Risk & Return Stand-alone and Portfolio Considerations

Efficient Market Hypothesis Securities are in equilibrium: “Fairly priced” 100,000+ analysts (MBAs, CFAs, PhDs) work for investment firms Analysts have access to data and $$ to invest Thus, price reflects news almost instantaneously One cannot “beat the market” except through good luck or inside information. Doesn’t mean you can’t make money.

Weak Form EMH Any information in historical prices is reflected in stock prices Semi-Strong Form EMH All public information is reflected in stock prices Strong Form EMH All information, even inside info, is embedded in stock prices EMH

Return Total dollar return Total dollar return income from investment + capital gain (loss) income from investment + capital gain (loss) Percentage return Percentage return dividend yield + capital gains yield dividend yield + capital gains yield You bought a stock for $35 and you received dividends of $1.25. The stock now sells for $40. You bought a stock for $35 and you received dividends of $1.25. The stock now sells for $40. What is your dollar return? What is your dollar return? What is your percentage return? What is your percentage return?

Risk Returns generally are uncertain. The greater the chance of a return below the expected return, the greater the risk. Risk Premium Risk Premium “Extra” return earned for taking on risk “Extra” return earned for taking on risk Return above the risk free rate (Treasury bills are considered risk-free) Return above the risk free rate (Treasury bills are considered risk-free)

Probability Distribution Rate of return (%) Stock X Stock Y

Distribution of Annual Returns

Expected Returns Expected returns are based on the probabilities of possible outcomes Expected returns are based on the probabilities of possible outcomes “Expected” means average if the process is repeated many times “Expected” means average if the process is repeated many times

Example: Expected Returns What are the expected returns for Stocks C & T? What are the expected returns for Stocks C & T? StateProbabilityCT StateProbabilityCT Boom0.315%25% Boom0.315%25% Normal Normal Recession???21 Recession???21 R C = R C = R T = R T =

Variance and Standard Deviation Both measure the volatility of returns Both measure the volatility of returns Variance is the weighted average of squared deviations Variance is the weighted average of squared deviations Std. Dev. is the square root of the variance (σ) Std. Dev. is the square root of the variance (σ)

Example: Variance and Std. Dev. E(R C ) = 9.9%;E(R T ) = 17.7% E(R C ) = 9.9%;E(R T ) = 17.7% Stock C Stock C Stock T Stock T

Example StateProb. ABC, Inc. (%) StateProb. ABC, Inc. (%) Boom.2516 Boom.2516 Normal.508 Normal.508 Slowdown.155 Slowdown.155 Recession.10-3 Recession.10-3 What is the expected return, variance, and std dev? What is the expected return, variance, and std dev? E(R) = E(R) = Variance = Variance = Standard Deviation = Standard Deviation =

Portfolio Return & Variance

Example Evenly split investment between A & B Evenly split investment between A & B State Prob. A B State Prob. A B Boom.430%-5% Boom.430%-5% Bust.6-10%25% Bust.6-10%25% Expected return and standard deviation Expected return and standard deviation Each state Each state The portfolio The portfolio

Another Example StateProb.XZ StateProb.XZ Boom.2515%10% Boom.2515%10% Normal.6010%9% Normal.6010%9% Recession.155%10% Recession.155%10% What are the expected return and standard deviation for a portfolio with an investment of $6000 in asset X and $4000 in asset Z? What are the expected return and standard deviation for a portfolio with an investment of $6000 in asset X and $4000 in asset Z?

Types of Risk Systematic Systematic Risk factors that affect a large number of assets Risk factors that affect a large number of assets Non-diversifiable risk, Market risk Non-diversifiable risk, Market risk Unsystematic Unsystematic Risk factors affecting a limited number of assets Risk factors affecting a limited number of assets Unique risk, Asset-specific risk, Idiosyncratic risk Unique risk, Asset-specific risk, Idiosyncratic risk

Portfolio Diversification Investment in several different asset classes Investment in several different asset classes 50 internet stocks - not diversified 50 internet stocks - not diversified 50 stocks across 20 industries - diversified 50 stocks across 20 industries - diversified Can substantially reduce returns variability without reducing expected returns Can substantially reduce returns variability without reducing expected returns A minimum level of risk cannot be diversified away A minimum level of risk cannot be diversified away

Unsystematic Risk Diversifiable or unsystematic risk can be eliminated by combining assets into a portfolio Diversifiable or unsystematic risk can be eliminated by combining assets into a portfolio Total risk = systematic risk + unsystematic risk Total risk = systematic risk + unsystematic risk Std. dev. of returns measures total risk Std. dev. of returns measures total risk If diversified, unsystematic risk is very small If diversified, unsystematic risk is very small

Systematic Risk Reward for bearing risk Reward for bearing risk No reward for unnecessary risk No reward for unnecessary risk Beta (β) measures systematic risk Beta (β) measures systematic risk Relative to overall market Relative to overall market What does beta tell us? What does beta tell us? β =1: asset has ____systematic risk as the market β =1: asset has ____systematic risk as the market β < 1: asset has ____systematic risk than the market β < 1: asset has ____systematic risk than the market β > 1: asset has ____systematic risk than the market β > 1: asset has ____systematic risk than the market

Total versus Systematic Risk Std DevBeta Security C20%1.25 Security C20%1.25 Security K30%0.95 Security K30%0.95 Which has more total risk? Which has more total risk? Which has more systematic risk? Which has more systematic risk? Which should have the higher expected return? Which should have the higher expected return?

Example: Portfolio Betas SecurityWeightBeta A.22.7 A.22.7 B.30.2 B.30.2 C.12.0 C.12.0 D.41.5 D.41.5 What is the portfolio beta? What is the portfolio beta? β P = w 1 β 1 + w 2 β 2 + w 3 β 3 +… = β P = w 1 β 1 + w 2 β 2 + w 3 β 3 +… =

Beta and the Risk Premium Risk premium = expected return – risk-free rate Risk premium = expected return – risk-free rate Higher beta ~ higher risk premium Higher beta ~ higher risk premium Can estimate the expected return when we know this relationship Can estimate the expected return when we know this relationship

Beta & Returns RfRf E(R A ) AA 0% 5% 10% 15% 20% 25% 30% Beta Expected Return Slope = Rise / Run = (E(R A ) – R f ) / (  A – 0)

Reward to Risk Ratio Slope of beta & return relationship Slope of beta & return relationship Reward to risk ratio or the risk premium Reward to risk ratio or the risk premium What if an asset has a reward-to-risk ratio of 8 (asset plots above the line)? What if an asset has a reward-to-risk ratio of 8 (asset plots above the line)? What if an asset has a reward-to-risk ratio of 7 (asset plots below the line)? What if an asset has a reward-to-risk ratio of 7 (asset plots below the line)?

Security Market Line SML represents market equilibrium SML represents market equilibrium In equilibrium, all assets and portfolios must have the same reward-to-risk ratio In equilibrium, all assets and portfolios must have the same reward-to-risk ratio SML slope is the reward-to-risk ratio: SML slope is the reward-to-risk ratio: (E(R M ) – R f ) /  M = E(R M ) – R f = mkt risk premium (E(R M ) – R f ) /  M = E(R M ) – R f = mkt risk premium

SML r (%) bibi Risk Compensation Riskfree Rate Market Risk Premium Premium for Riskier Stock 1.9

Capital Asset Pricing Model CAPM - relationship between risk and return CAPM - relationship between risk and return E(R A ) = R f +  A (E(R M ) – R f ) E(R A ) = R f +  A (E(R M ) – R f ) Risk free rate Risk free rate Return for bearing systematic risk Return for bearing systematic risk Amount of systematic risk Amount of systematic risk If we know an asset’s systematic risk, we can use the CAPM to determine its expected return If we know an asset’s systematic risk, we can use the CAPM to determine its expected return

r (%) b New SML Δ Inflation = 2% Impact of Inflation on SML Original SML

r M = 18% r M = 15% SML 1 r (%) SML 2 : Increased Risk Aversion Risk, β Δ RP M = 3% Impact of Risk Aversion on SML

Example - CAPM If the risk-free rate is 3% and the market risk premium is 8%, what is the expected return for each? If the risk-free rate is 3% and the market risk premium is 8%, what is the expected return for each? SecurityBeta A2.7 B0.4 C2.1 D1.6 Expected Return 3% + 2.7*8% 3% + 0.4*8% 3% + 2.1*8% 3% + 1.6*8%

New Example If the risk-free rate is 4% and the market risk premium is 6%, what is the expected return for each? If the risk-free rate is 4% and the market risk premium is 6%, what is the expected return for each? SecurityBeta Expected Return A2.0 B0.8