Portfolio optimization made doable or at least more doable

Brandt, Santa Clara, and Valkanov have an interesting working paper that should help investors create optimal portfolios.

I will let them explain their paper:

"We propose a simple new approach to equity portfolio optimization based on firm
characteristics. We parameterize the weight invested in each stock as a function of the firm's characteristics, with the implicit assumption that these characteristics fully capture all aspects of the joint distribution of returns that are relevant for forming optimal portfolios. We then estimate the coefficients of the portfolio policy by maximizing the utility that would have been obtained by the investor from implementing the policy over the sample period."

In English? They develop a model that can be used to find optimal portfolio weights of assets based on the asset's characteristics. Moreover, the model is flexible enough to be altered to fit a variety of utility functions.

While some of us may question how "simple" the method is (the authors repeatedly claim it is simple), the paper really is much more practically applicable than many of the quantitative models based on the Markowitz optimal portfolio approach and it tends to based on firm characteristics (such as size and book to value ratios) that are readily available.

Again in the authors' words:

The most important aspect of our parameterization is that the coefficients are constant across assets and through time. Constant coefficients across assets implies that the portfolio policy only cares about the characteristics of the stocks, not about the stocks themselves. The implicit assumption is that the characteristics fully capture all aspects of the joint distribution of returns that are relevant for forming optimal portfolios. Constant coefficients through time means that the coefficients that maximize the investor's conditional expected utility at a given date are the same for all dates and therefore also maximize the investor's unconditional expected utility.

In the later sections of the paper, the authors relax many of the restrictive assumptions they used initially (for example they allow for the possibility of coefficients changing with the economy) and even create a real portfolio based on their model. Their model portfolio dramatically outperforms other market models.

The optimal portfolio has a volatility slightly larger than that of the market portfolio, 19% versus 16%, but has an average return of 24.4% as opposed to 12.0%. This translates into a certainty equivalent gain of 10%.

So what does their so-called optimal portfolio look like? Given what we know about anomalies and apparent inefficiencies (for example: value anomaly and size anomaly and momentum investing), it should not be surprising that the optimal portfolio had more small stocks and more value stocks.

"The market portfolio has a bias towards very large firms (due to value weighting) and firms with below average book-to-market ratios (growth), while it is neutral with respect to momentum. In contrast, the optimized portfolio has a slight bias toward small firms and much stronger biases toward high book-to-market ratio (value) firms and past winners."

The paper is available from the UCLA working paper site.