DR.CHENJIAZI ZHONG

Optimal diversification is one of the key insights of modern portfolio theory, however, due to estimation errors, theory-based portfolio strategies are not as good as one once thought; under some circumstances, the difference between sophisticated models and naive strategy is not statistically significant.

Naive diversification is instinctive common sense division of a portfolio, whereby an investor invests in a number of assets in the hope that the variance of the expected return on the portfolio is lowered. In contrast, an optimal portfolio is constructed to yield the maximum return at the minimum risk. Mean variance optimization, Monte Carlo simulation, and Treynor-Black model are all engineered to produce optimal portfolios.

The main argument is that methodological complexity and sophisticated models do not necessarily lead to investment optimality, and for the statistically-minded, complex approaches are seriously constrained by potential estimation errors.

Victor DeMiguel, Lorenzo Garlappi, and Raman Uppal from London Business School evaluated out-of-sample performance of sample-based mean-variance models, and the extensions designed to reduce estimation error, relative to the naive 1/N portfolio. They studied 14 models* (please see the list below) that were evaluated across seven datasets, and surprisingly found that none of these models in the literature is consistently better than the 1/N strategy in terms of Sharpe Ratio, certainly-equivalent return, and turnover. The gain from optimal diversification is more than offset by estimation errors.

The paper makes the statement that “although there has been considerable progress in the design of optimal portfolios, more effort and energy need to be devoted to improving the estimation of the moments of asset returns, especially expected returns.”

My daily work is evaluating different tactical, dynamic, and strategic asset allocation scenarios to eventually manage institutions’ portfolios. I would argue (partly for my own benefit) that the naive 1/N result may not hold 1) for investment horizons of one year and longer, and 2) when the asset classes to be selected particularly include fixed income securities and real estate vehicles beyond equities, cash and equivalents.

Envision that you have a group of investors who are characterized as “constantly relatively risk averse” and also exhibit preferences that are not locally mean-variance for long horizons, they would, at least on average, benefit from an optimizing asset allocation strategy.

Given the recent research results and debate, it may be more interesting to study how to value and hedge derivatives in the presence of parameter uncertainty, and how to make optimal asset allocation recommendation when investors’ expectations, investment opportunity sets, or the macroeconomic determinants are unknown. One good thing for the investment management industry is that “diversification is absolutely essential” is still the bottom line, although the benefits of advanced mathematical modeling are unclear.

*List of Asset Allocation Models Considered

1. Sample-based mean-variance
2. Bayesian diffuse-prior
3. Bayes-Stein
4. Bayesian Data-and-Model
5. Minimum-variance
6. Value-weighted market portfolio
7. MacKinlay and Pastor’s (2000) mission-factor model
8. Sample-based mean-variance with shortsale constraints
9. Baynes-Stein with shortsale constraints
10. Minimum-variance with shortsale constraints
11. Minimum-variance with generalized constraints
12. Kan and Zhou’s (2007) “three-fund” model
13. Mixture of minimum-variance and 1/N
14. Garlappi, Uppal, and Wang’s (2007) multi-prior model