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20
A Simulation Approach to Dynamic Portfolio Choice with an Application to Learning About Return Predictability
, 2005
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Learning under Ambiguity
 Review of Economic Studies
, 2002
"... This paper considers learning when the distinction between risk and ambiguity matters. It first describes thought experiments, dynamic variants of those provided by Ellsberg, that highlight a sense in which the Bayesian learning model is extremeit models agents who are implausibly ambitious about w ..."
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Cited by 31 (3 self)
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This paper considers learning when the distinction between risk and ambiguity matters. It first describes thought experiments, dynamic variants of those provided by Ellsberg, that highlight a sense in which the Bayesian learning model is extremeit models agents who are implausibly ambitious about what they can learn in complicated environments. The paper then provides a generalization of the Bayesian model that accommodates the intuitive choices in the thought experiments. In particular, the model allows decisionmakers ’ confidence about the environment to change — along with beliefs — as they learn. A portfolio choice application compares the effect of changes in confidence under ambiguity versus changes in estimation risk under Bayesian learning. The former is shown to induce a trend towards more stock market participation and investment even when the latter does not. 1
Optimal versus Naive Diversification: How . . .
, 2007
"... We evaluate the outofsample performance of the samplebased meanvariance model, and its extensions designed to reduce estimation error, relative to the naive 1/N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1/N rule in terms of Shar ..."
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Cited by 22 (1 self)
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We evaluate the outofsample performance of the samplebased meanvariance model, and its extensions designed to reduce estimation error, relative to the naive 1/N portfolio. Of the 14 models we evaluate across seven empirical datasets, none is consistently better than the 1/N rule in terms of Sharpe ratio, certaintyequivalent return, or turnover, which indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error. Based on parameters calibrated to the US equity market, our analytical results and simulations show that the estimation window needed for the samplebased meanvariance strategy and its extensions to outperform the 1/N benchmark is around 3000 months for a portfolio with 25 assets and about 6000 months for a portfolio with 50 assets. This suggests that there are still many “miles to go” before the gains promised by optimal portfolio choice can actually be realized out of sample.
Dynamic Portfolio Optimization with Transaction Costs: Heuristics and Dual Bounds
, 2010
"... We consider the problem of dynamic portfolio optimization in a discretetime, finitehorizon setting. Our general model considers risk aversion, portfolio constraints (e.g., no short positions), return predictability, and transaction costs. This problem is naturally formulated as a stochastic dynami ..."
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Cited by 6 (1 self)
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We consider the problem of dynamic portfolio optimization in a discretetime, finitehorizon setting. Our general model considers risk aversion, portfolio constraints (e.g., no short positions), return predictability, and transaction costs. This problem is naturally formulated as a stochastic dynamic program. Unfortunately, with nonzero transaction costs, the dimension of the state space is at least as large as the number of assets and the problem is very difficult to solve with more than one or two assets. In this paper, we consider several easytocompute heuristic trading strategies that are based on optimizing simpler models. We complement these heuristics with upper bounds on the performance with an optimal trading strategy. These bounds are based on the dual approach developed in Brown, Smith and Sun (2009). In this context, these bounds are given by considering an investor who has access to perfect information about future returns but is penalized for using this advance information. These heuristic strategies and bounds can be evaluated using Monte Carlo simulation. We evaluate these heuristics and bounds in numerical experiments with a riskfree asset and three or ten risky assets. The results are promising: The differences between the heuristic strategies and the dual bounds are typically small, suggesting these easytocompute heuristic strategies are nearly optimal. Subject Classifications
Collateralized Borrowing and LifeCycle Portfolio Choice
, 2006
"... We examine the effects of collateralized borrowing in a realistically parameterized lifecycle portfolio choice problem. We provide basic intuition in a twoperiod model and then solve a multiperiod model computationally. Our analysis provides insights into lifecycle portfolio choice relevant for ..."
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Cited by 2 (2 self)
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We examine the effects of collateralized borrowing in a realistically parameterized lifecycle portfolio choice problem. We provide basic intuition in a twoperiod model and then solve a multiperiod model computationally. Our analysis provides insights into lifecycle portfolio choice relevant for researchers in macroeconomics and finance. In particular, we show that standard models with unlimited borrowing at the riskless rate dramatically overstate the gains to holding equity when compared with collateralconstrained models. Our results do not depend on the specification of the collateralized borrowing regime: the gains to trading equity remain relatively small even with the unrealistic assumption of unlimited leverage. We argue that our results strengthen the role of borrowing constraints in explaining the portfolio participation puzzle, that is, why most investors do not own stock.
TwoFund Separation under Model MisSpecification
, 2008
"... The twofund separation theorem tells us that an investor with quadratic utility can separate her asset allocation decision into two steps: First, find the tangency portfolio (TP), i.e., the portfolio of risky assets that maximizes the Sharpe ratio (SR); and then, decide on the mix of the TP and the ..."
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Cited by 1 (1 self)
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The twofund separation theorem tells us that an investor with quadratic utility can separate her asset allocation decision into two steps: First, find the tangency portfolio (TP), i.e., the portfolio of risky assets that maximizes the Sharpe ratio (SR); and then, decide on the mix of the TP and the riskfree asset, depending on the investor’s attitude toward risk. In this paper, we describe an extension of the twofund separation theorem that takes into account uncertainty in the model parameters (i.e., the expected return vector and covariance of asset returns) and uncertainty aversion of investors. The extension tells us that when the uncertainty model is convex, an investor with quadratic utility and uncertainty aversion can separate her investment problem into two steps: First, find the portfolio of risky assets that maximizes the worstcase SR (over all possible asset return statistics); and then, decide on the mix of this risky portfolio and the riskfree asset, depending on the investor’s attitude toward risk. The risky portfolio is the TP corresponding to the least favorable asset return statistics, with portfolio weights chosen optimally. We will show that the least favorable statistics (and the associated TP) can be found efficiently by solving a convex optimization problem. 1
Forecasting Stock Market Returns: The Sum of the Parts is More than the Whole
, 2008
"... We propose forecasting separately the three components of stock market returns: dividend yield, earnings growth, and priceearnings ratio growth. We obtain outofsample Rsquared coefficients (relative to the historical mean) of nearly 1.6 % with monthly data and 16.7 % with yearly data using the mo ..."
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Cited by 1 (0 self)
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We propose forecasting separately the three components of stock market returns: dividend yield, earnings growth, and priceearnings ratio growth. We obtain outofsample Rsquared coefficients (relative to the historical mean) of nearly 1.6 % with monthly data and 16.7 % with yearly data using the most common predictors suggested in the literature. This compares with typically negative Rsquares obtained in a similar experiment by Goyal and Welch (2008). An investor who timed the market with our approach would have had a certainty equivalent gain of as much as 2.3 % per year and a Sharpe ratio 77 % higher relative to the historical mean. We conclude that there is substantial predictability in equity returns and that it would have been possible to time the market in real time.
© 2011 INFORMS Dynamic Portfolio Optimization with Transaction Costs: Heuristics and Dual Bounds
"... We consider the problem of dynamic portfolio optimization in a discretetime, finitehorizon setting. Our general model considers risk aversion, portfolio constraints (e.g., no short positions), return predictability, and transaction costs. This problem is naturally formulated as a stochastic dynami ..."
Abstract
 Add to MetaCart
We consider the problem of dynamic portfolio optimization in a discretetime, finitehorizon setting. Our general model considers risk aversion, portfolio constraints (e.g., no short positions), return predictability, and transaction costs. This problem is naturally formulated as a stochastic dynamic program. Unfortunately, with nonzero transaction costs, the dimension of the state space is at least as large as the number of assets, and the problem is very difficult to solve with more than one or two assets. In this paper, we consider several easytocompute heuristic trading strategies that are based on optimizing simpler models. We complement these heuristics with upper bounds on the performance with an optimal trading strategy. These bounds are based on the dual approach developed in Brown et al. (Brown, D. B., J. E. Smith, P. Sun. 2009. Information relaxations and duality in stochastic dynamic programs. Oper. Res. 58(4) 785–801). In this context, these bounds are given by considering an investor who has access to perfect information about future returns but is penalized for using this advance information. These heuristic strategies and bounds can be evaluated using Monte Carlo simulation. We evaluate these heuristics and bounds in numerical experiments with a riskfree asset and 3 or 10 risky assets. In many cases, the performance of the heuristic strategy is very close to the upper bound, indicating that the heuristic strategies are very nearly optimal. Key words: dynamic programming; portfolio optimization
Why optimal diversification cannot outperform naive diversification: Evidence
, 2013
"... from tail risk exposure ..."