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116
Universal Portfolios
, 1996
"... We exhibit an algorithm for portfolio selection that asymptotically outperforms the best stock in the market. Let x i = (x i1 ; x i2 ; : : : ; x im ) t denote the performance of the stock market on day i ; where x ij is the factor by which the jth stock increases on day i : Let b i = (b i1 ; b i2 ..."
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Cited by 207 (5 self)
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We exhibit an algorithm for portfolio selection that asymptotically outperforms the best stock in the market. Let x i = (x i1 ; x i2 ; : : : ; x im ) t denote the performance of the stock market on day i ; where x ij is the factor by which the jth stock increases on day i : Let b i = (b i1 ; b i2 ; : : : ; b im ) t ; b ij 0; P j b ij = 1 ; denote the proportion b ij of wealth invested in the jth stock on day i : Then S n = Q n i=1 b t i x i is the factor by which wealth is increased in n trading days. Consider as a goal the wealth S n = max b Q n i=1 b t x i that can be achieved by the best constant rebalanced portfolio chosen after the stock outcomes are revealed. It can be shown that S n exceeds the best stock, the Dow Jones average, and the value line index at time n: In fact, S n usually exceeds these quantities by an exponential factor. Let x 1 ; x 2 ; : : : ; be an arbitrary sequence of market vectors. It will be shown that the nonanticipating sequence ...
Dynamic Asset Allocation under Inflation
 Journal of Finance
, 2002
"... Wachter, two anonymous referees, and participants at the Brown Bag Micro Finance Lunch Seminar at the Wharton ..."
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Cited by 81 (2 self)
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Wachter, two anonymous referees, and participants at the Brown Bag Micro Finance Lunch Seminar at the Wharton
Optimal Dynamic Portfolio Selection: MultiPeriod MeanVariance Formulation
 Math. Finance
, 1998
"... The meanvariance formulation by Markowitz in 1950s and its analytical solution by Merton in 1972 paved a foundation for modern portfolio selection analysis in single period. This paper considers an analytical optimal solution to the meanvariance formulation in multiperiod portfolio selection. Spec ..."
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Cited by 60 (3 self)
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The meanvariance formulation by Markowitz in 1950s and its analytical solution by Merton in 1972 paved a foundation for modern portfolio selection analysis in single period. This paper considers an analytical optimal solution to the meanvariance formulation in multiperiod portfolio selection. Specifically, analytical optimal portfolio policy and analytical expression of the meanvariance efficient frontier are derived in this paper for the multiperiod meanvariance formulation. An efficient algorithm is also proposed in this paper in finding an optimal portfolio policy to maximize a utility function of the expected value and the variance of the terminal wealth. Key Words: Multiperiod portfolio selection, multiperiod meanvariance formulation, utility function. This research was partially supported by the Research Grants Council of Hong Kong, grant no. CUHK 4130/97E. The authors very much appreciate the constructive comments from Professor Stanley R. Pliska. y Author to whom a...
Heterogeneity and portfolio choice: theory and evidence
, 2004
"... In this paper, we summarize and add to the evidence on the large and systematic differences in portfolio composition across individuals with varying characteristics, and evaluate some of the theories that have been proposed in terms of their ability to account for these differences. Variation in bac ..."
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Cited by 57 (1 self)
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In this paper, we summarize and add to the evidence on the large and systematic differences in portfolio composition across individuals with varying characteristics, and evaluate some of the theories that have been proposed in terms of their ability to account for these differences. Variation in background risk exposurefrom sources such as labor and entrepreneurial income or real estate holdings, and from factors such as transactions costs, borrowing constraints, restricted pension investments and life cycle considerations – can explain some but not all aspects of the observed crosssectional variation in portfolio holdings in a traditional utility maximizing framework. In particular, fixed costs and life cycle considerations appear necessary to explain the lack of stock market participation by young and less affluent households. Remaining challenges for quantitative theories include the apparent lack of diversification in some unconstrained individual portfolios, and nonparticipation in the stock market by some households with significant financial wealth.
Markowitz’s meanvariance portfolio selection with regime switching: From discretetime models to their continuoustime limits
 IEEE Transaction on Automatic Control
, 2003
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Markowitz revisited: meanvariance models in financial portfolio analysis
 SIAM Rev
, 2001
"... Abstract. Meanvariance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. We describe in detail the interplay between objective and constraints in a number of singleperiod variants, including semivariance models. Particular emphasis is laid on avo ..."
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Cited by 35 (1 self)
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Abstract. Meanvariance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. We describe in detail the interplay between objective and constraints in a number of singleperiod variants, including semivariance models. Particular emphasis is laid on avoiding the penalization of overperformance. The results are then used as building blocks in the development and theoretical analysis of multiperiod models based on scenario trees. A key property is the possibility of removing surplus money in future decisions, yielding approximate downside risk minimization.
Optimal portfolio implementation with transactions costs and capital gains taxes, working paper
, 2000
"... We consider a multiasset investment fund that in the absence of transactions costs and/or taxes would hold assets in constant proportions. The problem is: what trading strategy should be implemented in the presence of transactions costs and/or capital gains taxes? Very frequent trading to maintain ..."
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Cited by 29 (0 self)
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We consider a multiasset investment fund that in the absence of transactions costs and/or taxes would hold assets in constant proportions. The problem is: what trading strategy should be implemented in the presence of transactions costs and/or capital gains taxes? Very frequent trading to maintain the target proportions will incur ruinous transactions costs, whilst infrequent trading will incur significant tracking error relative to the desired returns. Following standard industry practice, the objective is assumed to minimize the expected discounted sum of costs of trading plus the costs resulting from tracking errors. As suggested by the existence results of Akian, Menaldi, and Sulem [1996], the optimal strategy is characterized by a multidimensional notrade region. In contrast with earlier work, we develop a relatively simple means to compute this region and to determine the resulting annual turnover and tracking error of the optimal strategy. Almost surely, the strategy will require trading just one risky asset at any moment, although which asset is traded varies stochastically through time. Compared to the common practice of periodically rebalancing assets to their target proportions, the optimal strategy with the same degree of tracking accuracy will reduce turnover by almost 50%. We show how high trading costs will reduce initial commitments to illiquid markets. Our results are contrasted with the ad hoc approach that reduces expected returns to reflect transactions costs. Capital gains taxes add complexity due to the stochastic evolution of cost bases. We derive the optimal notrade region and the region requiring tax loss selling. Losses are not immediately realized when there are positive transactions costs, but only when they exceed a critical level. Capital gains taxes lead to lower initial investment levels.
Wealth inequality and asset pricing
 Review of Economic Studies
, 2001
"... anonymous referees for helpful discussions. In an ArrowDebreu exchange economy with identical agents except for their initial endowment, we examine how wealth inequality affects the equilibrium level of the equity premium and the riskfree rate. We first show that wealth inequality raises the equit ..."
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Cited by 23 (1 self)
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anonymous referees for helpful discussions. In an ArrowDebreu exchange economy with identical agents except for their initial endowment, we examine how wealth inequality affects the equilibrium level of the equity premium and the riskfree rate. We first show that wealth inequality raises the equity premium if and only if the inverse of absolute risk aversion is concave in wealth. We then show that the equilibrium riskfree rate is reduced by wealth inequality if the inverse of the coefficient of absolute prudence is concave. We also prove that the combination of a small uninsurable background risk with wealth inequality biases asset pricing towards a larger equity premium and a smaller riskfree rate.
Dynamic meanvariance portfolio selection with noshorting constraints
 SIAM J. Control Optim
"... Abstract. This paper is concerned with meanvariance portfolio selection problems in continuoustime under the constraint that shortselling of stocks is prohibited. The problem is formulated as a stochastic optimal linearquadratic (LQ) control problem. However, this LQ problem is not a conventional ..."
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Cited by 22 (7 self)
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Abstract. This paper is concerned with meanvariance portfolio selection problems in continuoustime under the constraint that shortselling of stocks is prohibited. The problem is formulated as a stochastic optimal linearquadratic (LQ) control problem. However, this LQ problem is not a conventional one in that the control (portfolio) is constrained to take nonnegative values due to the noshorting restriction, and thereby the usual Riccati equation approach (involving a “completion of squares”) does not apply directly. In addition, the corresponding Hamilton–Jacobi–Bellman (HJB) equation inherently has no smooth solution. To tackle these difficulties, a continuous function is constructed via two Riccati equations, and then it is shown that this function is a viscosity solution to the HJB equation. Solving these Riccati equations enables one to explicitly obtain the efficient frontier and efficient investment strategies for the original meanvariance problem. An example illustrating these results is also presented.