This In Practice piece gives a practitioner’s summary of the article “In Defense of Portfolio Optimization: What If We Can Forecast?,” by David Allen, Colin Lizieri, and Stephen Satchell, published in the Third Quarter 2019 issue of the *Financial Analysts Journal*.

## What’s the Investment Issue?

One of the most well-known approaches to portfolio construction is mean–variance optimization, where capital is allocated to risky assets by maximising expected returns for a given level of risk. It can be contrasted with more passive equal-weighted investment strategies, such as the 1/*N* approach, which involves dividing a portfolio equally between assets.

The criticism of mean–variance optimization as an “error maximiser” with poor out-of-sample results—particularly when forecasting skill is assumed to be very low—has led much finance literature to conclude that naive, equal-weighted investment strategies are superior. The authors challenge these assumptions and explore the relationship between forecasting ability and investor welfare to compare mean–variance and equal-weighted investment strategies.

## How Do the Authors Tackle the Issue?

The authors’ methodology has three facets: an analytic approach, a simulation approach, and an out-of-sample empirical evaluation. First, they formulate a model that brings together two key factors that contribute to investor welfare: estimation error and forecasting ability (approximated using information ratios, a measure of investor skill). They use this model to investigate the expected utility of an investor with a mean–variance approach at a defined level of forecasting ability. They use the same data sets as an influential 2009 study by DeMiguel, Garlappi, and Uppal (DGU), which found that the 1/*N* approach was consistently superior to 13 other models for portfolio allocation, and compare results.

Next, the authors use a simulation to compare the expected performance of the mean–variance and 1/*N* strategies. They generate 150 monthly market returns and consider two levels of investor skill—almost zero skill and modest skill—in different investment universe sizes. Over a simulation period of 60 months, they examine the significance of the results for each of the two portfolio construction techniques.

Finally, they conduct an out-of-sample empirical evaluation of the performance of mean–variance. Over 25 years from 1990 to 2014, they examine the constituents of the S&P Broad Market indexes from three regions: Asia ex Japan, Europe, and the United States, which includes all publicly listed equities with market values in excess of $100 million. They use seven individual forecasting variables—such as price momentum, earnings momentum, and return on equity—and then look at metrics, including Sharpe ratios, to evaluate subsequent portfolio performance.

## What Are the Findings?

Using their analytic approach, the authors demonstrate that mean–variance outperforms 1/*N*, even when forecasting ability is zero. They conclude that the divergent findings of the DGU study—that 1/*N* generally led to superior performance—are the result of a flaw in the application.

With the simulation approach, the authors find that when forecasting ability is low, investor welfare falls as the size of the investment universe increases. Under these circumstances, investors are best off adopting the 1/*N* investment strategy. However, at an information coefficient of 0.07—a relatively modest skill level—a mean–variance investor performs at least as well as a 1/*N* investor for every universe size and at every level of risk aversion. With modest forecasting skill, expanding the size of the investment universe under mean–variance leads to an increase in investor welfare.

The empirical study produces higher Sharpe ratios and lower standard deviations than 1/*N* for most of the seven forecasting variables in each of the three regions.

## What Are the Implications for Investors and Investment Managers?

The authors state that the findings of their study support an intuitive logic: Investors who have forecasting skill should make use of it; those who don’t are better served by equal weighting.

This result disputes the conclusions of much recent finance literature suggesting that, in most cases, 1/*N* outperforms mean–variance. Studies such as DGU have argued that vast amounts of data over long estimation windows are required for mean–variance to be preferable to equal-weighted strategies—a requirement that becomes more onerous as the size of the investment universe grows.

By contrast, the authors find that even with short estimation periods and relatively simple forecasting models, mean–variance is often superior for investor welfare. They argue that it is reasonable to assume some forecasting ability in investors, provided that estimation error is taken into account. In precisely those conditions where estimation error effects should be most severe, their empirical results suggest that mean–variance still produces better outcomes more often than not.