Analyzing the Style of Fund Managers - A Quantitative Approach
Team Latte
December 19, 2006

With equity markets scaling new highs every day there is a lot of interest in hedge funds. Investing directly in stock markets is a no-brainer these days then why should an investor invest in funds in a hedge fund or an investment fund? It will make sense only if the fund manager's return are going to beat the market. Of course, the million dollar question is what do we mean by the "market"? We'll see that shortly. Sophisticated investors are asking the question: what is the probability that over a certain period a fund manager will outperform the global equity markets?

Let's say that we are interested in evaluating the performance of a hedge fund manager who invests in global equities and follows a simple long/short strategy (long some stocks and short other stocks). How do we do that? The fund manager is not going to divulge to us which stocks he is shorting and which stocks he is buying. There will be no detailed information available to us - or to external investors - as to the nature of the assets in the manager's portfolio, the sector mix, the currency mix, etc. So how can assess his performance?

We can use a quantitative technique called the "style analysis" pioneered by William Sharpe in the early 1990s.

The objective of style analysis is to construct a benchmark portfolio from a set of known market indices against which to compare the performance of a fund's actively managed portfolio. Let us say that we identify a global equity portfolio, across currencies, essentially a basket of global equity indices (the major ones plus the emerging markets ones) which more or less replicates the universe of the fund manager. Each index in that portfolio, is weighted by a weight, positive or negative, . Thus the value of the weighted (basket) portfolio will be given by

Any fund manager investing in global equities can be benchmarked against this basket portfolio of global equity indices. This is what we mean by "market".

All the component indices, are observable in the market and if the weights are properly chosen or estimated (this is a million dollar question though!) then the fair value of the basket portfolio at any point in time can be calculated from the market data. Therefore, a fund manager's return can be compared to the return from this basket (benchmark) market portfolio. Let's rewrite the above equation in terms of the component returns:

Where, are returns from the respective equity indices and is the benchmark basket portfolio return. The weights remain the same. Now a fund manager's return should, at least be equal, to the above portfolio return otherwise why would anyone invest in his fund. The whole point in investing in a hedge fund or any fund, is so that investors get better returns than the market (portfolio). Of course, a big assumption here is that the investor is savvy enough to construct the above basket portfolio from market indices and more importantly he can invest in all the relevant markets to replicate the above basket portfolio. But theoretically speaking every investor can.

Thus the fundamental issue in analyzing the return of a fund is to figure how much excess return it generates over and above the benchmark basket portfolio return constructed from the market indices. In other words, if a fund return is denoted by then the excess return will be given by:

The excess return is also called the "tracking error" or "random noise". This is a non-factor return and characterizes the investment style of the manager as well as the return profiles of the individual assets in the manager's portfolio.

Though in an ideal situation, a manager would like to see this excess return always have a positive value, in practice in the case of an active hedge fund this excess return will take on random values from one period to other. The excess return will be a mix of positive and negative values across a certain mean, but totally random. And if we are using this excess return to assess the fund manager then we need to observe this across many different periods, otherwise we may get misleading information due to statistical reasons. However, over a number of periods - over which return is estimated - the excess return should give us a fair indication of a manager's investment capabilities.

In fact, the above is an optimization problem, or more appropriately a quadratic programming problem. What we are interested in analyzing is not the excess return per se, but the variance of the excess return. The lower the variance the better will be the fund performance.

Two important points need to be addressed though:

• The choice of market indices, to create a benchmark portfolio: how do we choose these indices?
• More importantly, the estimation of factor (index) weights, to create the basket portfolio? Some of these will be positive and some negative (to reflect long and short) but they should add up to one. The goal of the quadratic programming is to choose the weights in such a manner that the excess return, or the "tracking error", is minimized. But a large sample of funds in the same category needs to analyzed to get the correct weights that would generate a theoretically fair basket portfolio.

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