# Tag Info

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Larry Harris has a chapter on performance evaluation in Trading and Exchanges. He states that over a long period of time, a skilled asset manager will consistently have excess returns whereas a lucky one will be expected to have random and unpredictable returns. Thus, we start with the portfolio's market-adjusted return standard deviation: \...

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Some links: http://www.scribd.com/doc/34567320/Untangling-Skill-and-Luck http://web.ist.utl.pt/adriano.simoes/tese/referencias/Papers%20-%20Pedro/UK%20mutual%20fund%20performance%20Skill%20or%20luck.pdf Below is some code that I used recently to illustrate luck (and con-games). The story went like this: I'll dream up your lucky lottery number for 2010......

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In order to have a shot at separating skill from luck, you need a sense of what luck looks like. I think the best chance of understanding luck is to use random portfolios. See, for instance: http://www.portfolioprobe.com/about/random-portfolios-in-finance/

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Here are couple references. Especially the first link to Andy Lo's paper contains a list of Sharpe ratios of popular mutual and hedge funds: The Statistics of Sharpe Ratios Dow Jones Credit Suisse Hedge Fund Index Hedge Fund Performance and Generalized Sharpe Ratios I would go with the first paper.

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The answer your are looking for might be the story in "Benchmarking Measures of Investment Performance with Perfect-Foresight and Bankrupt Asset Allocation Strategies", by Grauer (Journal of Portfolio Management). While this work main concerns are the differential ranking of various performance measures and with negative betas for market timing strategies, ...

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In this case, the t-statistic is used to determine if the returns are statistically different from zero (the theoretical mean). A small t-statistic would imply that the null hypothesis (no significant excess return) cannot be rejected. Newey-West standard errors are used to correct for the correlations of error terms over time. I have written a Matlab ...

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Edited Comments: Sharpe Ratio covers both future and historical time frames (as @Freddy points out). Referencing the "Geometric Return and Portoflio Analysis", for the historical calculation, you want to make as few assumptions as possible (in my opinion). Let $m_i \triangleq$ the monthly return for period $i$ and $r_t \triangleq$ annual return, for $i\... 5 This optimization is trivial $$w^{T,J}_i = \begin{cases} 1 \quad \text{if } i=\arg \max_i R^{T,J}(S_i) \\0 \quad \text{otherwise} \end{cases}$$ That is to say, when you optimize only one weight will be nonzero. That's because these ratios incorporate no notion of distributional width, and therefore do not reward diversification. With no concentration ... 4 Read Fooled by Randomness by Nassim Taleb. In a nutshell, he says that you can only tell the difference by understanding the risks that were taken. Lucky investors can win for many years before blowing up. Even if he doesn't blow up, there is no way to know what might have happened if the risks turned out badly. 4 Take a look at White's Reality Check. Another very crude way would be to calculate a "skill score" (from The Mathematics of Technical Analysis, p325) $$\tt{skill\ score} = \frac{SKILL\_correct - NOSKILL\_correct}{Total\ decisions - NOSKILL\_correct}$$ SKILL_correct: the profitable trades NOSKILL_correct: randomly assigned trades that were profitable ... 4 I would even stick to the original paper by Sharpe (1966): Mutual Fund Performance. The Journal of Business Vol. 39, No. 1, Part 2 pp.119--138 If you look at the numbers on Page 6 you can see that the funds sharpe ratios roughly are between$0$and$1$. Since the Sharpe ratio already adjusts for the risk-free rate, you cannot really argue about its ... 3 The PerformanceAnalytics library reflects several years worth of development by Brian Peterson and Peter Carl, as well as multiple collaborators. It is fairly widely used, tested and debugged. Basic software engineering practices suggest that you should strive to re-use it if possible. Options for that include accessing a remote R instance via RServe (... 3 Perhaps check out Poti and Levich (2009), or in a different setting but from one of the same authors, Poti and Wang (2010) "The coskewness puzzle" in JBF. They directly address the issue of what level of SR is plausible. 3 Pardon the lack of an actual link, and the formatting, but in footnote 6 of "Alpha is Volatility times IC times Score", Grinold, Richard C., Journal of Portfolio Management, Summer 1994 v20 n4 p9(8), Grinold suggests that "a truly outstanding manager" might have an information ratio of 1.33: (6) A rough guideline for determining the required IC comes from ... 3 Check out the last chapter in Grinold's classic Active Portfolio Management (2nd Ed) for a discussion on separating luck from skill 3 I was going to suggest that you use alpha, which is the measure of a managers excess return beyond their benchmark. But here is an alternative view which is quite interesting. http://money.usnews.com/money/blogs/Fund-Observer/2010/06/24/just-how-lucky-is-your-mutual-fund-manager 3 There is no universally accepted answer for the main problem here which is the denominator for the return calculation is zero or near zero. There are a few common solutions to this issue. The most simple solution is to use the total portfolio notional as the divisor for the PnL. This can be considered the PnL contribution of that long/short sub-portfolio ... 2 Martijn Cremers and Antti Petajisto have a series of papers using the concept of "Active Share," a new measure of active portfolio management which represents the share of portfolio holdings that differ from the benchmark index holdings, to evaluate mutual fund managers. They find that the most active stock pickers have outperformed their benchmark indices ... 2 I remember an article from graduate school that describes a methodology for measuring the true timing ability of a money manager. I don't remember the name of the article nor the name of the author, however, I do remember some of the details of the article. Maybe someone else has run across it and would be kind enough to post the appropriate reference. ... 2 This is a very common and serious problem among academic papers and with some hedge fund marketing material's, I can almost guarantee that the high ratio of 7 was with-out transaction cost's and that when included this 7 will drop down some where between 0 and 1. 2 cost of leverage for equity only long/short investing is a function of the margin deal you can negotiate with your broker, if you have a large amount of capital. If you don't have significant capital to start with, then it's likely you'll only be able to get 2x leverage with a loan rate between 4% and 10% (retail reg-t margin rates at most brokers) This ... 2 I think you need to exactly define which ratio you are talking about. For example the ex-post Sharpe ratio's components are all well known. You have your realized returns, risk free returns (or whatever other benchmark you define your excess returns against) and realized volatility of returns. For realized asset returns you should not use log returns but ... 2 There are a number of issues here. First, there are a number of methodologies called “performance attribution” each providing answers to different questions. So I am not sure what type of question you wish to address. I will here assume that you wish to evaluate the effects of investment decisions as opposed to the effects of market factors. I will also ... 2 More measurable effects to add to your list: "window dressing" - returns of the fourth quarter or 12th month (i.e. year-end) are higher on average than oher returns; the same to returns of 4th months (qtr-end) vs. others; "herding": changes in asset-classes shares of "big" funds (whatever you define "big") granger-cause changes in asset-classes shares of "... 2 I think the only valid answer is you can't. The techniques you describe would work of the signal was much stronger than the noise but it seems that with your fund returns this is not the case. You could try to get more data or look at other risk measures like max drawdown to get some idea of the risks involved. 2 Ideally you'd want to use daily returns and just annualise it, but if you only have monthly returns then calculating the weighted variance in the following way might do it: $$Var = \frac{\sum_{i=0}^{24}(R_i - \mu)^2}{24 + \frac{21}{31}} + \frac{\frac{21}{31} (R_{25}' - \mu)^2}{24 + \frac{21}{31}}$$ $$Vol = \sqrt{Var}$$ Where$R_i\$ is the returns of ...

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Long story short, thanks to Dirk Eddelbuettel's suggestion I played a bit with rredis and indeed it offers quite a number interesting solutions. However, I still decided to start to write my own performance analytics library (albeit obviously smaller and more specific to my use case) in combination with an established Math/Stats library because I need more ...

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In Forecasting Financial Market Volatility Ser-Huang Poon dedicated entire chapter to the question, so the issue is far from simple. I don't believe there one single best way because of many questions that depend on model form and application such as Should one evaluate volatility or variance, or perhaps ln(vol)? What is the benchmark - volatility is latent,...

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Thanks for the answers and comments above. In particular to Eric Brady, who had me reading a lot of Bayesian papers. In the end, I think the answer to the question is that on the monthly time-frame robust factor algorithms aren't really necessary. On daily and lower time frames, large spikes in returns due to events (earnings ect.) can really mess with ...

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Whether or not it is flawed in practice depends on dynamic the risk exposures really are. Many factors or indices used for style analysis actually require dynamic trading to maintain - so you could potentially have a fund that trades a lot while still generating a return series that can be be modeled out of sample with static exposures. One relatively ...

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