4 Risks Of Statistical Arbitrage

On the other hand, the arbitrageur buys a treasury bond, with the same maturity as the swap, with the money borrowed through a repurchase agreement known as repo. Entering this part of the trade the arbitrageur earns the treasury rate TR and pays the repo rate r t . The overall cash flow of the trade is ( L t − r t ) − ( S R − T R ) where S R − T R is the fixed interest rate component and L t − r t is the floating rate part which needs to be rolled periodically . The strategy generates a positive income as long as the floating yield exceeds the fixed one.

In this article, we will be discussing a couple of papers related to stochastic control based approaches, which had the highest impact in this domain. We will not be discussing pairs selection techniques here, and interested readers can refer to the Stock Selection Methods using Copula and Machine Learning for Pairs Selection articles. The objective of these methods is to identify the optimal portfolio holdings in the legs of a pairs trade compared to other available assets. Stochastic control theory is used to determine value and optimal policy functions for this portfolio problem. It does sound a bit complicated, but, I’ll try to keep things simple and explain the intuition behind how and why these methods work.

Fig 3C plots the information in Fig 3A and 3B using a shorter period, from 2008–2009 only, and overlay the results of the two models on top of each other using only one graph. Fig 3C shows that the information presented in Fig 3A and 3B are not identical to each other. The purpose of this post was to show how we can combine the standard approach to statistical arbitrage, which is based on classical econometric theory, with modern machine learning algorithms, such as genetic programming. This frees us to consider a very much wider range of possible trade entry and exit strategies, beyond the rather simplistic approach adopted when pairs trading was first developed.

The Journal Of Portfolio Management

In Table 2, we find that the expected return of statistical arbitrage of are least 4.8% for the synthetic asset constructed by the two different factor models. Table 1 shows the expected returns of using the optimal statistical arbitrage strategies for different transaction costs and “a.” The optimal solution for “a” is from Eq . In the Table, “c” represents the transaction cost, and “a” represents the entry-level.

Yet some blame stat-arb traders for destabilizing the markets in the 2007 and 2008 crises. Stat-arb can lead to a boon in competent hands and a bust in semi-proficient applications. Statistical arbitrage generally includes correlated stocks or securities.

The researcher might understandably be persuaded, wrongly, that the same is likely to hold true in future. Another useful test procedure is to compare the strategy performance with that of a portfolio constructed using standard mean-variance optimization . The test indicates that a portfolio constructed using the traditional Markowitz approach produces a similar annual return, but with 2.5x the annual volatility (i.e. a Sharpe ratio of only 1.6). What is impressive about this result is that the comparison one is making is between the out-of-sample performance of the strategy vs. the in-sample performance of a portfolio constructed using all of the available data. So does this mean that for the average quantitative strategist investors statistical arbitrage must remain an investment concept of purely theoretical interest? Firstly, for the investor, there are plenty of investment products available that they can access via hedge fund structures .

Principal Component Analysis

The Ornstein Uhlenbeck process can be considered as the continuous-time analog of the AR process. Because the Ornstein Uhlenbeck process is static, the return is deterministic. Convertible Arbitrage is one of the most popular capital structure strategies and involves buying a portfolio of convertible bonds while selling short the underlying stocks . Intuitively, if the stock increases in price, the bonds will appreciate and if the stock falls the short position will profit. In some versions, the interest rate risk is hedged with treasury futures or interest rate swaps. In addition to credit arbitrage and convertible arbitrage, other capital structure arbitrage strategies focus on the spread between bonds and equities of the same company.

Here, we provide a description of the various arbitrages while we refer to the relative papers for a more rigorous formulation. There are also other mean reversion trading elements when exploiting an arbitrage opportunity, such as identifying how long it should take for a spread to revert to the mean. This is called the half-life of the mean, and for that, I highly recommend reading my favorite books on statistical arbitrage. We’ll now turn our gold and gold miner relationship into a pair trading strategy. Autoregression is a time series model that uses historical observations as input to a regression equation to predict the next step’s value. This is why it’s called autoregression – it “regresses against itself” as it uses data from the same input at previous time steps.

Delta neutral is a portfolio strategy consisting of positions with offsetting positive and negative deltas so that the overall position of delta is zero. I tend not to get involved in Q&A with readers of my blog, or with investors. I am at a point in my life where I spend my time mostly doing what I want to do, rather than what other people would like me to do. And since I enjoy doing research and trading, I try to maximize the amount of time I spend on those activities.

The value +1 indicates a strong positive correlation, zero indicates no relationship, and -1 indicates a strong negative relationship. We can see in the above heatmap that there are multiple pairs with a strong positive correlation. Plot Pearson correlation of daily returns to get the basic idea about the relationship. Figure 2.8.1 — can be bound for example by percentagesNot only is it important to define when to buy and sell, it is also necessary to build in a trigger out. Figure 2.4.1The residuals are the differences between the natural log of the price of stock A and the corresponding point on the regression line. Essentially they are turned into a residual series which also has to be stationary I.

The way to do it would be by way of linear regression of the natural logarithms of the prices of the stocks A and B. That statistical property we were referring to was stationarity by the cointegration approach. Then if we were to combine these series in a specific ratio, we would get a new series μt consisting of only the non-random components of the AR models.

• By closing out its positions quickly, the fund put pressure on the prices of the stocks it was long and short.
• Additionally, each type of statistical arbitrage strategy carries strategy risk.
• The two figures show the same overall pattern as those of Figs ​ Figs4 4 and ​ and5.
• The enhanced strategy generated the daily Sharpe ratio of 6.07% in the out-of-sample period from January 2013 through October 2016 with the correlation of -.03 versus S&P 500.
• Large positions in both stocks are needed to generate sufficient profits from such minuscule price movements.

This is now under way, using execution algos that are designed to minimize the implementation shortfall (i.e to minimize any difference between the theoretical and live performance of the strategy). As the speed at which the time series correct themselves from this disequilibrium, we can see that this formalizes the way cointegrated variables adjust to match their long-run equilibrium. Very large datasets – comprising voluminous numbers of symbols – present challenges for the analyst, not least of which is the difficulty of visualizing relationships between the individual component assets. Absent the visual clues that are often highlighted by graphical images, it is easy for the analyst to overlook important changes in relationships. However, by fitting a 2-state Markov model we are able to explain as much as 65% in the variation in the returns process .

Indexing And Statistical Arbitrage

The new portfolio underperforms the index during 2014, but with lower volatility and average drawdown. The idea is to examine the characteristics of the returns process and assess its predictability. In the previous post I outlined some of the available techniques used for modeling market states. The following is an illustration of how these techniques can be applied in practice. But it is also clear that there are many other significant correlations between non-conjugate pairs.

Statistical arbitrage uses statistics and mathematical models to profit from relationships between financial instruments. Statistical arbitrage is a class of trading strategies that use statistical and econometric techniques to exploit historically related financial instruments’ relative mispricings. On a stock-specific level, there is risk of M&A activity or even default for an individual name.

Pairs Trading With Markov Regime

That said, spreads of this kind can nonetheless be extremely volatile. If you want statistical arbitrage to work, you have to rely on your broker to execute your orders. Many times, you have Underlying to have split-second execution in order to profit from this type of trading strategy. In some cases, the broker will not be able to fill your trade and they will simply cancel the order.

Understanding The Statistical Arbitrage Risk Premium

The expected Sharpe ratio of optimal statistical arbitrage of Berkshire A and replicating asset pair. The “pairs” rule is sufficiently obvious that it could almost be implemented manually. Statistical arbitrage took off when it started identifying trades whose basis was not obvious. For example, one quantitative fund found its machine learning algorithms making offsetting commodity trades on Monday and Friday. The quant fund’s algorithm profited by taking advantage of the Friday price drop and Monday price uptick. We have used the training dataset until this point to finalize the stock pair for our strategy.

We find a general definition, which includes all SA strategies and propose a classification system measuring the strategies’ risk and return profile. This facilitates the inclusion of new strategies and measures as they emerge. Our analysis allows investors to have a common framework to evaluate investment opportunities and brings clarity in SA investing, guiding theoretical development and empirical testing. Mathematically speaking, the strategy is to find a pair of stocks with high correlation, cointegration, or other common factor characteristics.

Recently I have been working on the problem of how to construct large portfolios of cointegrated securities. My focus has been on ETFs rather that stocks, although in principle the methodology applies equally well to either, of course. It is possible to trade passively, crossing the spread to trade the other leg when the first leg trades. If paying the spread on both legs is going to jeopardize the profitability of the strategy, it is probably better to reject the pair. The analysis in Appendix II suggests that the residual process is stable and Gaussian.

Do and Faff examine the impact of trading costs on pairs trading profitability. For statistical arbitrage, issues such as when, how, and the impact of transaction costs are important. And ​ and7A 7A plot the relationship between the transaction costs and “a.” Figs ​ Figs6B 6B and ​ and7B 7B plot the relationship between the transaction costs and the expected return of the optimal trading strategy.

We will start with an initial capital of 100,000 and calculate the maximum number of shares position for each stock using the initial capital. On any given day, total profit and loss from the first stock will be total holding in that stock and cash position for that stock. Similarly, profit and loss for the second stock will be total holding in the stock and cash for that stock.

Therefore, its price is expected to go down hence we want to short this stock and long the other one. Backtesting allows us to gauge how well our pairs triangular arbitrage trading using cointegration approach is doing. One of the best ways to help structure a good trading strategy is to analyze the P/L from the backtests.

This can help address the issue of a lack of uniform definitions in hedge funds where several classification systems are still in use with significant differences among them . Traders soon began to think of these “pairs” not as an isolated block to be executed and its hedge, but rather as two sides of the same trading strategy, where profits could Futures exchange be made rather than simply as hedging tool. These pair trades eventually evolved into several more sophisticated strategies aimed at taking advantage of statistical differences in security prices due to liquidity, volatility, risk, or other fundamental or technical factors. We now classify these strategies collectively as statistical arbitrage.

Specifically the excess return of Berkshire A is the as the dependent variable and the factors on the right-hand-side of Eq and Eq are the independent variables. The estimated coefficients are then used as the portfolio weights for the construction of the replicating asset. The returns of the replicating portfolio will, in the long run, match the returns of the Berkshire A stock, since the replicating portfolio is constructed from theoretically correct asset pricing model specifications. In the remainder of our paper, we will denote the replicating portfolios as simply Buffett- or five-factor model. Second, we use the replicating portfolios as input to the pair trading simulation tests.

The popularity of the strategy continued for more than two decades and different models were created around it to capture big profits. Term structure arbitrage is a common SA strategy which typically involves taking market-neutral long-short positions at different points of a term structure as suggested by a relative value analysis . Positions are held until the trade converges and the mispricing disappears. Term structure arbitrage is particularly common in fixed income and commodities. In spite of being one of the most common SA strategies, the literature on implementations of yield curve arbitrage is quite limited and mostly focuses on interest rates models .

Evaluating Classification Models Using Confusion Matrix

An employee stock option is a grant to an employee giving the right to buy a certain number of shares in the company’s stock for a set price. A contra market is one that tends to move against the trend of the broad market or has a low or negative correlation to the broader market.

Author: Ben Lobel