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## Investment Portfolios Striking Facts about

Asbury College, US has reference to this Academic Journal, September 14, 2015Onassis Lecture1Why Traditional Asset Allocation Overstates the Benefits of Diversification Onassis Prize Lecture 2015Cass Business School, LondonSeptember 14, 2015Based on ?Volatility, Correlation, in addition to Diversification in a Multi-Factor World,? Journal of Portfolio Management, Winter 2013Striking Facts about Investment PortfoliosEven really well-diversified portfolios are quite volatileThe volatility of a large positively-weighted portfolio such as the S&P 500 is typically about 50% as high as the average volatility of its constituentsWell-diversified portfolios areHighly correlated within the same asset classMuch less correlated across asset classesFixed-Income vs. Equities vs. CommoditiesAcross broad country indexesAcross industry sectorsSeptember 14, 2015Onassis Lecture2EmpiricallyFor example, in the decade 2001-2010S&P500 had monthly standard deviation of 16.3%; it?s constituent equities averaged 36.1%Correlations: S&P500 in addition to Barclay?s Bond Aggregate: -0.0426S&P500 in addition to GS Commodities: 0.266Barclay?s Bonds in addition to GS Commodities: 0.0113This is typical of most decades in addition to indexes in developed countriesSeptember 14, 2015Onassis Lecture3

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These Empirical Regularities ImplyThere are common underlying systematic influences, or risk drivers, or ?factors? that limit diversification within an asset class; otherwise diversified portfolios would have much smaller volatilitiesThere are multiple systematic factors; otherwise diversified portfolios would be more correlated across asset classes, countries, in addition to sectorsThis explains why multi-factor strategies have recently become so ubiquitous among sophisticated investorsSeptember 14, 2015Onassis Lecture4Asset AllocationAsset allocationDetermines weightings across asset classes, or industry sectors, or countriesThe practical mechanismAllocates among portfolios (e.g., indexes) that are already diversified across individual assetsExample: 60% equities (FTSE index), 40% bonds (Barclay?s index)September 14, 2015Onassis Lecture5Benefits of DiversificationFollowing Markowitz, diversification has long been thought so that be most effective when assets or portfolios are not very correlatedBut, I claim, low correlation between returns on portfolios of assets can fail so that properly measure the potential benefits of diversificationTo understand the reason, we must first understand correlations among portfolios that are driven by the same underlying multiple factors but alongside differing sensitivities (or ?loadings?) on those factorsSeptember 14, 2015Onassis Lecture6

Correlation in addition to Multiple FactorsFor illustration, imagine a world where ALL asset returns are determined at time t by the simplest multi-factor model, just two factors, f1 in addition to f2, driving every asset, i, through sensitivities, ?i,1 in addition to ?i,2, in addition to alongside idiosyncratic risk ?i,tRi,t = Ei + ?i,1 f1,t + ?i,2 f2,t + ?i,t(Ei is the mean return on asset i, while the factors in addition to ? have zero means.)September 14, 2015Onassis Lecture7Correlations of perfectly-diversified portfoliosSuppose that two portfolios, A in addition to B, are being considered in consideration of an asset allocation in addition to that both are so well-diversified that they have negligible remaining idiosyncratic volatility; RA,t = EA + ?A,1 f1,t + ?A,2 f2,tRB,t = EB + ?B,1 f1,t + ?B,2 f2,tDespite both being perfectly diversified, A in addition to B will be perfectly correlated if in addition to only if their ?s are proportional; i.e., if in consideration of some k?0 both ?A,1=k?B,1 in addition to ?A,2=k?B,2 (The formal proof relies on the Cauchy inequality)Within an asset class, portfolios alongside similar sensitivities will usually be highly related (because ??s are roughly proportional), but this is not typical across asset classes, sectors, or countriesSeptember 14, 2015Onassis Lecture8For exampleSuppose factor 1 is related so that shocks in real output in addition to factor 2 is related so that shocks in expected inflationClass A consists of equities in addition to Class B consists of bondsA positive shock in factor 1 would increase returns in A but not affect B as muchDepending on identities of the underlying factors in addition to the respective sensitivities of classes A in addition to B, their correlation could even be negative even though they are perfectly dependent on the same underlying factorsAnother Example: a global energy factor in addition to equities in Saudi Arabia versus Hong KongSeptember 14, 2015Onassis Lecture9

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Numerical ExampleSuppose the two factors have the same volatility in addition to are uncorrelatedLet ?A,1=k1?B,1 in addition to ?A,2=k2?B,2; i.e., the ??s are not equi-proportionalWhat?s the inter-class correlation in consideration of different values of k1 in addition to k2?In next figure, the k?s vary over -1 so that +1September 14, 2015Onassis Lecture10The Extent of Correlation even alongside perfect diversification September 14, 2015Onassis Lecture11Well-diversified but Weakly Correlated PortfoliosDiversification across two asset classes often seems powerful because most mixed allocations (such as 60-40) appear so that substantially reduce volatilityBut holding the respective portfolio compositions constant when allocating across them potentially overstates the benefitTo see this, consider structuring an investment portfolio from assets in the first class (A) that matches extremely well the factor sensitivities of the original portfolio in the second class (B)This is straightforward when there is a large enough menu of available derivatives or when short positions are feasible in addition to inexpensive; the results in returns would beRA,t = EA + ?B,1 f1,t + ?B,2 f2,t + ?A,t RB,t = EB + ?B,1 f1,t + ?B,2 f2,t + ?B,t (There can be some remaining idiosyncratic risk, hence the ??s) September 14, 2015Onassis Lecture12

What?s the maximum diversification benefit in this case?It is easy so that show that the minimum variance portfolio from combining portfolio B alongside the ?B structured portfolio of class A assets has a weighting w in portfolio B (and 1-w in structured portfolio A) equal tow = Var(?A,t)/[Var(?A,t)+Var(?B,t)]In other words, if the structured portfolio from the class A assets has no idiosyncratic component, diversifying into B brings no benefit in terms of risk reduction alone; w is zero. This is true even though the correlation is weak between the original indexes of classes A in addition to BAny benefit from the above combination would have so that be in terms of enhanced return, not reduced riskSeptember 14, 2015Onassis Lecture13Diversification Benefits: a Better MeasureIf the ?B-structured B-mimicking portfolio composed of A assets has an r-square on the underlying factors close so that 1.0, there will be negligible diversification benefits from combining B in addition to A. (The same would be true going the other direction; i.e., structuring from B so that match the A index.)The initial impression of strong diversification benefits, suggested by the simple correlation between the initial indexes from A in addition to B, doesn?t take account of more refined structuresCorrelation between portfolios of assets is an imperfect measure of diversification potential. There is virtually no benefit from diversification when factor r-squares are close so that 1.0 (in either A or B) even when correlation appears so that be weak between their indexes The r-squares of the indexes, not their correlation, is a better (inverse) measure of potential diversification benefits; high r-square, low benefitsOf course, a full-blown Markowitz mean/variance analysis of individual assets in A in addition to B would yield a correct measure, but this is rarely considered.September 14, 2015Onassis Lecture14The diversification benefit of adding individual assets so that diversified portfoliosIn the well-known Treynor/Black analysis, the impact of adding an individual asset so that an existing portfolio depends on their relative expected returns in addition to their correlation (individual asset alongside portfolio)But suppose the individual asset is iRi,t = Ei + ?i,1 f1,t + ?i,2 f2,t + ?i,tAnd a (perfect) i-mimicking portfolio (P) alongside exactly matching sensitivities can be engineered from among the portfolio assets already held; i.e., RP,t = EP + ?i,1 f1,t + ?i,2 f2,t There can be no genuine reduction in risk from adding the asset, regardless of its correlation alongside the original portfolio. (Adding i so that the portfolio would be beneficial only if Ei > EP)September 14, 2015Onassis Lecture15

Identifying the underlying risk drivers is critical. What are they?They must be high-frequency changes in market perceptions of pervasive macro-economic conditionsActual macro shocks are low frequencyEven sector or country-specific shocks are potentially diversifiableSince we?re dealing alongside perceptions, they could includeRational anticipations of change in macro conditions that are truly pervasive (real output growth, real interest rates, inflation, etc.)Behavior-driven pervasive shocks in confidence or risk perceptions (panics, liquidity crises, etc.) September 14, 2015Onassis Lecture16Empirical Implementation: Varieties of Factor EstimationStatistical methodsPrinciple componentsFactor AnalysisPre-specified macro-economic variablesGDP, real interest, investor confidence, inflation, etc.Proxy factor portfolios suggested by asset pricing (i.e., alongside sensitivities related so that returns)Fama/French, Carhart, Pastor/Stambaugh, Litterman/Scheinkman (for bonds) many otherSimply a bunch of rather heterogeneous indexes or tradable portfoliosSeptember 14, 2015Onassis Lecture17Thanks in consideration of your kind attention

## Parkinson, Mary General Manager

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