Burns Statistics -- Working Papers


	Working Papers Previous years: 2006 2005 2004 2003 2002 Please register if you would like to be informed of new working papers and other news from Burns Statistics. You can send comments to patrick@burns-stat.com. 2007 Patrick Burns. "Cramer vs. Pseudo-Cramer" (pdf) This version: 03 October 2007 Abstract: A recent Barron's article examined the efficacy of stock recommendations on the television show Mad Money. Statistical analyses of stock recommendations are scrutinized here in detail, and a powerful analysis using random portfolios is suggested. Differences between simple returns and log returns are discussed, as is the usefulness of the statistical bootstrap. The cost to individuals of trading stocks can easily overwhelm even quite good recommendations. Patrick Burns. "Dart to the Heart" (pdf) This version: 08 March 2007 Abstract: Most likely you know of the stock market dartboard game: some reputed experts are pitted against a portfolio that was selected "by throwing darts". This makes compelling journalism -- especially when the darts win -- but is less than perfect science. However, a more rigorous version of this game is good science. The enhanced method generally goes by the name of "random portfolios" or "Monte Carlo simulation". It has the power to radically transform the practice of fund management -- a dart to the heart. We will start by taking a close look at performance measurement. We will then move on to some wider issues of fund management. A slightly edited version of this appeared in the March 2007 issue of Professional Investor under the title "Bullseye". 2006 Patrick Burns. "Random Portfolios for Evaluating Trading Strategies" (pdf) This draft: 13 January 2006 Abstract: Random portfolios can provide a statistical test that a trading strategy performs better than chance. Each run of the strategy is compared to a number of matching random runs that are known to have zero skill. Importantly, this type of backtest shows periods of time when the strategy works and when it doesn't. Live portfolios can be monitored in this way as well. This allows informed decisions -- such as changes in leverage -- to be made in real-time. An R package associated with this paper is available from the public domain code area. More on random portfolios can be found on the random portfolios page. 2005 Patrick Burns. "Multivariate GARCH with Only Univariate Estimation" (pdf) This draft: 01 March 2005 Abstract: This brief note offers an explicit algorithm for a multivariate GARCH model, called PC-GARCH, that requires only univariate GARCH estimation. It is suitable for problems with hundreds or even thousands of variables. PC-GARCH is compared to two other techniques of getting multivariate GARCH using univariate estimates. 2004 Patrick Burns. "Performance Measurement via Random Portfolios" (pdf) This draft: 02 December 2004 Abstract: Problems with performance measurement using information ratios relative to a benchmark are exposed. Random portfolios (that obey constraints but disregard utility) are shown to measure investment skill effectively. Investment mandates can also be based on random portfolios -- this allows active fund managers more freedom to implement their ideas, and provides the investor more flexibility to gain utility. The issue of the proper attitude towards tracking error is broached, but left largely undecided. There is also a critique of Fisher's method of combining p-values that shows Stouffer's method to be preferable. A revised version of this with some additional material appears as "Random Portfolios for Performance Measurement" in Optimisation, Econometric and Financial Analysis E. Kontoghiorghes and C. Gatu, editors. Springer. More on random portfolios may be found in Random Portfolios in Finance. Patrick Burns. "Permuting Super Bowl Theory" (pdf) This draft: 02 January 2004 Abstract: The quality of stock market predictions based on the winner of the Super Bowl is examined using permutation tests. These tests are very easy to perform in modern computing environments like the R language. One key point that comes to light is that the success rate of a prediction is not a good measure of its usefulness. Statistically significant success in prediction does not automatically lead to economically profitable strategies. Associated software and data are discussed in R for the Super Bowl. 2003 Patrick Burns. "Sharper Fund Management" (pdf) This draft: 17 November 2003 Abstract: The current practice of fund management can be altered to improve the lot of both the investor and the fund manager. Tracking error constraints in mandates can be replaced by an evaluation of the added value provided to the investor by the fund manager. The value of the manager depends not only on the outperformance of the manager's fund, but also on its volatility and its correlation to the rest of the investor's portfolio. Hyperpassive funds -- an approach suggested by the new mandate scheme -- show promise. Patrick Burns. "The Technical Analysis Challenge" (pdf) This draft: 07 October 2003 Abstract: We report on a study of the ability of analysts to distinguish an actual price series of an equity from random alternatives. Virtually all of the statistical tests on the results support the hypothesis that no skill was exhibited in selecting the correct response. Many of the analysts were extremely over-confident about their ability to select correct answers. The one area where it seems skill might have been exhibited is in the selection of correct answers that happened to be far from the random choices. Pointers to the graphs and data for the test, results of the participants, and so on can be found here. Instructions for using the data in R are in R for the Technical Analysis Challenge. Patrick Burns. "Portfolio Sharpening" (pdf) This draft: 21 September 2003 Abstract: We explore the effective gain or loss in alpha from the point of view of the investor due to the volatility of a fund and its correlations to other asset classes. Fund managers and investors can be guided by this to increase the utility that is ultimately delivered to the investor. In this analysis of investor utility, the Sharpe ratio is shown to be misleading and the tracking error has no role at all. A new class of funds -- called "hyperpassive" -- is suggested which are similar to traditional index funds, but which aim to deliver a comparable expected return with less volatility than the benchmark. It is also shown that the optimal allocation to additional asset classes can be surprisingly high when the correlations are small. Accompanying software is available in the public domain area. Patrick Burns. "Does My Beta Look Big in This?" (pdf) This draft: 15 July 2003 Abstract: Simulations are performed which show the difficulty of actually achieving realized market neutrality. Results suggest that restrictions on the net value of the fund are particularly ineffective. A negative correlation -- that is, market negativity -- is proposed as a more reasonable target, both on theoretical and practical grounds. Random portfolios -- portfolios that obey given constraints but are otherwise unrestricted -- prove themselves to be a very effective tool to study issues such as this. More on random portfolios may be found in Random Portfolios in Finance. Patrick Burns. "On Using Statistical Factor Models in Optimizing Long-Only Portfolios." (pdf) This draft: 6 May 2003 Abstract: Realized tracking errors are examined for a series of optimized portfolios using various estimates for the variance matrix. It is clear that the benchmark should be added mathematically to the variance matrix using the constituent weights -- this dramatically outperforms the case where the benchmark is a separate asset in the return matrix or where relative returns are used. The common belief that factor models are to be preferred to sample variance estimates is confirmed, but only on condition that the benchmark is added mathematically to the variance matrix. 2002 Patrick Burns. "The Quality of Value at Risk via Univariate GARCH." (pdf) This draft: 10 October 2002 Abstract: The estimation of value at risk using univariate GARCH models is examined. A long history of the S&P 500 is used to compare these estimators with several other common approaches to value at risk estimation. The test results indicate that GARCH estimates are superior to the other methods in terms of the accuracy and consistency of the probability level. Although all of the GARCH models tested performed relatively well, the quality of the value at risk estimate does depend on which particular GARCH model is used. Weighting recent observations more heavily when fitting the GARCH model seems to be beneficial. Patrick Burns. "Robustness of the Ljung-Box Test and its Rank Equivalent." (pdf) This draft: 6 October 2002 Abstract: The Ljung-Box test is known to be robust. This paper reports on simulations that show just how robust it is in finite samples. Even so, we demonstrate some practical applications where the robustness of the test fails dramatically. The Ljung-Box test on the ranks of the data provides a suitably robust alternative when the distribution is extremely long-tailed. In particular, the rank Ljung-Box test is highly recommended over the Ljung-Box test for evaluating the adequacy of GARCH models. Simulations also explore properties of the test when applied to binary data. There is some evidence that the test starts to deteriorate as the number of lags exceeds 5% of the length of the series whether or not the data are long-tailed. Go to Burns Statistics Home. Last Modified: 2007 March 08 Direct access to this page is http://www.burns-stat.com/pages/working.html