# II: Portfolio Theory I 2: Measuring Portfolio Return 3: Measuring Portfolio Risk 4: Diversification

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Introduction to Financial Markets

II: Portfolio Theory I 2: Measuring Portfolio Return3: Measuring Portfolio Risk4: Diversification

Return & Risk Oltheten & Waspi 2012Markets are efficient only if return exactly compensates for risk Chapter 2: Measuring Portfolio ReturnMeasuring Portfolio ReturnHolding Period ReturnCash Flow Adjusted Rate of ReturnTime Weighted versus Statistical Rates of ReturnInternal Rate of Return Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnHolding Period Return\$2,400,000 = \$1.20 = \$1 + 20%\$2,000,000\$1,600,000 = \$0.80 = \$1 - 20%\$2,000,000For every \$ you started with you now have \$1.20\$ you started with+ 20%For every \$ you started with you now have only \$0.80\$ you started with- 20%Chapter 2: Measuring Portfolio ReturnHolding Period ReturnWhen you use the alternate formula you are subtracting out the \$ you started with at the very beginning\$2,400,000 - \$2,000,000 = 1.20 1 = .20 = +20% \$2,000,000\$\$ you started with\$ you started with Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnCash Flow Adjusted Rate of ReturnWe want to measure investment returnsWe adjust so that the rate of return is not distorted by cash flows over which the investment manager has no control.

Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnCash Flow Adjusted Rate of ReturnEach Investment Manger began the month of September with \$1million. At the end of the monthAlice: \$1m to \$1.56 millionBob: \$1m to \$1.54 millionCarol: \$1m to \$1.50 million Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnCash Flow Un-adjustedSlope of 50% Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnCash Flow AdjustedEach investment manager received an additional \$300,000 from the client during the monthAlice: before the open on the firstBob: on the tenthCarol: after the close on the thirtiethCannot measure as a rate of return any money that the investment manager did not generate. Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnCash Flow Adjusted Rate of ReturnAlice:

Bob:

Carol:

Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnCash Flow Adjusted Slope of 20% not 50% Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnCash Flow AdjustedDecember 31Market Value:\$34,978,567.03January 3:Bond Income:\$14,400.00January 15:Pension contribution:\$3,098.10January 18:Bond Income:\$600.00January 21:Pension Payments- \$9,879.20January 22:Dividend received\$1,700.00January 31:Pension contribution\$3,098.10January 31Market Value\$34,993,897.09 Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnTime-Weighted verses StatisticalTime Weighted:combines time periods using Geometric totals and averages

Statistical: combines time periods using arithmetic totals and averages Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnTime-Weighted verses StatisticalJanuary February March April May June- 50% +50% -50% +50% -50% +50%Six month return = ? Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnStatisticalTotal Return =

Average Return = Variance =

Standard Deviation = Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnStatisticalStatistical returns assume that the return in one month is independent of the returns of any other month. February April JuneJanuary March May - 50%- 50%- 50%+ 50%+ 50%+ 50%\$1,000,000 Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnTime-WeightedTotal Return =

Average Return = Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnTime-WeightedTime Weighted returns assume that returns in one month are reinvested in the following month\$421,875\$1,000,000\$500,000\$281,250\$750,000\$375,000\$562,500January February March April May June- 13.4%

Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnTime-Weighted = Holding PeriodIn the absence of excluded cash flows, time weighted returns equal holding period returns.\$421,875\$1,000,000\$500,000\$281,250\$750,000\$375,000\$562,500January February March April May June- 13.4%

Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnInternal Rate of ReturnInternal rate of return (IRR) is the rate of return that renders the Net Present Value (NPV) equal to zero. Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnInternal Rate of ReturnDec 31, 2012 Dec 31, 2013 Dec 31, 2014 Dec 31, 2015 Dec 31, 2016 -\$10,000 +\$510 +\$2,000 +\$4,500 +5,000 Oltheten & Waspi 2012IRR = 6%Chapter 2: Measuring Portfolio ReturnIn Summary: Measuring ReturnHolding Period Rate of ReturnCash Flow Adjusted Rate of ReturnTime Weighted vs Statistical Rates of ReturnInternal Rate of Return Oltheten & Waspi 2012Chapter 2: Measuring Portfolio ReturnMeasuring RiskRisk versus UncertaintyStandard Deviation ()Coefficient of Variation (CV)Beta () Oltheten & Waspi 2012Chapter 3: Measuring Portfolio RiskRisk vs UncertaintyIn this example there is risk but no uncertainty

Oltheten & Waspi 2012Chapter 3: Measuring Portfolio RiskRisk vs UncertaintyStock returns are normally distributed (more or less) so there is risk, but there is still uncertainty5 sigma eventr~ N(0, 1) Oltheten & Waspi 2012Chapter 3: Measuring Portfolio RiskIn the normal distribution 99.74% of the observationsare within 3standard deviationsof the mean.Standard Deviation Oltheten & Waspi 2012Chapter 3: Measuring Portfolio RiskStandard DeviationEasy to visualizeProbability of making a lossProbability of making a loss Oltheten & Waspi 2012Chapter 3: Measuring Portfolio RiskCoefficient of Variation Risk per unit of ReturnCV = . E[R]

Oltheten & Waspi 2012Chapter 3: Measuring Portfolio RiskCoefficient of VariationIs the added return worth the added risk? Oltheten & Waspi 2012Chapter 3: Measuring Portfolio RiskBetaCaptures Market Risk(Market Model)We will generate the market model through our discussion of diversification Oltheten & Waspi 2012Chapter 3: Measuring Portfolio RiskIn Summary: Measuring RiskRisk versus UncertaintyStandard DeviationCoefficient of VariationBeta Oltheten & Waspi 2012Chapter 3: Measuring Portfolio RiskRisk PreferencesRisk AverseInvestors accept risk only if they are compensatedRisk NeutralInvestors are blind to risk and simply choose the highest expected returnRisk LovingInvestors actually derive utility from risky behavior (like gambles) Oltheten & Waspi 2012Chapter 3: Measuring Portfolio RiskDiversificationDiversification reduces risk exposure when returns are imperfectly correlated.Covariance & Correlation (review) Oltheten & Waspi 2012Chapter 4: DiversificationCovarianceExpectations vs ActualStocks: =11%, =14.3062Bonds: =7%, =8.1650 Oltheten & Waspi 2012Chapter 4: DiversificationCovarianceDeviations for the expected valueStocks: =11%, =14.3062Bonds: =7%, =8.1650 Oltheten & Waspi 2012Chapter 4: DiversificationCovarianceVariance = average squared deviation:Covariance = average product of the deviations:

StocksBondsCombinedSquared DeviationDevDeviation2DevDeviation217%289-10%10017% * -10% = -170%1%10%01% * 0% = 0% -18%32410%100-18% * 10% = -180% = =2 =2 = Covariance = = = Oltheten & Waspi 2012Chapter 4: DiversificationCorrelation= Covariance (Stocks, Bonds) (Stocks) (Bonds)

= = = 0Ocean Waves = +1Scaffold = -1Teeter-Totter Oltheten & Waspi 2012Chapter 4: DiversificationPortfolio Risk & ReturnPortfolio Returnweighted average return of components= w1 r1 + w2 r2 Portfolio VarianceWeighted variance of components adjusted for the correlation coefficient= w1212 + 2(w111,2w22) + w2222

Oltheten & Waspi 2012Chapter 4: DiversificationPortfolio Risk & Return: an exampleA portfolio of two stocksTardis Intertemporal E[r] = 15% = 20%Hypothetical ResourcesE[r] = 21% = 40%r = 0.30

Oltheten & Waspi 2012Chapter 4: DiversificationEfficient Portfolio Frontier Oltheten & Waspi 2012Chapter 4: DiversificationEfficient Portfolio Frontier (=0.3) Oltheten & Waspi 2012Chapter 4: DiversificationEfficient Portfolio Frontier Oltheten & Waspi 2012Chapter 4: DiversificationEfficient Portfolio Frontier (=0.3)rf = 10% Oltheten & Waspi 2012Chapter 4: DiversificationLimits of DiversificationUnsystematic RiskIndustry or firm specific can be diversified awaySystematic RiskEconomy wide - cannot be diversified away Oltheten & Waspi 2012Chapter 4: DiversificationII: Portfolio Theory I