Pairs trading is a neutral investment strategy based on the use of correlation value phenomenon of certain securities.

For example, in the case of higher oil prices, the majority of shares of oil companies also start to rise in price, and vice-versa, in case of falling oil prices, most oil stocks will fall in price.

However, each of these stocks will rise or fall in their own way, some of them more, some less.

The basic principle of pairs trading is to identify pairs of securities with a high degree of correlation, one of which is significantly increased or decreased in value relative to the other, then there is a short selling of overvalued securities and buying of undervalued securities.

Thus, a beta – neutral portfolio, is yield of which will depend not on the overall direction of the market, and the future value of the relationship of one security to another.

The calculation of the basic parameters

For example, consider a couple of shares of Lukoil and Gazprom Neft, the correlation coefficient which in 2009 was 0,743. The calculation of the correlation coefficient is calculated as:

rho_ {AB} = frac { mathrm {Cov} _ {AB}} { sigma_ {A} sigma_ {B}}

where:

ρAB – the coefficient of correlation between the return of an asset A and asset B;

CovAB – A covariance of asset returns and profitability of the asset B;

σA – the standard deviation of return on asset A;

σB – the standard deviation of return on asset B;

In order to determine the ratio of the value of the two assets is sufficient to divide the price of one asset on the price of the other :

where:

PLKOHt – the value of shares Lukoil at time t (31.12.2009);

PSIBNt – share price, Gazprom Neft at time t (31.12.2009);

Now you need to determine the coefficients of the assets in the equity beta neutral portfolio.

In 2009, the Beta coefficient of shares of Lukoil was 1.01. In the case of shares of Gazprom Neft, the beta coefficient was 0.87. With this data, it is easy to determine the share of each share in a market- neutral portfolio:

mathrm {X} _ mathrm {LKOH} = 0,46; quad mathrm {X} _ mathrm {SIBN} = 0,54

The next step is to build a relationship of historical values of assets, for that the above procedure is performed for each time t in the period under review. It should be noted that the value of beta coefficients at each time may have a different meaning, which also affect the proportional factor, so each time point all the coefficients are recalculated.

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