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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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Dec 18
I am finally back China from the 24th Australasian Finance & Banking Conference, 22 hours long flight from London -> Shanghai -> Sydney is more challenging than I thought. In the following posts I will select a few papers I personally feel interesting, hope you can enjoy reading them as I do.

Stock Market Fragility and the Quality of Governance of the Country: relationship between the quality of governance of a country and its degree of financial fragility.

The Ultimate Irrelevance Proposition in Finance?: Over 80% of published studies are distinguishing between statistical and economic significance and about quantifying and interpreting the economic magnitudes of the statistical relationships they measure. Yet, only 10% of them acknowledge limits to the power of their tests and fewer still do anything about them. What can you learn from the paper to change your writing style in order to increase chance of being accepted?

Information Management in Financial Markets: Implications for Stock Momentum and Volatility: the amount of positive information released by a company is positively related to both its future stock performance and future positive releases, suggesting that companies tend to ration the delivery of positive news and create sustainable price trends.

A full list of the PhD forum papers can be downloaded at PhD forum.
Oct 13
Library of econometric functions for performance and risk analysis of financial portfolios. This library aims to aid practitioners and researchers in using the latest research in analysis of both normal and non-normal return streams.

We created this library to include functionality that has been appearing in the academic literature on performance analysis and risk over the past several years, but had no functional equivalent in R. In doing so, we also found it valuable to have wrapper functions for functionality easily replicated in R, so that we could access that functionality using a function with defaults and naming consistent with common usage in the finance literature. The following sections cover Performance Analysis, Risk Analysis (with a separate treatment of VaR), Summary Tables of related statistics, Charts and Graphs, a variety of Wrappers and Utility functions, and some thoughts on work yet to be done.

Aug 9
Performance attribution is used as a way to check the relative performance of portfolio against selected Benchmark, the difference of which is called active return. Brinson method decomposes active return to asset selection effect and industry selection effect, helping investor realize where the active return is from, which asset or industry has a biggest  contribution to the active return of portfolio, ect.

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