Abstract not found

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 extreme-it 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 decision-makers ’ 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

We consider the problem of dynamic portfolio optimization in a discrete-time, finite-horizon 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 non-zero 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 easy-to-compute 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 risk-free 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 easy-to-compute heuristic strategies are nearly optimal. Subject Classifications

The two-fund 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 risk-free asset, depending on the investor’s attitude toward risk. In this paper, we describe an extension of the two-fund 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 worst-case SR (over all possible asset return statistics); and then, decide on the mix of this risky portfolio and the risk-free 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

We examine the effects of collateralized borrowing in a realistically parameterized life-cycle portfolio choice problem. We provide basic intuition in a two-period model and then solve a multi-period model computationally. Our analysis provides insights into life-cycle 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 collateral-constrained 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.

We propose forecasting separately the three components of stock market returns: dividend yield, earnings growth, and price-earnings ratio growth. We obtain outof-sample R-squared 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 R-squares 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.

We consider the problem of dynamic portfolio optimization in a discrete-time, finite-horizon 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 easy-to-compute 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 risk-free 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