Treynor-Black Model

The Treynor-Black model is a portfolio-optimization model that seeks to maximize a portfolio's Sharpe Ratio by combining an actively managed portfolio built with a few mispriced securities and a passively managed market index fund.

The Treynor-Black model, published in 1973 by Jack Treynor and Fischer Black, assumes that the market is highly, but not perfectly efficient. Some investors have information that can be used to generate abnormal returns, or alpha, from a few mispriced securities.

The passively invested market portfolio contains securities in proportion to their market value, and it is assumed that the expected return and standard deviation can be estimated through macroeconomic forecasting.

In the active portfolio — which is a long/short fund — each security is weighted according to the ratio of its alpha to its unsystematic risk (the industry-specific risk that is inherently unpredictable. This ratio is called the Treynor-Black ratio or appraisal ratio, and measures the value the security would add to the portfolio, on a risk-adjusted basis. The higher a security's alpha, the higher the weight assigned to it. The more unsystematic risk the stock has, the less weight is assigned to it.

The Treynor-Black model does provide an efficient way of implementing an active investment strategy. Yet, because it is hard to pick stocks accurately as the model requires, and restrictions on short selling may limit the ability to exploit market efficiencies and generate alpha, the model has gained little traction with investment managers.