Chapter 5 Risk and ReturnReturnsHolding Period ReturnsHistorical ReturnsRisk Using Variance or Standard DeviationsRisk as UncertaintyReturns in an Uncertain WorldSlide 8Risk and Return TradeoffProblemsChapter 5Chapter 5Risk and ReturnRisk and ReturnReturnsReturnsDollar and PercentageDollar and PercentageHolding Period ReturnsHolding Period ReturnsConverting to Annual ReturnsConverting to Annual ReturnsHistorical ReturnsHistorical ReturnsRisk using Variance or Standard DeviationRisk using Variance or Standard DeviationRisk as UncertaintyRisk as UncertaintyReturns in an Uncertain WorldReturns in an Uncertain WorldRisk and Return TradeoffRisk and Return TradeoffReturnsReturnsCalculating a returnCalculating a returnDollar ReturnDollar ReturnEnding Value + Distributions – Original CostEnding Value + Distributions – Original CostExample 5.1, Bought Trading Card for $5.00 and Example 5.1, Bought Trading Card for $5.00 and sold it for $6.25, Dollar Return (Profit) $1.25sold it for $6.25, Dollar Return (Profit) $1.25Percentage ReturnPercentage Return[(Ending Value + Distributions) / Original Cost] – 1[(Ending Value + Distributions) / Original Cost] – 1Example 5.1, $1.25 / $5.00 = 25%Example 5.1, $1.25 / $5.00 = 25%Calculating a return with distributionsCalculating a return with distributionsExample 5.2, Stock with dividendExample 5.2, Stock with dividendHolding Period ReturnsHolding Period ReturnsHolding 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 heldheldNot consistent with interest rates from Chapter 4Not consistent with interest rates from Chapter 4Need to convert to annual basis for comparisonNeed to convert to annual basis for comparisonAnnualized return = (1 + HRP)Annualized return = (1 + HRP)nn – 1 – 1Warning on extrapolation of holding period Warning on extrapolation of holding period returns for less than a yearreturns for less than a yearCompounding requires each additional investment Compounding requires each additional investment period with same holding period returnperiod with same holding period returnHistorical ReturnsHistorical ReturnsYear by Year ReturnsYear by Year ReturnsFour different investmentsFour different investments3-Month Treasury3-Month TreasuryLong-Term Government BondsLong-Term Government BondsLarge Company StocksLarge Company StocksSmall Company StocksSmall Company StocksLarge Swings from year to yearLarge Swings from year to yearMost consistent performer, 3-Month TreasuryMost consistent performer, 3-Month TreasuryRelationship 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 tradeoffRisk Using Variance orRisk Using Variance orStandard DeviationsStandard DeviationsMeasure of the swing from year to year: Measure of the swing from year to year: Variance or Standard DeviationVariance or Standard DeviationGreater the variance or standard deviation the Greater the variance or standard deviation the greater the potential outcomesgreater the potential outcomesStandard Deviation (Standard Deviation (σσ) = Variance) = Variance1/21/2 ( (σσ22))Normal Distribution helps explain probability of Normal Distribution helps explain probability of a potential outcomea potential outcome 12naveragexxVaria nc eiRisk as UncertaintyRisk as UncertaintyRisk is the uncertainty in the outcome of an Risk is the uncertainty in the outcome of an eventeventAn 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-freeExample of a horse raceExample of a horse raceBefore the race, all horses entered in the race have a Before the race, all horses entered in the race have a chance to winchance to winHowever, some have a better chance to win than However, some have a better chance to win than othersothersStandard Deviation will be one measure of riskStandard Deviation will be one measure of riskReturns in an Uncertain WorldReturns in an Uncertain WorldInvestments or bets are made prior to the Investments or bets are made prior to the eventeventNeed to calculate the expected outcome Need to calculate the expected outcome of the eventof the eventNeed the list of all potential outcomesNeed the list of all potential outcomesNeed the chance of each potential outcomeNeed the chance of each potential outcomeExpected Return = Expected Return = ΣΣ outcome outcomeii x probability x probabilityiiPayoff or return for investment is the outcomePayoff or return for investment is the outcomeReturns in an Uncertain WorldReturns in an Uncertain WorldVariance or Standard Deviation in Uncertain Variance or Standard Deviation in Uncertain WorldWorldNeed the probabilities of all outcomesNeed the probabilities of all outcomesNeed the expected outcomeNeed the expected outcomeΣΣ(outcome(outcomeii – expected outcome) x probability – expected outcome) x probabilityiiExample 5.3 – Expected Return of Long BondExample 5.3 – Expected Return of Long BondFour potential outcome (states of the world)Four potential outcome (states of the world)Probability of each outcome known (or estimated)Probability of each outcome known (or estimated)Calculate expected return of 6.35%Calculate expected return of 6.35%Calculate variance of 0.7275% or standard deviation Calculate variance of 0.7275% or standard deviation of 0.8529%of 0.8529%Risk and Return TradeoffRisk and Return TradeoffObjective: Maximize Return and Minimize RiskObjective: Maximize Return and Minimize RiskMust tradeoff increases risk and return with Must tradeoff increases risk and return with decreasing risk and returndecreasing risk and returnInvestment 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 riskInvestment 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 returnWhat to do when one investment has both What to do when one investment has both higher return and more risk versus
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