# Statistical Arbitrage Definition

# Statistical Arbitrage Definition

Contents

We combine the findings of the previous sections and propose a general definition and classification system. Statistical Arbitrage strategies can be applied to different financial instruments and markets. The Executive Programme in Algorithmic Trading includes a session on “Statistical Arbitrage and Pairs Trading” as part of the “Strategies” module. Many of our EPAT participants have successfully built pairs trading strategies during their course work. Additionally, while the market risk is reduced from arbitrage strategies, it’s important to check for correlation between arbitrage strategies, portfolios, and positions during the portfolio construction process.

The Center’s goal is to address the most important and pressing issues in risk management and portfolio management. Let’s go with tickers BANKBARODA and SBIN and further test the stationarity of spread using the Augmented Dickey-Fuller test. A time series is considered stationary if parameters such as mean and variance do not change over time and there is no unit root. We will first calculate the hedge ratio between these two tickers using OLS regression. Then, using the hedge ratio, we will calculate the spread and run the Augmented Dickey-Fuller test.

## Series

Our first step is to decide the stock universe and identify the pairs with high correlation. It is very important that this is based on economic relationships such as companies with similar businesses, else it might be spurious. I have taken all constituents of NSE-100 which are categorized as ‘FINANCIAL SERVICES’ companies.

His results show that gross profits-to-assets has the same power as book-to-market in predicting the cross-section of average returns. Also, profitable firms produce significantly higher returns than unprofitable firms, despite having significantly higher valuation ratios. Fama and French added the factors of profitability and investment to the three-factors model and showed that the five-factor model explains between 71% and 94% of the cross-section variance of expected returns on the portfolios. StatArb is an evolved version of pair trading strategies, in which stocks are put into pairs by fundamental or market-based similarities. 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.

The null hypothesis of the DF test is that μt is a unit root series, and the alternative is that it is a stationary series. Where β is the cointegration coefficient, μt is the estimated values of the error . This sort of avalanche effect is the reason why the dollar-neutral strategies melt down in high-vol environments.

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. A positive expected excess returns requires defining the risk free and a probability measure. In the case of a zero-cost trading strategy, the risk free is equal to zero. Defining an acceptably small potential loss requires identifying a set of suitable risk measures and criteria to establish what is acceptably small.

## How Statistical Arbitrage Affects Markets

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. Section 2 discusses the literature related to statistical arbitrage and factor models. Section 3 presents the data and statistical arbitrage trading model of the Ornstein Uhlenbeck process. Section 4 presents the results of the empirical analysis and examines robustness to varying transaction costs.

- It is very important that this is based on economic relationships such as companies with similar businesses, else it might be spurious.
- These assumptions make the problem simpler, as we only need to calculate the portfolio weights for the spread process as a whole.
- These networks are mathematical or computational models based on biological neural networks.

Financial markets are in constant flux and evolve based on events occurring across the globe. Hence, profit from statistical arbitrage models cannot be guaranteed all the time. Additionally, profitable statistical arbitrage strategies are in high demand as who wouldn’t want near riskless profits? The challenge is that once enough players discover the statistical relationship, the profits are often “arbitraged” away. Over a finite period of time, a low probability market movement may impose heavy short-term losses. If such short-term losses are greater than the investor’s funding to meet interim margin calls, its positions may need to be liquidated at a loss even when its strategy’s modeled forecasts ultimately turn out to be correct.

This is why every trading expert says that “past results are no indication of future performance.” The market has to behave similar to how it has behaved in the past in order for a strategy like this to work. You always have to be aware of this risk if you are going to use statistical arbitrage. Characterizing time series allows us the liberty of creating or using models that could lead to us realizing important information.

## We And Our Partners Process Data To:

This repository contains three ways to obtain arbitrage which are Dual Listing, Options and Statistical Arbitrage. Visualize the portfolio performance along with z-score, upper, and lower thresholds. We start with the initial capital of 100,000 and calculate the number of shares to buy for each stock.

They also show that the distance method generates insignificant excess returns, but the cointegration method provides a high, stable, and robust return. Statistical arbitrage identifies and exploits temporal price differences between similar assets. We propose a unifying conceptual framework for statistical arbitrage and develop a novel deep learning solution, which finds commonality and time-series patterns from large panels in a data-driven and flexible way. First, we construct arbitrage portfolios of similar assets as residual portfolios from conditional latent asset pricing factors.

In particular Schaefer and Strebulaev show that structural models provide accurate predictions of the sensitivity of corporate bond returns to changes in the value of equity . Other strategies instead focus on the spread between CDS and corporate bonds or different types of credit default swaps . 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.

A point to note here is that Statistical arbitrage is not a high-frequency trading strategy. It can be categorized as a medium-frequency strategy where the trading period occurs over the course of a few hours to a few days. Going back to our pairs trading example, if it’s cointegrating at 99% probability and you apply leverage, what happens when it stops working seemingly out of nowhere? When a strategy has a beta of zero, which means it’s returns are not affected by the market’s price movement, it’s market-neutral. The pairs trading strategy mentioned above is a market-neutral strategy. Statistical arbitrage, also known as stat arb, refers to any trading strategy that uses statistical and econometric techniques to profit with an element of market risk reduction.

## Statistical Arbitrage Risk Premium

They compare the model with subsequent observations of the spread to determine appropriate investment decisions. They believe this approach can be applied to any financial market to gain wealth, even though it is at times out of equilibrium. Therefore, it is necessary to deal with the stability of the time series data. The Ornstein Uhlenbeck process is a stationary Gauss Markov process, and is homogeneous in time. The process can be viewed a modification of random walk in continuous time or Wiener process.

You would check TradingView, assuming it existed back then, to perform a quick inspection of the two stocks. For instance, the gold, gold miner, and oil triplet previously discussed have gone in and out of cointegration. What happens if Apple’s price is up by 1.90% on the day but the ETF fund flows are triangular arbitrage negative? Invesco will likely need to purchase or sell disproportionate amount of Apple to keep their ETF weighting representative of the index weighting. 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.

## High Frequency And Dynamic Pairs Trading Based On Statistical Arbitrage Using A Two

If the market state can be forecast successfully, we can use that information to increase our capital allocation during periods when the process is predicted to be in State 1, and reduce the allocation at times when it is in State 2. In fact this strategy has higher returns, Sharpe Ratio, Sortino Ratio and lower drawdown than many of the earlier models. Builder has no difficulty finding strategies that produce a smooth equity curve, with decent returns, low drawdowns and acceptable Sharpe Ratios and Profit Factors – at least in backtest! Of course, there is a way to go here in terms of evaluating such strategies and proving their robustness.

We assume that the synthetic asset formed by the Berkshire Hathaway stock and its replicating portfolio can be described by the Ornstein Uhlenbeck process. Our main results show that the replicating portfolio can be effectively paired with the original asset in a pairs trading statistical arbitrage framework and verify that this method is rewarded. 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 .

We can use Fourier transforms to help identify the cyclical behavior of the strategy alpha and hence determine the best time-frames for sampling and trading. Typically, these spectral analysis techniques will highlight several different cycle lengths where the alpha signal is strongest. In this series of posts I want to focus foreign exchange market on applications of machine learning in stat arb and pairs trading, including genetic algorithms, deep neural networks and reinforcement learning. Then, with selected pairs, if the difference between the price of elements in a pair diverged by more than a threshold(ex. 2 standard deviations), the positions are opened.

## A Practical Application Of Regime Switching Models To Pairs Trading

They find average annualized excess returns of about 11% for the top pairs portfolios and that the profits do not appear to be caused by simple mean reversion. However, Do and Faff apply the Gatev et al. methodology with more Day trading recent data and find the profit show a declining trend when the naive trading rule is used. In the newer study, they considered transaction costs and allowed securities to be matched across 48 Fama-French industries.

Author: Corinne Reichert