Chapter Outline Expected Returns and Variances of a portfolio
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0 Return risk and the Security market line Chapter 13Return risk and the Security market line
1 Chapter Outline Expected Returns and Variances of a portfolio Announcements, Surprises, and Expected ReturnsRisk: Systematic and UnsystematicDiversification and Portfolio RiskSystematic Risk and BetaThe Security Market Line (SML)
2 Expected Returns (1)Expected returns are based on the probabilities of possible outcomesExpected means average if the process is repeated many timesExpected return = return on a risky asset expected in the future
3 Expected Returns (2) Probability Expected return Stock A Stock B Boom 0.220%15%Normal0.410%8%Recession-5%2%RA =RB =If the risk-free rate = 3.2%, what is the risk premium for each stock?
4 Variance and Standard Deviation (1) Unequal probabilities can be used for the entire range of possibilitiesWeighted average of squared deviations
5 Variance and Standard Deviation (2) Consider the previous example. What is the variance and standard deviation for each stock?Stock AStock B
6 Portfolio = a group of assets held by an investor PortfoliosThe risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assetsPortfolio = a group of assets held by an investorPortfolio weights = Percentage of a portfolio’s total value in a particular asset
7 Portfolio WeightsSuppose you have $ 20,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security?$5,000 of A$9,000 of B$5,000 of C$1,000 of D
8 Portfolio Expected Returns (1) The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolioYou can also find the expected return by finding the portfolio return in each possible state and computing the expected value
9 Expected Portfolio Returns (2) Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio?A: 19.65%B: 8.96%C: 9.67%D: 8.13%E(RP) =
10 Portfolio Variance (1) Steps: Compute the portfolio return for each state: RP = w1R1 + w2R2 + … + wnRnCompute 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 asset
11 Portfolio Variance (2) Consider the following information Invest 60% of your money in Asset AState Probability A BBoom % 10%Recession % 30%What is the expected return and standard deviation for each asset?What is the expected return and standard deviation for the portfolio?
13 Another Way to Calculate Portfolio Variance Portfolio variance can also be calculated using the following formula:Correlation is a statistical measure of how 2 assets move in relation to each otherIf the correlation between stocks A and B = -1, what is the standard deviation of the portfolio?
19 Diversification (1)There are benefits to diversification whenever the correlation between two stocks is less than perfect (p < 1.0)If two stocks are perfectly positively correlated, then there is simply a risk- return trade-off between the two securities.
21 Expected vs. Unexpected Returns Expected return from a stock is the part of return that shareholders in the market predict (expect)The unexpected return (uncertain, risky part):At any point in time, the unexpected return can be either positive or negativeOver time, the average of the unexpected component is zeroTotal return = Expected return + Unexpected return
22 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 returnAnnouncement = Expected part + Surprise
23 Systematic Risk Risk factors that affect a large number of assets Also known as non-diversifiable risk or market riskExamples: changes in GDP, inflation, interest rates, general economic conditions
24 Unsystematic Risk Risk factors that affect a limited number of assets Also known as diversifiable risk and asset-specific riskIncludes such events as labor strikes, shortages.
25 Returns Unexpected return = systematic portion + unsystematic portion Total return can be expressed as follows:Total Return = expected return + systematic portion + unsystematic portion
26 Effect of Diversification Portfolio diversification is the investment in several different asset classes or sectorsDiversification is not just holding a lot of assetsPrinciple of diversification = spreading an investment across a number of assets eliminates some, but not all of the risk
27 The Principle of Diversification Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returnsReduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from anotherThere is a minimum level of risk that cannot be diversified away and that is the systematic portion
30 Diversifiable (Unsystematic) Risk The risk that can be eliminated by combining assets into a portfolioIf we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify awayThe market will not compensate investors for assuming unnecessary risk
31 Total RiskThe 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
32 Systematic Risk Principle There is a reward for bearing riskThere is no reward for bearing risk unnecessarilyThe expected return (and the risk premium) on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away
33 Measuring Systematic Risk Beta (β) is a measure of systematic riskInterpreting beta:β = 1 implies the asset has the same systematic risk as the overall marketβ < 1 implies the asset has less systematic risk than the overall marketβ > 1 implies the asset has more systematic risk than the overall market
35 Total vs. Systematic Risk Consider the following information:Standard Deviation BetaSecurity A 20%Security B 30%Which security has more total risk?Which security has more systematic risk?Which security should have the higher expected return?
37 Portfolio BetasConsider the previous example with the following four securitiesSecurity Weight BetaABCDWhat is the portfolio beta?
38 Beta and the Risk Premium The higher the beta, the greater the risk premium should beThe relationship between the risk premium and beta can be graphically interpreted and allows to estimate the expected return
39 Consider a portfolio consisting of asset A and a risk-free asset Consider a portfolio consisting of asset A and a risk-free asset. Expected return on asset A is 20%, it has a beta = 1.6. Risk- free rate = 8%.
41 Reward-to-Risk Ratio: The reward-to-risk ratio is the slope of the line illustrated in the previous slideSlope = (E(RA) – Rf) / (A – 0)Reward-to-risk ratio =If an asset has a reward-to-risk ratio = 8?If an asset has a reward-to-risk ratio = 7?
42 The Fundamental Result The reward-to-risk ratio must be the same for all assets in the marketIf one asset has twice as much systematic risk as another asset, its risk premium is twice as large
43 Security Market Line (1) The security market line (SML) is the representation of market equilibriumThe slope of the SML is the reward-to- risk ratio: (E(RM) – Rf) / MThe beta for the market is always equal to one, the slope can be rewrittenSlope = E(RM) – Rf = market risk premium
45 The Capital Asset Pricing Model (CAPM) The capital asset pricing model 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 return
46 CAPMConsider the betas for each of the assets given earlier. If the risk-free rate is 4.5% and the market risk premium is 8.5%, what is the expected return for each?SecurityBetaExpected ReturnA3.6B.7C1.7D1.9
47 Factors Affecting Expected Return 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