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Style Analysis

Easy To Understand, Hard To Implement

Style analysis uses non-linear equations to figure out what's going on

Style Analysis is primary method used by Global Portfolio Review when analyzing investments so a brief explanation of the methodology is probably warranted. Style analysis was originally developed by William Sharpe in the late 1980s and he expanded on his work with the publication of an article in 1992 as well as with further work contained on his website . Sharpe won the Nobel Prize in Economics in 1990 for his years of work in the area of finance.

The concept of style analysis is loosely based on the findings by Gary Brinson et al. who found that over 90% of the variability of returns in pension funds could be explained by the differences in asset allocations. Obviously if over 90% of the differences in returns is explained by asset allocation, it would make great sense to find a way to figure out which asset classes each fund is invested in. Knowing this information would allow you to more accurately compare funds with similar asset allocations and, more importantly, allow you to create a custom benchmark for each mutual fund. This is what style analysis does.

In simple terms, style analysis asks the question, “What combination of market indices most closely fits the returns of the fund?” If we can figure out this combination of investments, we can see where the fund is investing, and how. By using a broad range of market indices, we can derive a lot of information about a fund, such as geographic distribution, market capitalization, growth/value styles, and even fixed income duration. Essentially, this process is like taking an MRI of your mutual fund – it’s fast and not invasive, but still provides you with a lot of very useful information.

The Mathematics

The calculations used in style analysis are rather complex because there is no formula to calculate what is going on. Rather, style analysis is performed using what is known as a “non-linear equation.” The easiest way to demonstrate style analysis is through a simple example.

Suppose there is a mutual fund and three market indices – one each for stocks, bonds, and cash – with the following returns over the last eight months:

These numbers are loaded into a computer program that handles non-linear problems and it is asked to find which combination of stocks, bonds, and cash best fits the returns achieved by the fund. In this case, constraints are used to ensure that the results are useful:

  • Short-selling is not permitted, so allocations to each index must be at least zero (0%).
  • Leverage is not permitted, so allocation to each index cannot exceed 100%.
  • The total allocation to stocks, bonds, and cash must equal 100%.

The computer program is asked to solve this problem by finding the combination of stocks, bonds, and cash which produces the smallest error between the fund’s returns and the return based on the estimated allocation. In this case, the computer program determined that the most accurate allocation was 50% stocks, 43% bonds, and 7% cash. This combination of assets resulted in an R-squared (i.e. how good the fit is) of 99.7%, which means that 99.7% of the variability of returns was explained by the asset allocation and 0.3% was due to some other factor – likely management ability.