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Successful Statistical Arbitrage

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 Jonathan Kinlay, Quantitative Research and Trading | Leading Expert in Quantitative Algorithmic Trading Strategies

 Sunday, March 1, 2015

https://www.linkedin.com/pulse/successful-statistical-arbitrage-jonathan-kinlay


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8 comments on article "Successful Statistical Arbitrage"

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 Alex Song, Senior Analyst at Chappuis Halder & Cie

 Sunday, March 1, 2015



Quick question: how could you improve the performance by simply combining 4 pairs? Thank you.


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 Gaurav Singh, High Frequency Trading

 Sunday, March 1, 2015



@Alex, I believe Jonathan is trying to optimize his exposures using multiple pairs instead of considering just single.

If multiple pairs are cointegrated and their corresponding spread has a near normal distribution than the whole portfolio can be considered stationary.

For example: If X and Y are independent random variables that are normally distributed (and therefore also jointly so), then their sum is also normally distributed. i.e., if

X ~ N(mu1, sigma1)

Y ~ N(mu2, sigma2)

Z=X+Y,

then

Z ~ N(mu1 + mu2, sigma1^2 + sigma2^2).

This means that the sum of two independent normally distributed random variables is normal, with its mean being the sum of the two means, and its variance being the sum of the two variances (i.e., the square of the standard deviation is the sum of the squares of the standard deviations).

This also satisfies that the entire residual (sum of all the residuals of the pairs) is stationary as well. Using this, one can find the optimal hedging condition creating a multi-legged scenario where one can manage risk, control the exposed position and reduce cost/maximize Profitablity.

This would cause a significant performace benefit by constructing a portfolio of pairs instead of relying on just one pair.

Best,

GS.


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 Alex Song, Senior Analyst at Chappuis Halder & Cie

 Sunday, March 1, 2015



@Gaurav thanks for your detailed explanation. I fully understand until " using this one can find optimal hedging condition creating a multi-legged scenario". Could you please explain more? Say we have 4 residuals in the example above, what are the objective and constrained functions for optimization? Thank you in advance. Alex


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 Gaurav Singh, High Frequency Trading

 Sunday, March 1, 2015



@Alex, :)

We need to either maximize the profit or minimize the costs.

Profit Fuction(P) = Sells - Buys (maximize)

Cost Function(C) = Sells + Buys (minimize)

Constrained Function (Cx) = a1 * x1 + b1 * x2 ....... where a1, a2 .. are stocks are x1, x2 are positions (that we can take)

Using some linear/quadratic optimization, we can achieve the longthe/short positions that we should take in order to maximize(P) or minimize(C) or both.

Hope this throws some light.

Best Regards,

GS.


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 Jonathan Kinlay, Quantitative Research and Trading | Leading Expert in Quantitative Algorithmic Trading Strategies

 Monday, March 2, 2015



Gaurav's explanation is detailed and very clear.


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 Alex Song, Senior Analyst at Chappuis Halder & Cie

 Monday, March 2, 2015



@Gaurav thanks very much. That was clear :)


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 Gaurav Singh, High Frequency Trading

 Monday, March 2, 2015



Most welcome @Alex. Glad you liked it.


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 Bharath Rao, Co-Founder, Head of Products

 Thursday, May 21, 2015



Valuable one. Portfolios of pairs is better than the pairs taken on their own. Pairs do lose cointegration property for significant mounts of time.

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