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 Sharpe ratio evaluates the performance of a portfolio or a single investment against the risk-free rate of return. The standard risk-free return rate is the U.S. Treasury.

History of the Treynor-Black Model

The Treynor-Black model, published in 1973 by Jack Treynor and Fischer Black, assumes that the market is highly—but not perfectly—efficient. Following the model, an investor who agrees with the market pricing of an asset may also believe that they have additional information that can be used to generate abnormal returns—known as alpha—from a few mispriced securities. The investor using the Treynor-Black model will select a mix of securities to create a dual-partitioned portfolio. One portion of the portfolio is a passive investment, and the other part is an active investment.

Treynor-Black Dual Portfolio

The passively invested market portfolio contains securities in proportion to their market value, such as with an index fund. The investor assumes that the expected return and standard deviation of these passive investments 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. Unsystematic risk is the industry-specific risk attached to an investment or an inherently unpredictable category of investments. Examples of such risk include a new market competitor who gobbles up market share or a natural disaster that destroys revenue.

The Treynor-Black ratio or appraisal ratio measures the value the security under scrutiny would add to the portfolio, on a risk-adjusted basis. The higher a security's alpha, the higher the weight assigned to it within the active portion of the portfolio. The more unsystematic risk the stock has, the less weighting it receives.

Final Thoughts on Treynor-Black

The Treynor-Black model does provide an efficient way of implementing an active investment strategy. 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.