Treynor-Black Model: Meaning and Examples

What Is the 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 Sharpe ratio evaluates the relative risk-adjusted performance of a portfolio or a single investment against the risk-free rate of return, such as the yield on U.S. Treasury securities.

The Treynor-Black model effectively calls for two portfolio segments: an actively managed portion containing underpriced stocks, and a passive segment that follows an indexing strategy.

Understanding the Treynor-Black Model

The Treynor-Black model was published in 1973 by economists Jack Treynor and Fischer Black. Treynor and Black assumed that the market is highly but not perfectly efficient. Following their model, an investor who largely agrees with the market pricing of an asset may also believe that they have additional information that can be used to generate excess returns—known as alpha—from a select few mispriced securities.

The investor using the Treynor-Black model will thus select a small mix of underpriced securities to create a dual-partitioned portfolio, based on their own research and insight. One portion of the portfolio follows a passive index investment, and the other part an active investment in those mispriced securities.

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

The 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.