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Quantitative Finance Collector is a blog on Quantitative finance analysis, financial engineering methods in mathematical finance focusing on derivative pricing, quantitative trading and quantitative risk management. Random thoughts on financial markets and personal staff are posted at the sub personal blog.

Dec 8
Choosing an appropriate performance measure is important for fund investors, nevertheless, many researchers find empirically that the choice of measures does not matter because those measures generate identical rank ordering, even though the distribution of fund returns is non-normal. In this paper we certify their findings by proving the monotonicity of several widely used performance measures when the distribution is a location-scale family. The mutual fund monthly return data from 1997 to 2015, together with simulation results, collaborate with our proof.

An adequate risk-adjusted return performance measure to select investment funds is crucial for financial analysts and investors. Sharpe ratio has become a standard measure by adjusting the return of a fund by its standard deviation (Sharpe, 1966), nevertheless, practitioners often question this measure mainly for its invalidity if the distribution of fund returns is beyond normal (Kao, 2002; Amin and Kat, 2003; Gregoriou and Gueyie, 2003, Cavenaile, et al, 2011, Di Cesare, et al, 2014). Several new measures have been proposed and investigated to overcome this limitation of the Sharpe ratio, however, Eling (2008)
finds choosing a performance measure is not critical to mutual fund evaluation, Eling and Schuhmacher (2007) compare the Sharpe ratio with 12 other measures for hedge funds and conclude that the Sharpe ratio and other measures generate virtually identical rank ordering, despite the significant deviations from normal distribution. Similar evaluation includes Eling and Faust (2010) on funds in emerging markets, Auer and Schuhmacher (2013) on hedge funds, and Auer (2015) on commodity investments.

This paper proves that several widely used performance measures are monotonic if the distribution of asset returns is a LS family, a family of univariate probability distributions parametrized by a location and a non-negative scale parameters that is commonly applied in finance (Levy and Duchin, 2004). Our proof certifies the empirical findings in other studies on the indifference of choosing a performance measure when valuing a fund. We show that those measures generate virtually the same rank ordering using monthly mutual fund return data from 1997 to 2005 and Monte-Carlo simulations. Therefore this paper contributes to both the academia and industry by clarifying the phenomenon.

For example, the below figure plots the correlation and confidence intervals based on 2000 simulations for each sample size. For simplicity, we show the results for the Sharpe (ρ1), the Sharpe-Omega (ρ2) and the Sortino ratio (ρ3) only. Consistent with the previous finding, the rank correlation among these performance measures is roughly equal, and is approaching one with the increase of sample size.
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Jul 28
Another interesting paper forthcoming in Journal of Finance investigates the stock picking and market timing abilities of mutual fund managers.

We propose a new definition of skill as a general cognitive ability to either pick stocks or time the market at different times. We find evidence for stock picking in booms and for market timing in recessions. Moreover, the same fund managers that pick stocks well in expansions also time the market well in recessions. These fund managers significantly outperform other funds and passive benchmarks. Our results suggest a new measure of managerial ability that gives more weight to a fund’s market timing in recessions and to a fund’s stock picking in booms. The measure displays far more persistence than either market timing or stock picking alone and can predict fund performance.

Feb 15
Improving the accuracy of mutual funds' performance prediction is an interesting and endless topic. A paper published in Review of Financial Studies by Amihud and Goyenko (2013) No. 26 (3) investigates this issue at a new angle: Lower R2 indicates greater selectivity, and it significantly predicts better performance. Nice.

We propose that fund performance can be predicted by its R2, obtained from a regression of its returns on a multifactor benchmark model. Lower R2 indicates greater selectivity, and it significantly predicts better performance. Stock funds sorted into lowest-quintile lagged R2 and highest-quintile lagged alpha produce significant annual alpha of 3.8%. Across funds, R2 is positively associated with fund size and negatively associated with its expenses and manager's tenure.

Journal paper, Working paper.
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