- Treynor and Black developed a portfolio optimization model that seeks to maximize a portfolio’s Sharpe Ratio through a combination of an actively managed portfolio component built with a few select mispriced securities and a passively managed market index portfolio component.
- Treynor-Black assumes that markets are highly, but no perfectly efficient.
- Macroeconomic forecasting can be applied to calculate the expected return and standard deviation of the portfolio.
- Securities can be assessed for mispricing by comparing the forecasted return with the required return based on the Security Market Line.
- Mispricing presents the opportunity for abnormal return, where abnormal return is the analyst’s expected return minus the required return dictated by the Security Market Line.
- The cost of less than full market diversification is reflected by the variance of the residual error of the active securities.

## Treynor-Black Process

- Economists create forecasts to derive inputs for the security representing the market portfolio.
- Security analysts isolate the few securities mispriced by the market.
- The portfolio manager constructs the optimal portfolio.
- Post investment period quality analysis can be done by:
- Measuring the correlation squared of the security analyst’s forecasted alphas to actual alphas realized.
- A high correlation will give the portfolio manager confidence in the analysts’ abilities to correctly identify mispriced securities in the future.

## Limitations of Treynor-Black for Investors

- Some investors may prohibit their portfolio managers from short selling, which limits the ability to exploit overpriced assets.
- Treynor-Black relies on successfully forecasting alpha, which is incredibly difficult for even well trained analysts.

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