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Different Risk-Adjusted Fund Performance Measures - a Comparison

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Different Risk-Adjusted Fund Performance Measures - a Comparison

Referee Report for Economics

Manuscript # 385

"Different Risk-Adjusted Fund Performance Measures: A Comparison"


This paper compares various risk-adjusted performance measures for a set of mutual funds.

The authors argue that performance measures based on Value-at-Risk (VaR) or Extreme Value

Theory (EVT) are more appropriate than other popular performance measures such as the

Sharpe ratio (SR), the Treynor index (TI) or Jensen´s Alpha (JA) . They propose a performance

index similar to the SR and the TI based on losses calculated by means of VaR together with

EVT. They find that EVT-VaR measures are more appropriate in the presence of non-normal


Main Comments

The topic of the paper is of relevance for financial practitioners as well as academics and it is

certainly applicable to the current financial stability context. The paper is also generally wellwritten.

However, I have some comments for its improvement.

1. The contribution of the paper is not clearly stated. In the 6th paragraph of the

introduction, the authors suggest that their main contribution is the construction of a

performance index based on EVT-VAR. However, it is not very clear why the new

proposed measure should be better in relation to existing measures as it is now

explained. It is true that VaR or EVT should be more reliable measures for extreme

events but when looking at formula (13) it is not apparent why this measure should be

more reliable than the traditional measures. The denominator has, in fact, an "extreme

return" as opposed to the SR or TI which have strictly second moments, so it is not very

straight forward to relate these measures. A better job should be done at explaining the

implications of such VaR based measure, how it relates to other measures and why it

should be better.

2. Why have the measures been compared only in a "static" way? It is widely known in the

finance literature that asset return volatility is time-varying, and to some extent, also

expected returns. It would be possible to go around the latter by arguing market

efficiency (which is also questionable) but it is certainly much more difficult to argue

against time-variability of the standard deviation in the VaR measures (or in the SA and

TI ratios). This is very important as the "good" or "bad" applicability of a particular

performance measure could be sample dependent and as it is now with unconditional

measures, this is hard to uncover. For instance, while the authors account for nonnormality

of returns in the modified-VaR measure by means of a Corner-Fisher quantile,

they assume a constant standard deviation which means that in periods of high volatility

they could still understate the VaR. So at the minimum, the performance comparisons

should be done for the full sample and different sub-samples and it should be tested

whether the measures obtained are significantly different over different samples.

3. The authors concentrate on top 10 and bottom 10 funds for their analysis and discarded

the other funds "for the sake of simplicity". However, by choosing only the "tail" funds,


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