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Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?
We evaluate the out-of-sample performance of the sample-based mean-variance 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, certainty-equivalent 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 sample-based mean-variance 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.
Journal Article
Keynes Meets Markowitz: The Trade-Off Between Familiarity and Diversification
We develop a model of portfolio choice to nest the views of Keynes, who advocates concentration in a few familiar assets, and Markowitz, who advocates diversification. We use the concepts of ambiguity and ambiguity aversion to formalize the idea of an investor's \"familiarity\" toward assets. The model shows that for any given level of expected returns, the optimal portfolio depends on two quantities: relative ambiguity across assets and the standard deviation of the expected return estimate for each asset. If both quantities are low, then the optimal portfolio consists of a mix of familiar and unfamiliar assets; moreover, an increase in correlation between assets causes an investor to increase concentration in familiar assets (flight to familiarity). Alternatively, if both quantities are high, then the optimal portfolio contains only the familiar asset(s), as Keynes would have advocated. In the extreme case in which both quantities are very high, no risky asset is held (nonparticipation).
This paper was accepted by Brad Barber, Teck Ho, and Terrance Odean, special issue editors.
Journal Article
Vast Portfolio Selection With Gross-Exposure Constraints
This article introduces the large portfolio selection using gross-exposure constraints. It shows that with gross-exposure constraints, the empirically selected optimal portfolios based on estimated covariance matrices have similar performance to the theoretical optimal ones and there is no error accumulation effect from estimation of vast covariance matrices. This gives theoretical justification to the empirical results by Jagannathan and Ma. It also shows that the no-short-sale portfolio can be improved by allowing some short positions. The applications to portfolio selection, tracking, and improvements are also addressed. The utility of our new approach is illustrated by simulation and empirical studies on the 100 Fama-French industrial portfolios and the 600 stocks randomly selected from Russell 3000.
Journal Article
Dynamic Trading with Predictable Returns and Transaction Costs
We derive a closed-form optimal dynamic portfolio policy when trading is costly and security returns are predictable by signals with different mean-reversion speeds. The optimal strategy is characterized by two principles: (1) aim in front of the target, and (2) trade partially toward the current aim. Specifically, the optimal updated portfolio is a linear combination of the existing portfolio and an \"aim portfolio,\" which is a weighted average of the current Markowitz portfolio (the moving target) and the expected Markowitz portfolios on all future dates (where the target is moving). Intuitively, predictors with slower mean-reversion (alpha decay) get more weight in the aim portfolio. We implement the optimal strategy for commodity futures and find superior net returns relative to more naive benchmarks.
Journal Article
Portfolio Choice with Illiquid Assets
We present a model of optimal allocation to liquid and illiquid assets, where illiquidity risk results from the restriction that an asset cannot be traded for intervals of uncertain duration. Illiquidity risk leads to increased and state-dependent risk aversion and reduces the allocation to both liquid and illiquid risky assets. Uncertainty about the length of the illiquidity interval, as opposed to a deterministic nontrading interval, is a primary determinant of the cost of illiquidity. We allow market liquidity to vary from “normal” periods, when all assets are fully liquid, to “illiquidity crises,” when some assets can only be traded infrequently. The possibility of a liquidity crisis leads to limited arbitrage in normal times. Investors are willing to forgo 2% of their wealth to hedge against illiquidity crises occurring once every 10 years.
This paper was accepted by Itay Goldstein, finance.
Journal Article