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Portfolio ConstructionSlide 2Slide 3Portfolio Construction within the larger context of asset allocationSlide 5Slide 6Mean Variance OptimizationSlide 8MVO: One risky and one risk-free assetSlide 10Slide 11MVO: Two risky assetsSlide 13Slide 14Slide 15Slide 16Slide 17MVO: Two risky and one risk-free assetSlide 19MVO: All risky assets (market) and one risk-free assetInvestor Risk Tolerance and CMLPortfolio Possibilities Combining the Risk-Free Asset and Risky Portfolios on the Efficient FrontierAssumptions / Limitations of Markowitz Portfolio TheorySlide 24Slide 25Practical Application of MVOSlide 27Slide 28Slide 29Slide 30Slide 31ReadingsPortfolio Construction01/26/092Portfolio Construction•Where does portfolio construction fit in the portfolio management process? •What are the foundations of Markowitz’s Mean-Variance Approach (Modern Portfolio Theory)? Two-asset to multiple asset portfolios.•How do we construct optimal portfolios using Mean Variance Optimization? Microsoft Excel Solver.3Portfolio Construction•How do we incorporate IPS requirements to determine asset class weights?•What are the assumptions and limitations of the mean-variance approach?•How do we reconcile portfolio construction in practice with Markowitz’s theory?4Portfolio Construction within the larger context of asset allocation•IPS provides us with the risk tolerance and return expected by the client•Capital Market Expectations provide us with an understanding of what the returns for each asset class will be5Portfolio Construction within the larger context of asset allocationC1: CapitalMarket ConditionsI1: Investor’s Assets,Risk AttitudesC2: PredictionProcedureC3: Expected Ret,Risks, CorrelationsI2: Investor’s RiskTolerance FunctionI3: Investor’s RiskToleranceM1: OptimizerM2: Investor’sAsset MixM3: Returns6Portfolio Construction within the larger context of asset allocation•Optimization, in general, is constructing the best portfolio for the client based on the client characteristics and CMEs.•When all the steps are performed with careful analysis, the process may be called integrated asset allocation.7Mean Variance Optimization•The Mean-Variance Approach, developed by Markowitz in the 1950s, still serves as the foundation for quantitative approaches to strategic asset allocation.•Mean Variance Optimization (MVO) identifies the portfolios that provide the greatest return for a given level of risk OR that provide the least risk for a given return.8Mean Variance Optimization•TO develop an understanding of MVO, we will derive the relationship between risk and return of a portfolio by looking at a series of three portfolios:•One risky asset and one risk-free asset•Two risky assets•Two risky assets and one risk-free asset•We will then generalize our findings to portfolios of a larger number of assets.9MVO: One risky and one risk-free asset•For a portfolio of two assets, one risky (r) and one risk-free (f), the expected portfolio return is defined as:•Since, by definition, the risk-free asset has zero volatility (standard deviation), the portfolio standard deviation is:frrrPRwREwRE *)1()(*)( rrPw*10MVO: One risky and one risk-free asset•With the portfolio return and standard deviation equations, we can derive the Capital Allocation Line (CAL):•Notice that the slope of this line represent the Sharpe ratio for asset r. It represents the reward-to-risk ratio for asset r.prfrfPRRERRE*])([)(11MVO: One risky and one risk-free asset•With one risky and one risk-free asset, an investor can select a portfolio along this CAL based on his risk / return preference.12MVO: Two risky assets•With two risky assets (1 and 2), as long as the correlation between the two assets is less than 1, creating a portfolio with the two assets will allow the investor to obtain a greater reward-to-risk ratio than either of the two assets provide.13MVO: Two risky assets•Portfolio expected return and standard deviation can be calculated as follows:)(*)(*)(2211REwREwREP122121222221212wwwwP121 ww 14MVO: Two risky assets•Remember that the correlation coefficient can be calculated as:Where and n = number of historical returns used in the calculations.212,112CovniiiRRRRnCov122112,1))((1115MVO: Two risky assets•These values (as well as asset returns and standard deviations) can be easily calculated on a financial calculator or Excel.16MVO: Two risky assets•By altering weights in the two assets, we can construct a minimum-variance frontier (MVF).•The turning point on this MVF represents the global minimum variance (GMV) portfolio. This portfolio has the smallest variance (risk) of all possible combinations of the two assets.•The upper half of the graph represents the efficient frontier.17MVO: Two risky assets•The weights for the GMV portfolio is determined by the following equations:1221222112212212w121 ww 18MVO: Two risky and one risk-free asset•We know that with one risky asset and the risk-free asset, the portfolio possibilities lie on the CAL. •With two risky assets, the portfolio possibilities lie on the MVF.•Since the slope of the CAL represents the reward-to-risk ratio, an investor will always want to choose the CAL with the greatest slope.19MVO: Two risky and one risk-free asset•The optimal risky portfolio is where a CAL is tangent to the efficient frontier. •This portfolio provides the best reward-to-risk ratio for the investor.•The tangency portfolio risky asset weights can be calculated as: 2,1212122212,122211*)()(*)(*)(*)(*)(CovrRErRErRErRECovrRErREwffffff20MVO: All risky assets (market) and one risk-free asset•We can generalize our previous results by considering all risky assets and one risk-free asset. The tangency (optimal risky) portfolio is the market portfolio. All investors will hold a combination of the risk-free asset and this market portfolio.•In this context, the CAL is referred to as the Capital Market Line (CML).21Investor Risk Tolerance and CML•To attain a higher expected return than is available at the market portfolio (in exchange for accepting higher risk), an investor can borrow at the risk free-rate.•Other minimum variance portfolios (on the efficient frontier) are not considered.22Portfolio Possibilities

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