riskFor well-diversified portfolios, unsystematic risk is very smallConsequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk
20 Systematic Risk Principle There is a reward for bearing riskThere is not a reward for bearing risk unnecessarilyThe expected return on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away
21 Measuring Systematic Risk How do we measure systematic risk?We use the beta coefficient to measure systematic riskWhat does beta tell us?A beta of 1 implies the asset has the same systematic risk as the overall marketA beta < 1 implies the asset has less systematic risk than the overall marketA beta > 1 implies the asset has more systematic risk than the overall market
22 Table 11.8www: Click on the Web surfer icon to go to Yahoo! Finance’s stock screener where you can screen stocks based upon their betas. Students are often interested to see the range of betas that are out there.
23 Example: Work the Web Many sites provide betas for companies Yahoo! Finance provides beta, plus a lot of other information under its profile linkClick on the Web surfer to go to Yahoo! FinanceEnter a ticker symbol and get a basic quoteClick on key statisticsBeta is reported under stock price history
24 Total versus Systematic Risk Consider the following information:Standard Deviation BetaSecurity C 20%Security K 30%Which security has more total risk?Which security has more systematic risk?Which security should have the higher expected return?Security K has the higher total riskSecurity C has the higher systematic riskSecurity C should have the higher expected return
25 Example: Portfolio Betas Consider the previous example with the following four securitiesSecurity Weight BetaDCLKKOINTCKEIWhat is the portfolio beta?.133(4.03) + .2(.84) (1.05) + .4(.59) = 1.22Which security has the highest systematic risk? DCLKWhich security has the lowest systematic risk? KEIIs the systematic risk of the portfolio more or less than the market? more
26 Beta and the Risk Premium Remember that the risk premium = expected return – risk-free rateThe higher the beta, the greater the risk premium should beCan we define the relationship between the risk premium and beta so that we can estimate the expected return?YES!
27 Example: Portfolio Expected Returns and Betas 0%5%10%15%20%25%30%0.511.522.53BetaExpected ReturnE(RA)RfThis is based on Fig. 11.2a in the book.Point out that there is a linear relationship between beta and expected return. Ask if the students remember the form of the equation for a line.Y = mx + bE(R) = slope (Beta) + y-interceptThe y-intercept is = the risk-free rate, so all we need is the slopeA
28 Reward-to-Risk Ratio: Definition and Example The reward-to-risk ratio is the slope of the line illustrated in the previous exampleSlope = (E(RA) – Rf) / (A – 0)Reward-to-risk ratio for previous example = (20 – 8) / (1.6 – 0) = 7.5What if an asset has a reward-to-risk ratio of 8 (implying that the asset plots above the line)?What if an asset has a reward-to-risk ratio of 7 (implying that the asset plots below the line)?Ask students if they remember how to compute the slope of a line: rise / runIf the reward-to-risk ratio = 8, then investors will want to buy the asset. This will drive the price up and the return down (remember time value of money and valuation). When will trading stop? When the reward-to-risk ratio reaches 7.5.If the reward-to-risk ratio = 7, then investors will want to sell the asset. This will drive the price down and the return up. When will trading stop? When the reward-to-risk ratio reaches 7.5.
29 Market EquilibriumIn equilibrium, all assets and portfolios must have the same reward-to-risk ratio, and each must equal the reward-to-risk ratio for the market
30 Security Market LineThe security market line (SML) is the representation of market equilibriumThe slope of the SML is the reward-to-risk ratio: (E(RM) – Rf) / MBut since the beta for the market is ALWAYS equal to one, the slope can be rewrittenSlope = E(RM) – Rf = market risk premiumBased on the discussion earlier, we now have all the components of the line:E(R) = [E(RM) – Rf] + Rf
31 Capital Asset Pricing Model The capital asset pricing model (CAPM) defines the relationship between risk and returnE(RA) = Rf + A(E(RM) – Rf)If we know an asset’s systematic risk, we can use the CAPM to determine its expected returnThis is true whether we are talking about financial assets or physical assets
32 Factors Affecting Expected Return Pure time value of money – measured by the risk-free rateReward for bearing systematic risk – measured by the market risk premiumAmount of systematic risk – measured by beta
33 Example: CAPMConsider the betas for each of the assets given earlier. If the risk-free rate is 3.15% and the market risk premium is 9.5%, what is the expected return for each?Security Beta Expected ReturnDCLK (9.5) = %KO (9.5) = 11.13%INTC (9.5) = %KEI (9.5) = 8.755%
35 Quick Quiz Homework: 2, 4, 9 (ignore Variance), 12, 14 How do you compute the expected return and standard deviation for an individual asset? For a portfolio?What is the difference between systematic and unsystematic risk?What type of risk is relevant for determining the expected return?Consider an asset with a beta of 1.2, a risk-free rate of 5%, and a market return of 13%.What is the reward-to-risk ratio in equilibrium?What is the expected return on the asset?Homework: 2, 4, 9 (ignore Variance), 12, 14Reward-to-risk ratio = 13 – 5 = 8%Expected return = (8) = 14.6%
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