Below you can find information on some quantitative areas that have been of interest to me. If you happen to have something to share, such as a fresh paper, please feel free to email me.

1. Money manager Performance Evaluation and Attribution, including my recent paper

2. Jump-Diffusion models, parameter estimation and derivative pricing.

3. Statistical Arbitrage / Quantitative Trading   <- Last update: 08/23/2011

4. Extreme Value - Theory and Applications

5. Machine Learning (e.g., Neural Networks)

6. My reviews of QuantFinance and Software books on Amazon 

Money manager Performance Evaluation and Attribution (e.g., in mutual fund industry)

Here you can find my PDF presentation on Mutual Fund Performance Evaluation based on the results obtained up to October 2006. A very detailed survey can be found in Cuthberston. Some of the key papers are posted below. You can also check out the website of Prof. Russ Wermers who is one of the leading researchers in the area.

1. Hendricks, Patel, Zeckhauser, 1993 "Hot hands in Mutual Funds", compare this paper to Carhart 1997

2. Diebold, Mariano, 1995 "Comparing Predictive Accuracy", comparison of forecasters (possibly traders)

3. Ferson and Schadt, 1996, "Measuring fund strategy",  introduction of the conditional multifactor model

4. Carhart, 1997 "On persistence in mutual fund performance", introduction of Carhart four-factor model

5. Daniel et al, 1997  "Measuring Mutual Fund performance",    introduction of holdings-based performance measures

6. Chen et al, 1999, "The value of active mutual fund management", looking into trades-based performance measurement

7. White, 2000, "A reality check for data snooping", - multiple comparisons of technical trading rules

8. Coval et al, 2005, "Can individual investros beat the market?", utilizes a real dataset from  a large brokerage firm and claims that the answer is YES

9. Wermers, Jan 2006, "Performance evaluation with portfolio holdings information", survey of holdings-based performance measures

10. Kosowski et al, 2006, "Can mutual fund "stars" really pick stocks?" - another influential paper

11. Cuthbertson et al, 2006, a survey of mutual fund studies, 1986-2006

12. Avramov, Wermers, 2006, "Investing in mutual funds when returns are predictable" - this is an important reference paper for the  two articles of Avramov et al. (2010) discussed below.

13.  Mamaysky et al, 2007, "Improved forcasting of mutual fund alphas and betas"  - increasing the quality of performance measures

14. Tuzov, 2007, "An overview of mutual fund performance evaluation studies" (presentation in pdf)

15. Barras et al, May 2008 , "False Discoveries in mutual fund performance" - a direct attempt to incorporate multiple comparisons into mutual fund performance evaluation. My own PhD research resulted in a sequel to this paper. Please see my paper below.

16. Romano et al,  2007, "Control of the false discovery rate under dependence" - not specifically on mutual funds, but performance evaluation in general

17. Huij and Verbeek,  2008,  "On the use of multifactor models" - criticism of the popular 4-factor Carhart model

18. Aldridge,  2009,  "Improving accuracy of high-frequency trading forecasts"    

    This paper introduces a way to measure the performance of a high-frequency trading strategy. An important idea behind Aldridge's approach is not the utilization of well-known ROC curve, but recognizing that trading decisions are made all the time. A trader's decision to do nothing at time t is just as informative as his decision to buy or sell. If he did nothing and avoided losing money, he has to get just as much credit as for making money by going long/short. Implementing this approach is fairly simple for fully automated strategies, and an interesting question is whether a similar idea can work for human-generated trades. In any case, trade-based performance measures (e.g., Chen et al, 1999 ) are the most powerful compared to multifactor-based (e.g., Carhart) or holdings-based (Daniel et al).

19. Jagannathan et al,  2010,  "Do hot hands exist among hedge fund managers?"    

    This paper was published in Journal of Finance in Feb 2010 and addresses a number of issues that were ignored in earlier performance evaluation papers. In 1990's it was a standard practice to use the last period alphas to predict the next period alphas, and the former were treated as observed predictors. This paper acknowledges that it is not so, and incorporates the estimated nature of such values into the model. Another important issue is how to account for the fund closure / liquidation. A fund is likely to get closed for new investors when it's successful, and to liquidate when it's not. In both cases, the returns data stop coming to the hedge fund database, which biases the results. In the end, the authors find a sizable proportion of outperforming funds, but one should not forget that it's all conditioned on a particular multifactor model. If an alternative set of risk factors is proposed in the future (like it happened in the mutual fund literature), it is quite possible that the hedge fund performance will have to be re-evaluated considerably.

20. N. Tuzov, F. Viens,  2010,  "Mutual fund performance: false discoveries, bias, and power"  

    The link above will take you to a publicly available abstract. I can't post the full version here, but I can share it if you contact me.

    The studies of mutual fund performance go back at least 40 years. One of the first was that of Jensen (1968), whose tool was CAPM and the famous "Jensen's alpha". Then, as new models and better datasets were introduced, the (academic) mutual fund literature grew accordingly. Some of the recent developments can be found in the papers posted above.

    The issue of "multiple inference" (a.k.a. "multiple testing") was not investigated until the work of Barras et al, which was published in Journal of Finance in Feb 2010. The "multiplicity" issue can be well illustrated by a "large competition" effect. Suppose you are told that there is this stock trader who proved himself by being on the right side in 90 out of 100 trades. It definitely looks like a great investment opportunity.

    However, if you were to find out that the trader was the winner of a stock picking contest with 2000 participants, the result doesn't look that convincing at all. The 2000 contestants might have picked stocks by throwing darts, and yet, because there are 2000 of them, at least one stands a good chance to score 90 out of 100 or higher. The winner is simply lucky, but he appears to be skillful to the investor, as long as the latter is unaware about the presence of the other 1999 participants.

    Barras et al investigate the issue using the 4-factor Carhart model to estimate the performance of each mutual fund individually. That is, the p-value for Carhart's alpha is the test statistic of interest. I also use Carhart model and a similar dataset, but my paper extends the work of Barras et al in two ways.

    1) Barras et al assume that the test statistics are independent across mutual funds. Secondly, they assume that the performance evaluation model (Carhart) is perfectly well specified. I show that these assumptions are not consistent with the data, and taking that into account can change the results dramatically. For instance, Barras et al  find a sizable proportion of outperformers based on pre-expense returns data. Also, they find that mutual funds are more likely to outperform in short term (presumably because in the  long term, the edge gets "arbitraged away"). However, as soon as a more flexible model that doesn't rely on the assumptions above is applied, all the evidence of outperformance vanishes.

    2) The absence of outperformance found above is of little surprise, because it is consistent with almost all of the mutual fund performance evaluation studies up to date. It is also consistent with so-called Efficient Market Hypothesis. In fact, Fama-French and Carhart models are routinely used to test newly proposed "market anomalies". However, when one fails to find evidence of something, there are two possible reasons for that: a) that "something" isn't there b) "something" is there, but the instrument used for searching is not sensitive enough.

    Therefore, it is of major interest to see whether Carhart and similar multifactor performance evaluation models can detect an economically significant level of outperformance. My results show that such detection ability ("statistical power") is very low. For instance, when, by construction, 122 funds in the population have Carhart alpha of 5% p.a., only 42 of them are included in the estimated proportion of outperformers, and 80 good funds are considered useless. Further, if one wants to construct an outperforming portfolio of funds, it's a problem also. Suppose the true number of outperformers is indeed 42, and you want all of them to be in your portfolio. Then, you will have to include about twice as many useless funds. That happens because the model has little ability to distinguish between outperformers and the rest, and, in order to make sure that all 42 outperformers are included, it must include a large amount of "garbage" as well.

    Theoretically, it is possible to increase the detection ability by increasing the amount of historical data. Unfortunately, the computations show that, to get decent improvement, one would have to have 20 to 30 years of monthly data per fund, which is beyond realistic.

    Oddly enough, this bad news can be seen as good, because it suggests that, in many cases, the tools to measure market inefficiencies are very imprecise. Correspondingly, the credibility of negative results, including Efficient Market Hypothesis itself, has to be on the same level as the precision of the employed test tools. In the case of multifactor models, the precision is very low. In that sense, I don't believe in the future of multifactor models. The holdings-based measures (see Wermers, 2006 and Kothari and Warner, 2001) appear to be a good alternative, but they require lots of disclosure from the fund manager.

    The statistical machinery used in my paper can be also applied to the problem of model selection. Suppose that you have a large number of candidate models, and assess them based on AIC. Remember that AIC, just like the p-value of Carhart's alpha, is a random quantity. It is quite possible that the model with the best AIC is simply "lucky" and there are simpler models that are just as good, although not so "lucky" in terms of AIC.

    Another, more direct application is evaluation of a large number of trading strategies. As soon as there is a test statistic to assess the performance of an individual strategy, it's possible to set up a procedure that would separate "lucky" strategies from the ones with true edge. In fact, an example of early "multiple testing" methodology can be found in White, 2000, who tests about 3600 daily trading strategies for S&P500 index.

21. Avramov et al,  2007-2010,  "Hedge funds, managerial skills, and macroeconomic variables."  

    This paper is inspired by Avramov and Wermers (2006), who exploit four macroeconomic predictors (default spread, dividend yield, term spread, Treasury yield) to forecast mutual fund performance. This sequel study looks into hedge funds: the monthly dataset includes about 8000 hedge funds observed between 1998 and 2008. Avramov et al. find that, to handle hedge fund data, the macroeconomic predictor set should be different from that used for mutual funds. As a result, they use the default spread and VIX.

    The optimal hedge fund portfolio is formed by maximizing the expected utility of future wealth. The distribution of that wealth is conditioned on the macroeconomic variables. Because the utility function is quadratic, this approach involves estimation of a huge (8000 by 8000 or so) variance-covariance matrix of hedge fund returns, and the amount of available data is not sufficient for that (this is a commonly acknowledged pitfall of Markowitz mean-variance framework).

    Still, the optimal portfolio appears to perform well and has a nice Fung-Hsieh seven-factor alpha. It does not disappear when Fung-Hsieh model is augmented with a few more factors, such as Pastor and Stambaugh liquidity factor. Overall, the idea of using macroeconomic variables for hedge fund portfolio selection appears to add value.

     

22. Avramov et al,  2010,  "Hedge fund predictability under the magnifying glass."   

    This paper is a sequel to the one above. The changes can be summarized as follows:

    1) Two new macro predictors, dividend yield and net aggregate flows into the hedge fund industry, are added to the default spread and VIX used in the previous paper.

    2) The quadratic utility / mean-variance framework is traded for the "ranking" approach. For each fund, a scalar signal is calculated. Then, the funds are ranked according to that statistic, and the top 10% are included in the portfolio.

     The sample includes over 7000 funds observed between 1997 and 2008. The authors attempt to incorporate such practical restrictions as illiquidity, possible liquidation of hedge funds, lags in reporting returns, redemption notice, and the typical number of funds in a fund of funds.

    The utilized statistical machinery boils down to multiple linear regression. The main finding of the paper is that the standard approach, when all four predictors are placed in the right-hand-side of the model, does not work. Still, it is possible to obtain a high-quality signal derived from the four predictors: fit a regression model separately for each predictor and take a simple average of the four signals. The "combination strategy" exhibits a good out-of-sample performance in 1997-2007 and a reasonably well performance in 2008. The performance evaluation criteria include Information Ratio, Sharpe Ratio, and the value of alpha from the augmented Fung-Hsieh model.

    Apparently, a predictive relationship between the four covariates and the future returns does exist, but its true form is not described well by multiple linear regression. The "combination strategy" essentially suggest an alternative form of that relationship, which turns out to be closer to reality.

     

23. Tuzov,  2011,  "Applied fund-of-funds construction: a robust approach"   (New)

    This white paper was inspired by the last two papers of Avramov et al. As we can see from these and many similar papers, it is typical for an academic approach to be based on ranking funds by a single quantitative measure. In practice, however, multiple quantitative metrics and due diligence factors are taken into account. Does it mean that the academic insights are useless, and, if not, how do we build a "bridge" between what academics and practitioners are accustomed to? I attempt to help the practitioners by proposing a simple and robust framework that provides an approximation to many "ranking" portfolio formation methods described in the academic literature.

    The computational part of this project has been developed in SAS (click  here to see).

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Jump-Diffusion models: parameter estimation and derivative pricing.

1. Ho, Perraudin, Sorensen, 1996, “A continuous time arbitrage pricing model with stochastic volatility and jumps”

2. Honore, 1998, “Pitfalls in estimating Jump-Diffusion Models”

3. Ramezani, Zeng, 1998, “Maximum Likelihood estimation of asymmetric Jump-Diffusion process”

4. Kou, 2002 “A Jump-Diffusion Model for Option Pricing”

5. Kou, Wang, 2003, “First passage times of a Jump-Diffusion process”

6. Ait-Sahalia, 2003, “Disentangling diffusion from jumps”

7. Kou, 2004 “Option pricing under a Double Exponential Jump-Diffusion Model”

8. Ramezani, Zeng, 2004, “An empirical assessment of the Double Exponential Jump-Diffusion process”

9. Tuzov, 2007 "GMM parameter estimation for the Double Exponential Jump-Diffusion process" (term paper)

The MLE estimation Double Exponential Jump-Diffusion model is far from simple. Therefore, in my term paper of 2007 I tried to estimate the parameters via GMM (strictly speaking, I utilize the "non-generalized" Method of Moments because the number of moments is equal to the number of parameters). The attempt resulted in a failure because of very high correlation of GMM moment conditions. SAS code and the data are available here. Apparently, this method doesn't work well in practice for this model. Correspondingly, Ramezani and Zeng are focusing on either MLE or MCMC estimation.         

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Statistical Arbitrage / Quantitative Trading

Interesting fact: While many people think that the inventor of Statistical Arbitrage was Nunzio Tartaglia (or even Paul Wilmott) the credit should go to Gerald Bamberger. After Dr. Bamberger left Morgan Stanley, he practiced the strategy during 1985-1989 as a partner in a hedge fund called BOSS Partners. Afterwards, Dr. Bamberger left the world of trading and earned a degree in law.  He presently works as a professor at State University of New York School of Law.

While there have been some relevant papers published (see below), it appears that books on how the strategy is implemented in practice are few. "Pairs trading" by Vidyamurthy used to be the best source available in 2004-2007 and possibly even further. My review is posted on Amazon, but here I want to elaborate: on pp 112-115 the author describes "tradability testing" which I think has a couple of errors.

First of all, "the model-free approach" - is it possible? The idea that the time series may be tested for stationarity without having to specify a parametric model is very attractive, and I got interested in it long before I read the book. However, none of my professors at Purdue Department of Statistics heard about a test of that kind. Therefore, one does have to specify a parametric model for the cointegration  residuals ( in ADF test it is taken to be AR(p) ).

Secondly, look at how the "bootstrap" is used. Suppose, you have a sequence of times when the residual series crosses zero: t1, t2, t3, tN. The times between subsequent crosses are, correspondingly, (t2-t1), (t3 - t2), etc. The author claims that "we look to estimate the distribution of the time between two crosses" based on the latter series. However, since the sample is small, the author suggests we resample with replacement from the original sample to obtain a much larger sample. The latter is then used to estimate the "probability distribution" and then "percentile levels can be constructed for the population".

Essentially, the author proposes a free data-generating machine. Think of it this way: the original sample (t2-t1), (t3 - t2), etc. has, say, 20 observations. That is hardly enough to estimate the probability distribution (cdf). But not to worry: using the procedure above, we can generate 100, 500, or even a million observations that are treated as i.i.d. sample to estimate the cdf. That's a bit too good to be true.

In reality, what one can hope to do in a small data situation is to use the bootstrap to find the standard error and confidence interval for the estimate of the MEAN time between two crosses. One will probably have to use a time series bootstrap because the (t2-t1), (t3 - t2), etc may be serially correlated. Again, the possible serial correlation was never mentioned by the author. But it is surely impossible to get a decent estimate of cdf based on 20 observations, bootstrap or no bootstrap.

Now, let me talk about how things have changed since I started this section in 2006. Back then, the "high-frequency trading" was not a household term. The "classical" statarb methods described in "Pairs trading" and many other sources assume that trading happens at a relatively low frequency, typically daily. The trader pays the full transaction cost, as if he were a long term investor, and usually holds the position open for a few days. Trading in / out of the stock more than, say, 10 times a day is definitely unprofitable. However, this is not the case with HFT. Being able to trade at a much higher frequency can be explained by at least two factors: acting as a market-maker who charges the bid-ask spread instead of paying it; receiving so-called rebates. This table contains a summary of HFT strategies. Technically speaking, some the quantitative methodology of HFT must have been derived from the "classical" statarb research.

• Engle, Granger, 1987, "Cointegration and error correction", - a fundamental paper on cointegration

• Kerry Patterson, 2000, - a good textbook with a number of cointegration examples

• B. Pfaff, 2005, - a practical guide on cointegration analysis in R

• Alexander, Dimitriu, 2002, "The Cointegration Alpha"

  An interesting study of how the theory of cointegration may be applied to creating a long-short market neutral strategy. Note that all assets in the cointegration approach are considered in levels (e.g., log-price) whereas the classical asset pricing theory (CAPM, APT, etc) operates with asset returns. The important implication is that if a certain portfolio outperforms the benchmark in levels (such portfolio is called “plus portfolio” in the paper) it won’t be necessarily outperforming in terms of returns. Putting the theory aside, the backtesting results (based on DJIA stocks) are encouraging, but only just.

• Zapart, 2003, "Statistical Arbitrage Trading with Wavelets"

A new option pricing model based on wavelets and neural networks is the basis of the proposed option trading strategy. Field tests use the real option prices from CBOE and the result looks promising even after transaction costs.  It would be also useful to know how much risk capital (e.g., to maintain margin) is required for the strategy.

• Hogan et al, 2004, "Testing market efficiency using Statistical Arbitrage"

Identifying market inefficiencies based on equilibrium models (e.g., CAPM) contains a “joint hypothesis” problem: if a trading strategy has a positive and significant alpha, it’s either because it is a “true anomaly” or the asset pricing model is misspecified. This paper introduces an intuitively appealing definition of “statistical arbitrage opportunity” that is independent of the equilibrium asset pricing model and thus gets around the joint hypothesis problem. A parametric test to check if a trading strategy is a statistical arbitrage is provided.  Note that the definition and test are based on the asset price levels as opposed to returns.

In particular, it turns out that the stock momentum effect is an arbitrage opportunity (“free lunch”) but the book-to-market ratio-based strategy is not (that is, B/M is a proxy for risk).  The size effect is not a free lunch either and, in any case, the paper confirms the claim that SMB factor has not been priced since mid-80s.

• Sudak, Suslova, 2005, "Behavioral Statistical Arbitrage"

This paper provides an overview of many popular results from Behavioral Finance and related stock market anomalies.  Some general information about Stat Arb strategies is also given.

However, the presented trading strategy is far from impressive: it is a mere exploitation of the well-known momentum effect combined with some restrictions whose target is to achieve market neutrality of the portfolio (“zero-beta” strategy).

Even if we assume that momentum effect is a “true anomaly” (as opposed to one more dimension of risk), the performance still has to be adjusted for at least market exposure via CAPM because even the “zero-beta” strategy has the real beta different from zero. Alternatively, one may test the strategy based on the method of Hogan et al. Oddly enough, this paper explicitly refers to Hogan et al but all it does is evaluate the performance based on the ratio of its annual return to its annual volatility (it’s not even clear whether the return is over the risk-free rate) and no transaction costs are taken into account.

•  Alexander, Dimitriu, 2005, "Indexing and Statistical Arbitrage" 
  
   Alexander, Dimitriu, 2005, "Indexing, Cointegration, and Equity Market Regimes"
   

  A conventional approach to index tracking is to construct a portfolio whose return is highly correlated with that of target index. In these two papers, however, the tracking portfolio is constructed based on price levels rather than returns. While both approaches may look similar, there is a large theoretical difference. Suppose that Xt and Yt denote log-prices, and dXt, dYt are log-returns. The conventional approach considers the regression:

  dYt = beta0 + beta1 * dXt + Eps_t,       where Eps_t is an independent white noise sequence.

  The tracking portfolio is considered good when the regression has a high R-squared, or, roughly speaking, the variance of Eps_t is small. Now try to integrate the expression above, and you will see that in levels:

  Yt = beta0 * t + beta1 * Xt + Zt,  where Zt is a random walk obtained from integrating Eps_t.

  Since Zt is an independent random walk, we see that, even under the absence of time trend (beta0 = 0), Xt and Yt are going to drift apart.  A high value of correlation of log-returns means that the divergence in levels will be relatively slow, but, given enough time, any magnitude of divergence can be reached. On the other hand, cointegration in levels, if present, rules out such situation by construction.

  However, in the first paper posted above, they do not find much empirical evidence in favor of cointegration vs. correlation. In the second paper, they look into the abnormal returns of cointegration-based portfolio. The abnormal returns are modeled with an elegant two-state Markov switching model. It turns out that most of the abnormal returns are associated with one particular Markov state. While not focused on trading applications, these papers enhance one's understanding of what modeling approaches are likely to be useful in the area as a whole.

•  Bourgeois, Minko, 2005, "Cointegration on the Equity Market"

  A fairly straightforward application of cointegration theory to the15 most liquid stocks taken from EuroStoxx50 index. Apart from stock pairs, triplets and quadruplets are also considered. The cointegration test is based on the method of Johansen. The results are quite promising even after transaction costs.

• Thomaidis et al, 2006, "An intelligent Statistical Arbitrage Trading system"

This is a good example of how a “pairs trading” kind of Stat Arb can be implemented for a particular pair of Indian stocks. While profitability of the proposed strategy is questionable due to transaction costs, the study is valuable from the methodological perspective. For instance, when a direct cointegration approach fails (Phillips-Perron tests shows no cointegration) they turn to modeling the spread via Neural Network-GARCH model with a separate rule for choosing the rolling window.

• Bock et al, 2008, "A regime-switching Relative Value Arbitrage rule "

And if for some reason you didn’t like the NN-GARCH model above,  this small paper throws another suggestion: a two-state Markov regime-switching model. While we are on regime-switching models, I may as well suggest that a more advanced multifractal version can also be used for spread modeling.

 

• Pole, 2007, "Statistical Arbitrage" - DO NOT buy this book. Check out my review on Amazon for the details.

• Fernholz and Maguire, 2007, " The Statistics of Statistical Arbitrage "

Describes a statistical arbitrage strategy that is essentially an automatic market-maker that generates high information ratios when tested on large-cap US stocks data. However, no transaction costs are taken into account and the execution is assumed instantaneous. It is too bad that these two prominent practitioners of Stat Arb at INTECH can not reveal how they actually do it.

•  Avellaneda, Lee, 2007, " Statistical Arbitrage in the US equities market "

  Describes Stat Arb strategies based on PCA and ETF multifactor models for US stock returns. Note that although the word “cointegration” is used, the “classical” cointegration tests, (like Phillips-Perron) are not used here. Instead, the residual returns from the multifactor model are integrated to obtain the residuals in levels of asset prices. Then a simple mean-reverting model is fit to them and trading starts only if the estimated parameters are consistent with good mean-reverting properties of residuals.

  After transaction costs, the strategies still look good. Comparing this to the paper of Zapart one may again say that it would be good to know the amount of risk capital that such strategy can require in order to measure the true profitability. Incidentally, the strategies reproduce the August 2007 blow that many quant hedge funds actually suffered.  

•  Galenko et al, 2007, " Trading in the Presence of Cointegration "

  This paper is remarkable because it establishes the properties of asset returns that are necessary and sufficient for the system to be cointegrated in levels.  These properties allow one to construct a statistical arbitrage strategy in which each transaction has a positive expected profit (at least in theory).

  The strategy is tested with four major indices: AEX, DAX, CAC, FTSE. First, the cointegration vector is found (via Johansen rank test) based on 1996-2001 data. Then, the weights for the four indices are estimated to achieve a positive expected return based on the abovementioned findings. The trading results (w/o transaction costs) for the period of 2001-2006 are quite good.

  It would be nice to see how the strategy works in the present environment and with real transaction costs. After all, it is unlikely that there are major inefficiencies in those four highly liquid indices.  Still, the underlying idea of this strategy can work quite well elsewhere.

•  Marshall et al, 2007, "Can commodity futures be profitably traded?"  

  This paper looks into the performance of popular technical trading rules (moving averages, support and resistance, etc) applied to 15 commodity futures such as cocoa, coffee, and gold. The daily data cover 1984-2005 and over 7000 specifications of trading rules are considered. Correspondingly, an important question is how to adjust for data snooping, i.e., the fact that a certain number of strategies will falsely appear outperforming (even out of sample) because the pool they are selected from is so large. This is done according to the method of White and, after data snooping is taken into account, there are no positive results.

•  Dunis et al, 2007, " Quantitative trading of gold and silver" 

  Similarly to the paper above, this study works with daily gold and silver spot data from 2000 to 2006. The Nearest Neighborhood and two Neural Network models are compared to ARMA benchmark. The results suggest that advanced models do add value compared to the benchmark and obtaining real trading profits is not out of question.

•  Perlin, 2007, "Pairs trading strategy at the Brazilian stock market" 

  This paper uses the simplest pairs trading strategy (minimal squared distance rule, no cointegration tests) and claims to obtain good results when trading daily.

•  Schumaker et al, 2007,  2008, "Evaluating a news-aware quantitative trader" 

  This study combines  well-known Momentum and Contrarian strategies with a news article prediction system. Naturally, the processing and quantification of textual information is a very challenging problem. Technically speaking, it is based on Support Vector Regression.  In the end, incorporating news adds significant value to the "plain vanilla" Momentum and Contrarian strategies.

•  Ed Thorp, 2008-2009 (courtesy of Wilmott Magazine)

A fascinating history of Statistical Arbitrage (with few quantitative details):

Part 1  Part 2  Part 3  Part 4   Part 5    Part 6

 

•  Triantafyllopoulos, Montana, 2009, "Dynamic modeling of mean-reverting spreads" 

  In this paper, the "spread" refers to a presumably stationary (mean-reverting) linear combination of two or more asset prices. To check the mean reversion property, it is assumed that the spread is an AR(1) process with time-varying coefficients. Note that the time-varying coefficients can be introduced by simply using a standard AR(1) with a rolling window, but then the analyst is to choose the window length manually.  In contrast, modeling the coefficients as time-varying makes the model self-tuning in that respect. A familiar state space model and Kalman filter are used for efficient on-line estimation. The noise variance in the state equation is estimated through the so-called component discounting.

  The authors demonstrate the model on two simple spreads, each containing only two assets, e.g., Exxon Mobil - Southwest Airlines. The mean reversion property is monitored on-line by re-estimating the AR(1) coefficients after each new observation. To me, this looks more flexible than the standard cointegration tests (their results are provided for comparison) that require the full sample and give a yes-no answer. 

   

•   Ahmed et al, 2009, "Statistical Arbitrage in High Frequency Trading" 

  Unlike all of the articles above, this paper uses high-frequency tick data from Nasdaq (incidentally, the authors make a point that Nasdaq data are better than TAQ). The paper proceeds as follows:

  1) The authors set up an order matching algorithm that consists of about twenty rules for handling incoming orders.

  2) The actual Nasdaq market, limit and cancellation orders for a number of stocks are fed into the engine. As a result, the engine shows a reasonable correspondence to reality in terms of how many shares change hands in the end.

  3) Using the birth-death chain model of Cont et al, the probability of an upward price move is estimated. The model includes covariates such as last trade price and ask volume. If the probability is over a certain threshold, the buy order is initiated.

  The authors test a few strategies using the tick data and the engine set up in Step 1) to simulate the actual trading environment. For technical reasons, the price impact of the orders generated by the strategy is not taken into account. As a result, the automated trading rules do not perform well, and the authors suggest that an expert should "assist" the strategy by assessing the market sentiment and setting the strategy parameters accordingly.

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Extreme Value - Theory and Applications

•  US energy market: Extreme Value Analysis

These are initial results from my joint project with Prof. Pilar Munoz who previously did similar research on European energy market.

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Machine Learning Applications

Agarwal and Merugu, two researchers from Yahoo Research Group, proposed a state-of-the-art machine learning method to build a movie recommendation system. The method combines both supervised and unsupervised machine learning techniques. I decided to extend the supervised part by using a Neural Network. To see if it adds any value, I compared both approaches on a real movie dataset. To find out more, please click here.

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