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
Money manager Performance Evaluation
and Attribution, including
my recent paper
Jump-Diffusion models, parameter estimation and
Statistical Arbitrage /
<- Last update: 08/23/2011
Extreme Value - Theory and Applications
Machine Learning (e.g., Neural
My reviews of QuantFinance and Software books on
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.
Patel, Zeckhauser, 1993 "Hot hands in Mutual Funds",
compare this paper to Carhart 1997
Diebold, Mariano, 1995 "Comparing Predictive Accuracy",
comparison of forecasters (possibly traders)
Ferson and Schadt, 1996,
"Measuring fund strategy",
introduction of the conditional multifactor model
1997 "On persistence in mutual fund performance",
introduction of Carhart four-factor model
Daniel et al, 1997 "Measuring Mutual Fund
introduction of holdings-based performance measures
Chen et al, 1999, "The value of active mutual fund
management", looking into
trades-based performance measurement
White, 2000, "A reality check for data snooping",
- multiple comparisons of technical trading rules
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
Wermers, Jan 2006, "Performance evaluation with
portfolio holdings information", survey of holdings-based performance measures
Kosowski et al, 2006, "Can mutual fund "stars" really
pick stocks?" - another influential
Cuthbertson et al, 2006, a survey of mutual fund
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.
Mamaysky et al, 2007, "Improved forcasting of
mutual fund alphas and betas" -
increasing the quality of performance measures
Tuzov, 2007, "An overview of mutual fund performance
evaluation studies" (presentation in pdf)
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.
Romano et al, 2007, "Control of the false
discovery rate under dependence"
- not specifically on mutual funds, but performance evaluation in general
Huij and Verbeek, 2008, "On the use of
- criticism of the popular 4-factor Carhart model
Aldridge, 2009, "Improving accuracy of high-frequency trading
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
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,
interesting question is whether a similar idea can work for human-generated
trades. In any case, trade-based performance measures (e.g.,
et al, 1999 ) are the most powerful compared to multifactor-based (e.g.,
or holdings-based (Daniel
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
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
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
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
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
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
who tests about 3600 daily trading strategies for S&P500 index.
Avramov et al, 2007-2010, "Hedge funds, managerial skills, and
This paper is
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.
Avramov et al, 2010, "Hedge fund predictability under the
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
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
2011, "Applied fund-of-funds construction: a robust approach"
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).
Sorensen, 1996, “A continuous time arbitrage pricing model with stochastic
volatility and jumps”
“Pitfalls in estimating Jump-Diffusion Models”
Zeng, 1998, “Maximum Likelihood estimation of asymmetric Jump-Diffusion
Kou, 2002 “A
Jump-Diffusion Model for Option Pricing”
Kou, Wang, 2003,
“First passage times of a Jump-Diffusion process”
2003, “Disentangling diffusion from jumps”
Kou, 2004 “Option
pricing under a Double Exponential Jump-Diffusion Model”
Zeng, 2004, “An empirical assessment of the Double Exponential
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
Apparently, this method doesn't work well in practice for this model.
Correspondingly, Ramezani and Zeng are focusing on either MLE
or MCMC estimation.
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
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.
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
Kerry Patterson, 2000,
- a good textbook with a number of cointegration
B. Pfaff, 2005,
- a practical guide on cointegration analysis in R
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
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.
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.
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
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.
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
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.
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.
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.
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
can also be used for spread modeling.
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
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
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
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.
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,
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):
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
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.
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
Extreme Value - Theory and Applications
are initial results from my joint project with Prof. Pilar Munoz who previously
did similar research on European energy market.
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
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