Chapter 7 – Risk, Return and the Chapter 7 – Risk, Return and the Security Market LineSecurity Market Line

Learning ObjectivesLearning Objectives Calculate Profit and Returns Calculate Profit and Returns Convert Holding Period Returns (HPR) to APRConvert Holding Period Returns (HPR) to APR Appreciate historical returnsAppreciate historical returns Calculate standard deviations and variancesCalculate standard deviations and variances Calculate standard deviations with future dataCalculate standard deviations with future data Understand risk and return tradeoffUnderstand risk and return tradeoff Interpret risk and return tradeoffInterpret risk and return tradeoff Discover how to remove some riskDiscover how to remove some risk Understand diversificationUnderstand diversification Explain systematic and unsystematic riskExplain systematic and unsystematic risk Understand Beta and what it measuresUnderstand Beta and what it measures

ReturnsReturns

Calculating a returnCalculating a return Dollar ReturnDollar Return

Ending Value + Distributions – Original CostEnding Value + Distributions – Original Cost Example 7.1, Bought Trading Card for $50 and Example 7.1, Bought Trading Card for $50 and

sold it for $55, Dollar Return (Profit) $5sold it for $55, Dollar Return (Profit) $5 Percentage ReturnPercentage Return

[(Ending Value + Distributions) / Original Cost] – 1[(Ending Value + Distributions) / Original Cost] – 1 Example 7.1, [$55 +$0 / $50] - 1 = 10%Example 7.1, [$55 +$0 / $50] - 1 = 10%

Calculating a return with distributionsCalculating a return with distributions Example 7.1, Stock with dividendExample 7.1, Stock with dividend [($47.82 + $0.90) / $42.00] – 1 = 16%[($47.82 + $0.90) / $42.00] – 1 = 16%

Holding Period ReturnsHolding Period Returns

Holding Period Returns (HRP)Holding Period Returns (HRP) The return for the length of time that investment is The return for the length of time that investment is

heldheld Not consistent with interest rates from Chapter 4Not consistent with interest rates from Chapter 4 Need to convert to annual basis for comparisonNeed to convert to annual basis for comparison

Annualized return = (1 + HRP)Annualized return = (1 + HRP)1/n1/n – 1 – 1 Warning on extrapolation of holding period Warning on extrapolation of holding period

returns for less than a yearreturns for less than a year Compounding requires each additional investment Compounding requires each additional investment

period with same holding period returnperiod with same holding period return

Risk as UncertaintyRisk as Uncertainty

Risk is the uncertainty in the outcome of an Risk is the uncertainty in the outcome of an event (potential good and bad outcomes)event (potential good and bad outcomes)

An event where the outcome is known before An event where the outcome is known before the event is free of uncertainty or risk-freethe event is free of uncertainty or risk-free

Trading Card could go down in value over timeTrading Card could go down in value over time Bought at $50 but sell at $41.50Bought at $50 but sell at $41.50 Return = [($41.50 - $50.00) / $50.00] -1 = -17%Return = [($41.50 - $50.00) / $50.00] -1 = -17%

Holding period return loss of -17% (bad Holding period return loss of -17% (bad outcome)outcome)

Historical ReturnsHistorical Returns

Year by Year Returns (See Table 7.1)Year by Year Returns (See Table 7.1) Four different investmentsFour different investments

3-Month Treasury Bill3-Month Treasury Bill Long-Term Government BondsLong-Term Government Bonds Large Company StocksLarge Company Stocks Small Company StocksSmall Company Stocks

What do we notice?What do we notice? Large Swings from year to yearLarge Swings from year to year Most consistent performer, 3-Month TreasuryMost consistent performer, 3-Month Treasury

Relationship of average return and standard Relationship of average return and standard deviation – first look at risk and return tradeoffdeviation – first look at risk and return tradeoff

Measuring Risk Using Variance Measuring Risk Using Variance

Measure of the swing from year to year: Measure of the swing from year to year: Variance Variance ((σσ22))

Greater the variance the greater the potential Greater the variance the greater the potential outcomesoutcomes

Standard Deviation (Standard Deviation (σσ) = Variance) = Variance1/21/2 [( [(σσ22))1/21/2]]

Historical Returns and VariancesHistorical Returns and Variances

Four Financial InstrumentsFour Financial Instruments Highest Return and Highest Variance – Small Highest Return and Highest Variance – Small

StocksStocks Lowest Return and Lowest Variance – U.S. Lowest Return and Lowest Variance – U.S.

Treasury BillTreasury Bill See Figure 7.3 page 196See Figure 7.3 page 196

Linear relationship of risk and returnLinear relationship of risk and return The greater the return the greater the varianceThe greater the return the greater the variance Relationship of risk and returnRelationship of risk and return

Returns in an Uncertain WorldReturns in an Uncertain World

Investments or bets are made prior to the Investments or bets are made prior to the eventevent

Need to calculate the expected outcome of Need to calculate the expected outcome of the eventthe event Need the list of all potential outcomesNeed the list of all potential outcomes Need the chance of each potential outcomeNeed the chance of each potential outcome

Expected Return = Expected Return = ΣΣ outcome outcomeii x probability x probabilityii

Payoff or return for investment is the outcomePayoff or return for investment is the outcome Example 7.3, Expected Return on a bondExample 7.3, Expected Return on a bond

Example 7.3 Example 7.3

States of the Economy (World)States of the Economy (World) Four potential economic statesFour potential economic states Each has positive probabilityEach has positive probability Bond has different “outcome” in each stateBond has different “outcome” in each state

Expected return is weighed averageExpected return is weighed average 15% x 2% + 45% x 5% + 30% x 8% + 10% x 10%15% x 2% + 45% x 5% + 30% x 8% + 10% x 10% On average we expect 5.95% returnOn average we expect 5.95% return

Variance uses same probabilities of the states of Variance uses same probabilities of the states of the economythe economy

Risk and Return TradeoffRisk and Return Tradeoff

Objective: Maximize Return and Minimize RiskObjective: Maximize Return and Minimize Risk Must tradeoff increases in risk and return with Must tradeoff increases in risk and return with

decreasing risk and returndecreasing risk and return Investment Rule #1 – Two assets with same expected Investment Rule #1 – Two assets with same expected

return, pick one with lower riskreturn, pick one with lower risk Investment Rule #2 – Two assets with the same risk, Investment Rule #2 – Two assets with the same risk,

pick one with higher returnpick one with higher return What to do when one investment has both What to do when one investment has both

higher return and more risk versus another higher return and more risk versus another asset?asset?

Must look to individual choiceMust look to individual choice

Diversification – Eliminating RiskDiversification – Eliminating Risk

Don’t put all your eggs in one basketDon’t put all your eggs in one basket Spread out your investment over a series of Spread out your investment over a series of

investmentsinvestments If a “bad outcome” should hit one investment a “good If a “bad outcome” should hit one investment a “good

outcome” in another investment could offset the bad outcome” in another investment could offset the bad outcomeoutcome

Combining Zig and ZagCombining Zig and Zag When one is up the other downWhen one is up the other down Consistent return from period to period Consistent return from period to period

Spreading investment lowers riskSpreading investment lowers risk

When Diversification WorksWhen Diversification Works

Co-movement of stock returnsCo-movement of stock returns Correlation CoefficientCorrelation Coefficient Covariance of two assets divided by their standard Covariance of two assets divided by their standard

deviations (equation 7.10)deviations (equation 7.10)

Positive Correlation Positive Correlation No benefit if perfectly positively correlatedNo benefit if perfectly positively correlated Example Peat and Repeat CompaniesExample Peat and Repeat Companies

Negative CorrelationNegative Correlation Eliminate all risk if perfectly negatively correlatedEliminate all risk if perfectly negatively correlated Example Zig and Zag CompaniesExample Zig and Zag Companies

Systematic and Unsystematic RiskSystematic and Unsystematic Risk

Systematic Risk – risk you cannot avoidSystematic Risk – risk you cannot avoid Unsystematic Risk – risk you can avoidUnsystematic Risk – risk you can avoid Adding more and more stocksAdding more and more stocks

As you add more stocks to portfolio you reduce more As you add more stocks to portfolio you reduce more of the unsystematic or firm-specific riskof the unsystematic or firm-specific risk

Marginal decline in eliminationMarginal decline in elimination Around 25 to 30 stocks can eliminate nearly all Around 25 to 30 stocks can eliminate nearly all

unsystematic riskunsystematic risk

Variance or Standard Deviation is measure of Variance or Standard Deviation is measure of both systematic and unsystematic riskboth systematic and unsystematic risk

Beta – Measure of Risk in a Beta – Measure of Risk in a PortfolioPortfolio

Using Beta for finding the risk of a portfolioUsing Beta for finding the risk of a portfolio In a well diversified portfolio only systematic risk In a well diversified portfolio only systematic risk

remainsremains Systematic risk of portfolio is weighted betasSystematic risk of portfolio is weighted betas

Example 7.4 (Henry and Rosie’s Betas)Example 7.4 (Henry and Rosie’s Betas) Henry average risk and beta is 1.0Henry average risk and beta is 1.0

0.25 x 0.8 + 0.25 x 1.2 + 0.25 x 0.6 + 0.25 x 1.40.25 x 0.8 + 0.25 x 1.2 + 0.25 x 0.6 + 0.25 x 1.4

Rosie is slightly conservative (investments) and beta Rosie is slightly conservative (investments) and beta is 0.94is 0.94 0.35 x 0.8 + 0.15 x 1.2 + 0.30 x 0.6 + 0.20 x 1.40.35 x 0.8 + 0.15 x 1.2 + 0.30 x 0.6 + 0.20 x 1.4

Using BetaUsing Beta

Beta FactsBeta Facts Beta of zero means no risk (i.e. T-Bill)Beta of zero means no risk (i.e. T-Bill) Beta of 1 means average risk (same as market risk)Beta of 1 means average risk (same as market risk) Beta < 1, risk lower than marketBeta < 1, risk lower than market Beta > 1, risk greater than marketBeta > 1, risk greater than market

Expected Return and Beta use asset weights in Expected Return and Beta use asset weights in portfolio for portfolio e(r) and portfolio for portfolio e(r) and ββ Expected Return = Expected Return = ΣΣ w wii x return x returnii

Beta = Beta = ΣΣ w wii x x ββii

Using BetaUsing Beta

Beta also determines expected return of Beta also determines expected return of individual assetindividual asset Known, risk-free rateKnown, risk-free rate Estimate, expected return on marketEstimate, expected return on market Each asset’s expected return function of its risk as Each asset’s expected return function of its risk as

measured by beta and the risk-reward tradeoff (slope measured by beta and the risk-reward tradeoff (slope of SML)of SML)

Company: A Portfolio of ProjectsCompany: A Portfolio of Projects

All companies are a portfolio of individual All companies are a portfolio of individual projects (or products and services)projects (or products and services)

Concept of portfolio helps explainConcept of portfolio helps explain Viewing each project or product with different level of Viewing each project or product with different level of

risk (project risk (project ββ) and contribution (expected return)) and contribution (expected return) Different project or product combinations can lower Different project or product combinations can lower

overall risk of the firmoverall risk of the firm

Projects plotting above the SML (buy)Projects plotting above the SML (buy) Projects plotting below the SML (sell)Projects plotting below the SML (sell)

Risk and Return in a Portfolio that Risk and Return in a Portfolio that is Not Well Diversifiedis Not Well Diversified

George Jetson investing choiceGeorge Jetson investing choice Only four assets in portfolio (equally weighted)Only four assets in portfolio (equally weighted) Expected return = 9.35%Expected return = 9.35% Standard Deviation = 4.29%Standard Deviation = 4.29% Weighted average standard deviations of four assets Weighted average standard deviations of four assets

= 4.4%= 4.4%

Little benefit from diversificationLittle benefit from diversification Portfolio needs more assets for benefits of Portfolio needs more assets for benefits of

diversificationdiversification

Security Market LineSecurity Market Line

AssumptionsAssumptions #1 – There is a reward for waiting#1 – There is a reward for waiting #2 – The greater the risk the greater the #2 – The greater the risk the greater the

expected rewardexpected reward #3 – There is a constant tradeoff between risk #3 – There is a constant tradeoff between risk

and rewardand reward E(return) = risk-free rate + slope (level of risk)E(return) = risk-free rate + slope (level of risk) Trick is to find the level of risk for an investment Trick is to find the level of risk for an investment

and the reward for riskand the reward for risk

CAPMCAPM Capital Asset Pricing Model (CAPM)Capital Asset Pricing Model (CAPM)

Expected return of an asset is a function ofExpected return of an asset is a function of The time value of moneyThe time value of money Reward for taking on riskReward for taking on risk Amount of riskAmount of risk

Security Market Line is application of CAPMSecurity Market Line is application of CAPM All firms plot on SML (ex-ante)All firms plot on SML (ex-ante)

Firms above the line are under pricedFirms above the line are under priced Firms below the line are over pricedFirms below the line are over priced

Security Market Line estimates expected returnsSecurity Market Line estimates expected returns

Applications of SMLApplications of SML

Two assets on the SML (two points)Two assets on the SML (two points) Find slope (reward for risk)Find slope (reward for risk) Find intercept (risk-free rate)Find intercept (risk-free rate) Equation of the line in general formEquation of the line in general form

Assets plotting off the lineAssets plotting off the line Find the “expected return” for the level of riskFind the “expected return” for the level of risk If the anticipated return is greater than the If the anticipated return is greater than the

expected return for that level of risk (asset expected return for that level of risk (asset plots above the line), buy assetplots above the line), buy asset

If return less, plots below the line, sell assetIf return less, plots below the line, sell asset

HomeworkHomework

Problem 6 –ReturnsProblem 6 –Returns Problem 12 – Variance and Standard DeviationProblem 12 – Variance and Standard Deviation Problem 15 – Portfolio Expected ReturnProblem 15 – Portfolio Expected Return Problem 16 – Portfolio Expected Variance and Problem 16 – Portfolio Expected Variance and

Standard DeviationStandard Deviation Problem 24 – SML applicationProblem 24 – SML application Problem 30 – SML applicationProblem 30 – SML application Problem 32 – Combining AssetsProblem 32 – Combining Assets