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21
Risk reduction in large portfolios: Why imposing the wrong constraints helps
, 2002
"... Green and Hollifield (1992) argue that the presence of a dominant factor is why we observe extreme negative weights in meanvarianceefficient portfolios constructed using sample moments. In that case imposing noshortsale constraints should hurt whereas empirical evidence is often to the contrary. ..."
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Cited by 146 (4 self)
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Green and Hollifield (1992) argue that the presence of a dominant factor is why we observe extreme negative weights in meanvarianceefficient portfolios constructed using sample moments. In that case imposing noshortsale constraints should hurt whereas empirical evidence is often to the contrary. We reconcile this apparent contradiction. We explain why constraining portfolio weights to be nonnegative can reduce the risk in estimated optimal portfolios even when the constraints are wrong. Surprisingly, with noshortsale constraints in place, the sample covariance matrix performs as well as covariance matrix estimates based on factor models, shrinkage estimators, and daily data.
Portfolio Selection with Parameter and Model Uncertainty: A MultiPrior Approach
, 2006
"... We develop a model for an investor with multiple priors and aversion to ambiguity. We characterize the multiple priors by a "confidence interval" around the estimated expected returns and we model ambiguity aversion via a minimization over the priors. Our model has several attractive featu ..."
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Cited by 91 (4 self)
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We develop a model for an investor with multiple priors and aversion to ambiguity. We characterize the multiple priors by a "confidence interval" around the estimated expected returns and we model ambiguity aversion via a minimization over the priors. Our model has several attractive features: (1) it has a solid axiomatic foundation; (2) it is flexible enough to allow for different degrees of uncertainty about expected returns for various subsets of assets and also about the returngenerating model; and (3) it delivers closedform expressions for the optimal portfolio. Our empirical analysis suggests that, compared with portfolios from classical and Bayesian models, ambiguityaverse portfolios are more stable over time and deliver a higher outof sample Sharpe ratio.
Predictable returns and asset allocation: Should a skeptical investor time the market
 Journal of Econometrics
, 2009
"... are grateful for financial support from the Aronson+Johnson+Ortiz fellowship through the Rodney L. White Center for Financial Research. This manuscript does not reflect the views of the Board of Governors of the Federal Reserve System. Predictable returns and asset allocation: Should a skeptical inv ..."
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Cited by 23 (0 self)
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are grateful for financial support from the Aronson+Johnson+Ortiz fellowship through the Rodney L. White Center for Financial Research. This manuscript does not reflect the views of the Board of Governors of the Federal Reserve System. Predictable returns and asset allocation: Should a skeptical investor time the market? We investigate optimal portfolio choice for an investor who is skeptical about the degree to which excess returns are predictable. Skepticism is modeled as an informative prior over the R 2 of the predictive regression. We find that the evidence is sufficient to convince even an investor with a highly skeptical prior to vary his portfolio on the basis of the dividendprice ratio and the yield spread. The resulting weights are less volatile and deliver superior outofsample performance as compared to the weights implied by an entirely modelbased Are excess returns predictable, and if so, what does this mean for investors? In classic studies of rational valuation (e.g. Samuelson (1965, 1973), Shiller (1981)), risk premia are constant over time and thus excess returns are unpredictable. 1
Model uncertainty, limited market participation, and asset pricing
, 2002
"... We demonstrate that limited market participation can arise endogenously in the presence of model uncertainty. Our model generates novel predictions on the relation between limited market participation, equity premium, and diversification discount. When the dispersion in investors ’ model uncertainty ..."
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Cited by 15 (1 self)
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We demonstrate that limited market participation can arise endogenously in the presence of model uncertainty. Our model generates novel predictions on the relation between limited market participation, equity premium, and diversification discount. When the dispersion in investors ’ model uncertainty is small, full market participation prevails in equilibrium. In this case, equity premium is unrelated to model uncertainty dispersion and a conglomerate trades at a price equal to the sum of its single segment counterparts. When model uncertainty dispersion is large, however, investors with high uncertainty optimally choose to stay sidelined in equilibrium. In this case, equity premium can decrease with model uncertainty dispersion. This is in sharp contrast to the understanding in the existing literature that limited market participation leads to higher equity premium. Moreover, when limited market participation occurs, a conglomerate trades at a discount relative to its single segment counterparts. The discount increases in model uncertainty dispersion and is positively related to the proportion of investors not participating in the markets.
Confidence in the Familiar: An International Perspective
, 2002
"... One striking feature of international portfolio investment is the extent to which equity portfolios are concentrated in the domestic equity market of the investor–the home bias puzzle. In this paper, Iexaminetheroleofinvestors’perceptionoftherisk of foreign investment on their portfolio choices. The ..."
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Cited by 9 (0 self)
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One striking feature of international portfolio investment is the extent to which equity portfolios are concentrated in the domestic equity market of the investor–the home bias puzzle. In this paper, Iexaminetheroleofinvestors’perceptionoftherisk of foreign investment on their portfolio choices. The expected returns and risk of foreign investment are specifiedthroughanassetpricingmodel with the home portfolio being the benchmark asset–the domestic CAPM of Pastor (2000). The model serves as a point of reference around which investors can center their prior beliefs. I focus on investors ’ prior beliefs that are consistent with the literature on confidence in the familiar–foreign equities, in terms of both expected returns and risk, being viewed less favorably than domestic equities. These prior beliefs are then combined with the data on G7 equities, and the revised beliefs are used to obtain the global optimal asset allocation. I find that in order to hold predominantly domestic equities, each G7 investor has to believe that the risk of foreign investment is several times higher than the actual risk. The home bias is more of a puzzle for a Japanese investor in the 1990’s and for a US investor in the earlier decades. Specifying investors ’ prior beliefs around the world CAPM does not help resolve the puzzle.
Ambiguous risk measures and optimal robust portfolios
 SIAM Journal on Optimization
"... Abstract. This paper deals with a problem of guaranteed (robust) financial decisionmaking under model uncertainty. An efficient method is proposed for determining optimal robust portfolios of risky financial instruments in the presence of ambiguity (uncertainty) on the probabilistic model of the re ..."
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Cited by 8 (0 self)
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Abstract. This paper deals with a problem of guaranteed (robust) financial decisionmaking under model uncertainty. An efficient method is proposed for determining optimal robust portfolios of risky financial instruments in the presence of ambiguity (uncertainty) on the probabilistic model of the returns. Specifically, it is assumed that a nominal discrete return distribution is given, while the true distribution is only known to lie within a distance d from the nominal one, where the distance is measured according to the Kullback–Leibler divergence. The goal in this setting is to compute portfolios that are worstcase optimal in the meanrisk sense, that is, to determine portfolios that minimize the maximum with respect to all the allowable distributions of a weighted riskmean objective. The analysis in the paper considers both the standard variance measure of risk and the absolute deviation measure.
Robust portfolios: contributions from operations research and finance
, 2009
"... In this paper we provide a survey of recent contributions to robust portfolio strategies from operations research and finance to the theory of portfolio selection. Our survey covers results derived not only in terms of the standard meanvariance objective, but also in terms of two of the most popu ..."
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Cited by 8 (1 self)
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In this paper we provide a survey of recent contributions to robust portfolio strategies from operations research and finance to the theory of portfolio selection. Our survey covers results derived not only in terms of the standard meanvariance objective, but also in terms of two of the most popular risk measures, meanVaR and meanCVaR developed recently. In addition, we review optimal estimation methods and Bayesian robust approaches.
Explicit reformulations of robust optimization problens with general uncertainty sets
 SIAM J. Optim
"... Abstract. We consider a rather general class of mathematical programming problems with data uncertainty, where the uncertainty set is represented by a system of convex inequalities. We prove that the robust counterparts of this class of problems can be equivalently reformulated as finite and explici ..."
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Cited by 5 (3 self)
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Abstract. We consider a rather general class of mathematical programming problems with data uncertainty, where the uncertainty set is represented by a system of convex inequalities. We prove that the robust counterparts of this class of problems can be equivalently reformulated as finite and explicit optimization problems. Moreover, we develop simplified reformulations for problems with uncertainty sets defined by convex homogeneous functions. Our results provide a unified treatment of many situations that have been investigated in the literature, and are applicable to a wider range of problems and more complicated uncertainty sets than those considered before. The analysis in this paper makes it possible to use existing continuous optimization algorithms to solve more complicated robust optimization problems. The analysis also shows how the structure of the resulting reformulation of the robust counterpart depends both on the structure of the original nominal optimization problem and on the structure of the uncertainty set. Key words. Robust optimization, data uncertainty, mathematical programming, homogeneous functions, convex analysis AMS subject classifications. 90C30, 90C15, 90C34, 90C25, 90C05.
Robust active portfolio management
 Journal of Computational Finance 11 Number
, 2008
"... In this paper we construct robust models for active portfolio management in a market with transaction costs. The goal of these robust models is to control the impact of estimation errors in the values of the market parameters on the performance of the portfolio strategy. Our models can handle a larg ..."
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Cited by 3 (0 self)
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In this paper we construct robust models for active portfolio management in a market with transaction costs. The goal of these robust models is to control the impact of estimation errors in the values of the market parameters on the performance of the portfolio strategy. Our models can handle a large class of piecewise convex transaction cost functions and allow one to impose additional side constraints such as bounds on the portfolio holdings, constraints on the portfolio beta, and limits on cash and industry exposure. We show that the optimal portfolios can be computed by solving secondorder cone programs – a class of optimization problems with a worst case complexity (i.e., cost) that is comparable to that for solving convex quadratic programs (e.g. the Markowitz portfolio selection problem). We tested our robust strategies on simulated data and on real market data from 20002003 imposing realistic transaction costs. In these tests, the proposed robust active portfolio management strategies significantly outperformed the S&P 500 index without a significant increase in volatility. 1