Using the Treynor-Black Model in Active Portfolio Management
Aruna Eluri, David S. Price, Kelly Walker
Course Project for IE590 Financial Engineering Purdue University, West Lafayette, IN 47907-2023 August 1, 2011
Abstract In 1973, Jack Treynor and Fischer Black published a mathematical model for security selection called the Treynor-Black model. The model finds the optimum portfolio to hold in the situation where an investor considers that most securities are priced effectively, but believes he has information that can be used to predict an abnormal performance of a few of them. The theory behind the model is presented, along with numerical examples to highlight specific realistic investment scenarios and how the model performs for each, showing the advantages and disadvantages of the model.
In developing investment strategy, there are two primary portfolio management styles – active and passive. Active management is a portfolio management strategy that has a goal of outperforming the market or some other investment benchmark index by making specific investment selections geared towards outperforming the market. Passive management is a strategy of being content to invest in an index fund that will closely replicate the investment weighting and returns of a specific index as the investor is not seeking to create returns in excess of that benchmark. The first style requires much more attention, effort, and diligence in obtaining and analyzing data, while the second requires much less dayto-day attention by its very nature.  To outperform the market and exploit market inefficiencies, the investment manager of an active portfolio purchases undervalued assets such as stocks or he short sells assets that are overvalued, or a combination of the two. Instead of always trying to increase value of a portfolio, the investor might also be trying to reduce the risk with respect to a benchmark index fund. 
Treynor-Black Model The skill of the investment manager and the availability of relevant data and its interpretation will largely determine the performance of an actively-managed investment portfolio. Approximately 20% of all mutual funds are pure index funds with the remainder being actively managed to some degree. In fact, 45% of all mutual funds are "closet indexers" funds whose portfolios mimic key indexes and whose performance is very closely correlated to an index and refer to themselves as “actively managed” purportedly to justify higher management fees. Results show that a large percentage of actively managed mutual funds rarely outperform their index counterparts over an extended period of time because of this. Often language in a prospectus of a closet indexer will state things such as "80% of holdings will be large cap growth stocks within the S&P 500", therefore the majority of their performance, less the larger fees, will be directly dependent upon the performance of the growth stock index they are benchmarking.  Because indexes themselves have no expenses whatsoever, it is possible that an active or passively managed mutual fund where the securities that comprise the mutual fund are outperforming the benchmark, could underperform compared to the benchmark index due to mutual fund fees and/or expenses. The demand for actively-managed continues to exist, however, because many investors are not satisfied with a benchmark return. In addition, active management looks like an attractive investment strategy to investors in volatile or declining markets or when investing in market segments that are less likely to be profitable when considered as whole.  Gaining knowledge about the future performance of assets is an extremely large endeavor requiring significant staff to research each industry and each company which is impractical for most, if not all, investment firms. The Treynor-Black model, however, assumes that individual portfolio managers...