Following our series on the measurement of portfolio performance. After Sharpe ratios and Treynor and Jensen's Alpha, consider measures which do not depend on a template. And first analysis of the allocation.

As we have seen previously, analysis of fund performance is to identify managers performing funds in light of the results. Performance attribution introduces another dimension. This method seeks to further explain why a particular fund has outperformed (or underperformed) compared to the index or benchmark portfolio. It is therefore a tool to identify and explain the causes of good or bad performance.

If we consider a portfolio of shares, we can identify four possible sources of performance

- The risk-free rate

- The general market performance

- The market timing (the ability to anticipate market developments).

- The selection of good titles.

The first two sources are identical for all managers. The last two, however, depend on him. How then to share the good or bad management of these 4 elements by a portfolio manager?

1 - Method DEA (data envelopment analysis)

This approach is very complex quickly addressed because it is a multifactor model extremely difficult.

The DEA method has been developed by Charnes, Cooper and Rhodes in 1978 and an application for ethical funds was made by Murthi, Choi and Desai in 1997. Measuring performance of ethical funds in this model allows to take into account the ethical component. The performance indicator takes into account the risk, performance, and the ethical component of investment costs (rights of entry and exit fees). The model focuses on different aspects commonly used for measuring performance (risk and profitability). But also ethical behavior. Taking into account all the variables of cost can lead to a more accurate measure of performance.

Measuring DEA efficiency is defined as the ratio between the weighted sum of outputs and the weighted sum of inputs. The idea is to define the performance measure by assigning each unit making the most favorable weights. These operations are best then entered into computer by maximizing the efficiency ratio of the unit. Are taken into account the efficiency ratios of all units provided that these ratios have a maximum correlation of 1.

2 - The model Mazuy and Treynor (1966)

The model of Treynor and Mazuy is based on market timing. This model introduces a quadratic term in the CAPM model to measure the ability of market timing manager is to tell the manager's ability to anticipate market developments. If it provides a higher market then it will own a share of the market portfolio exceeds that of the riskless asset. In the case of an advance down this proportion will be lower than the risk-free asset. It was therefore:

Laughs: the return of funds in period t

Rmt: the return of market portfolio over the period t

Rft: the interest rate without risk

αi: the ability to measure the selectivity

βi: model parameter

oi: measuring market-timing manager

εi: profitability residual

A significant and positive value of coefficient means that the manager has a high predictive ability (market timing).

However, empirical studies have shown that market-timing managers are generally very disappointing.