Asset Allocation: Management Style and Performance Measure

Introduction
In 1992, William Sharpe wrote the paper “Asset Allocation: Management Style and Performance Measure”. In that paper, Sharpe used various indices to shed light on the holdings/styles of various mutual funds. He also uses the estimated style to measure the astuteness of the fund manager’s selection abilities.

This paper will focus on replicating the methods used by Sharpe’s paper and will perform similar analysis. However, this paper will use Exchange Traded Funds (ETFs) to form the base asset classes instead of the various indices used by Sharpe. Using Sharpe’s methods, the group will use the returns 1 index, 4 funds and 6 ETFs to represent the 11 different asset classes and replicate the returns of the following 5 funds:

American Capital Income Builders Fund
Fidelity Contrafund
Franklin Income Fund
PIMCO Total Returns Fund
Vanguard Total Stock Market Fund

Methodology
To figure out the next month out of sample portfolio weights. We used a 60 month rolling window out of sample optimization procedure that has been programmed in matlab.

American Capital Income Builders fund Analysis
The style as represented by the 11 asset classes over the period of Jan 06 to Jan 10 is shown in the graph below:

This method of replication achieved an averaged R-squared (over the 48 periods) value of 0.855 for Capital. This means that on the average approximately 85.5% of the variation of the returns of Capital was captured by the 11 asset classes. As expected, the averaged R-squared value did improve when the constraint of no shorting was removed but this improvement was minute.

The complete analysis of the paper can be found here