Contents

The business of buying and selling securities, curreneies, and commodities on an international scale so as to take advantage of differences in rates of exchange and prices. Please check out my other articles/ posts on quantitative finance at my Linkedin page or on Medium. foreign exchange market As this is a market-neutral approach a lot depends on our ability to short sell which may be limited due to various reasons including regulations. Next, we follow the steps 1 to 4 for the second stock and sum up two asset’s positions for the total portfolio value.

He specializes in quantitative trading strategies and risk management. This book is the result of his own research and experience running a statistical arbitrage hedge fund for eight years. Pole is also the coauthor of Applied Bayesian Forecasting and Time Series Analysis. When a prominent statistical arbitrage model is created, it can sometimes affect the market.

- Swap spread arbitrage is immune from interest rate risk if both the repo rate and LIBOR react similarly to a move in rates.
- Historically, StatArb evolved out of the simpler pairs trade strategy, in which stocks are put into pairs by fundamental or market-based similarities.
- See the below decomposition of Apple’s price history, which we can see is in an uptrend and is also seasonal.

Mortgage arbitrage consists of buying mortgage-backed securities while hedging their interest rate exposure primarily through derivatives . The strategy provides a positive carry as the yield on MBSs is typically higher than that of comparable treasury bonds. As the spread earned is generally small, arbitrageurs use leverage to enhance returns. Mortgage arbitrage strategies can be classified based on the different types of MBS used. A popular implementation of the strategy is with pass-through MBSs which pass all of the interest and principal cash flows of a pool of mortgages to the pass-through investors .

As a trading strategy, statistical arbitrage is a heavily quantitative and computational approach to securities trading. It involves data mining and statistical methods, as well as the use of automated trading systems. Statistical arbitrage has become a major force at both hedge funds and investment banks.

They use the components of the S&P 500 index as an observation target. They argue that when the stock price deviates from equilibrium, the investor can enter the trade after controlling for risk and transaction costs. They also show that the distance method generates insignificant excess returns, but the cointegration method provides a high, stable, and robust return. This section presents the results of optimal statistical arbitrage trading of Berkshire Hathaway stock with its replicating asset. First, we construct a replicating asset, which will have similar risk and return characteristics with the actual Berkshire A stock price by using the five-factor model (Eq ) and the Buffett-factor model (Eq ). The factor loadings of the replicating asset are estimated by regressing the excess return of Berkshire A on right-hand-side factors of Eq and Eq .

## Build, Test, And Implement Statistical Arbitrage Trading Strategies With Matlab

Also known as pair trading, statistical arbitrage involves the buying and selling of securities based on their long term relationship to each other. That is to say, the price of stock for companies in the same sector of the economy may follow each other in some statistically significant manner. When that relationship varies from what is considered “normal” in the near term, an arbitrage opportunity may exist, since the expectation is the long-term relationship will eventually return. For example, there may be a long-term relationship between the price of FedEx common stock and that of UPS. When that relationship varies from the norm in the near term, price arbitrage exists if that relationship eventually returns to normal.

In a real world application, that discovery could only be made in real time, when the unknown, future ETFs prices are formed. So, because of the risk in trading equities, it is vitally important to spread the risk amongst a large number of pairs. That way, when one of your pairs trades inevitably blows up for one reason or another, the capital allocation is low enough not to cause irreparable damage to the overall portfolio. Nor are you over-reliant on one or two star performers that may cease to contribute if, for example, one of the stock pairs is subject to a merger or takeover. One of the questions of interest is the optimal sampling frequency to use for extracting the alpha signal from an alpha generation function.

According to Avellaneda and Lee , the term statistical arbitrage encompasses a variety of strategies characterized by systematic trading signals, market neutral trades and statistical methods. Montana defines SA as an investment strategy that exploits patterns detected in financial data streams. Burgess defines statistical arbitrage as a framework for identifying, modelling and exploiting small but consistent regularities in asset price dynamics. Thomaidis and Kondakis define SA as an attempt to profit from pricing discrepancies that appear in a group of assets. Do, Faff and Hamza claim that SA is an equity trading strategy that employs time series methods to identify relative mispricings between stocks. Burgess also describes statistical arbitrage as a generalization of a traditional arbitrage where mispricing is statistically determined through replicating strategies.

For example, the use of a common classification system allows investigating the profitability and riskiness of SA strategies across asset classes and time. This enables mapping pricing anomalies and can provide directions on how to improve pricing models. The existence of persistent SA opportunities in selected strategies can be used as an indicator to direct future research to less studied asset classes and instruments. Having a framework brings transparency to the term SA, helping investors in making investment decisions. For example, our definition of SA can be used in the hedge funds industry where there is no agreement on a standardized classification system of strategies .

There comes a point at which the portfolio has lost more than the risk-tolerance parameters allow, which means that humans step in. The humans start to liquidate, usually in a haphazard fashion, and these liquidations further throw off the correspondences. 1Ornstein-Uhlenbeck is a model used to describe the multivariate dynamics of financial variables . Based in Pittsburgh, Analyzing Alpha is a blog by Leo Smigel exploring what works in the markets.

## Related Terms

And it is no surprise, to perform it correctly, one must diligently examine, compare and contrast numerous test results, graphs and characteristics. For example, cointegration analysis alone can be performed in one of two methods – utilizing the Engle-Granger approach or the Johansen approach. Statistical Arbitrage are trading strategies that typically take advantage of either mean reversion in share prices or opportunities created by market microstructure anomalies. It is a highly quantitative analytical approach involving a well-diversified portfolio of securities. However, to illustrate the concept I will take the example of pairs trading involving only two cointegrated securities. Whilst both cointegration and correlation can measure asset prices that move together and hence establish a relationship, correlation breaks down on the long-term but is somewhat robust in identifying short-term relationships.

The estimated premium is therefore a valid basis for investment strategies. Statistical arbitrage risk can be estimated by using ‘elastic net’ estimation and related machine learning. This method selects a relatively small hedge portfolio from a large array of candidate stocks. There are various frameworks that could be used to identify a pair of stocks and build pairs trading strategies.

## Algorithmic Strategies Catalog

Because of this we propose to use the definition in conjunction with a classification scheme. For each trading strategy, the table reports whether the listed features are present or not. Statistical arbitrage still works as new instruments, exchanges, and financial markets create trading opportunities. Additionally, stat arb strategies that stopped working can come back into favor. Volatility arbitrage is a trading strategy that attempts to profit from the difference between the forecasted future price-volatility of an asset. Remember, most stock market crashes arise from issues with liquidity and leverage—the very arena in which statistical arbitrageurs operate.

Hogan’s SA partially requires acceptably small potential losses as the probability of a loss converges to zero with time. All definitions embed the concept of take profit as long as it is assumed that a strategy is closed at maturity or when the expected returns are no longer positive. AOs can be closed in stop loss if the triangular arbitrage realized loss is higher than what is acceptable according to the stress measures. Hogan’s SA has the concept of stop loss if it is assumed that a strategy is closed when the constraints on the probability of a loss are no longer satisfied. AA trades are closed in stop loss only if the gain-loss ratio is lower than one.

## Successful Statistical Arbitrage

Statistical arbitrage is also subject to model weakness as well as stock- or security-specific risk. The statistical relationship on which the model is based may be spurious, or may break down due to changes in the distribution of returns on the underlying assets. Factors, which the model may not be aware of having exposure to, could become the significant drivers of price action in the markets, and the inverse applies also. The existence of the investment based upon model itself may change the underlying relationship, particularly if enough entrants invest with similar principles. The exploitation of arbitrage opportunities themselves increases the efficiency of the market, thereby reducing the scope for arbitrage, so continual updating of models is necessary. Pairs selection is the first crucial step to building a pairs trading strategy.

Read daily pricing data from prices.csv and remove tickers where we have less than 10 years of data. Figure 2.4.2In order to make sure this is true, we test for cointegration by analyzing the residuals created by the regression. The test we shall use is the Dickey-Fuller test which will ultimately test for stationarity in the residual series. The cause of this inefficiency can be anything from a range of errors such as a delay in information relay.

## Examples Of Statistical Arbitrage In A Sentence

The company developed complex SA strategies for fixed income which were initially extremely successful. Nevertheless, SA continued to grow in popularity with applications progressively expanding to all asset classes. SA has become one of the main investment strategies in investment banks and mostly for hedge funds . In particular, the term SA is used to denote hedge funds that aim to exploit pricing anomalies in equity markets . Technological developments in computational modelling have also facilitated the use of SA in high frequency trading and with the so-called machine learning methods, such as neural networks and genetic algorithms .

## Pairs Trading With Stochastic Control And Ou Process

When one stock in a pair outperforms the other, the under performing stock is bought long and the outperforming stock is sold short with the expectation that under performing stock will climb towards its outperforming partner. Unlike traditional statistical Major World Indices arbitrage, risk arbitrage involves taking on some risks. The largest risk is that the merger will fall through and the target’s stock will drop to its pre-merger levels. Mergers that take a long time to go through can eat into investors’ annual returns.

When one stock in a pair outperforms the other, the poorer performing stock is bought along with the expectation that it climbs its outperforming partner. The position is hedged from market changes/movements by shorting the other outperforming stock. Statistical arbitrage strategy has become a major force at both hedge funds and investment banks. It is commonly accepted that Statistical Arbitrage started with Nunzio Tartaglia who, in the mid-1980s, assembled a team of quantitative analysts at Morgan Stanley to uncover statistical mispricing in equity markets . However, SA came to the fore as a result of Long-Term Capital Management , a hedge fund founded in 1994, where Nobel Prize winners Sholes and Merton both worked.

In this paper, we examine the statistical arbitrage trading between the Berkshire Hathaway stock and its replicating portfolio. For clarity of exposition, in the remainder of this paper the term “replicating portfolio” will be replaced with the term “replicating asset” where appropriate for increased clarity. First, we utilize the five-factor model and Buffett-factor model to construct the replicating asset.

By closing out its positions quickly, the fund put pressure on the prices of the stocks it was long and short. Because other StatArb funds had similar positions, due to the similarity of their alpha models and risk-reduction models, the other funds experienced adverse returns. In our previous article, we’ve discussed a couple of trading strategies exploiting arbitrage between similar stocks using stochastic optimal control methods. A major shortcoming of those approaches is that we restricted ourselves to constructing delta-neutral portfolios. Along with this, the ratio between the stocks in the portfolio is fixed at the start of the investment timeline. These assumptions make the problem simpler, as we only need to calculate the portfolio weights for the spread process as a whole.

Author: Julia Horowitz