advanced-algorithmic-trading

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Coefficients:
(Intercept) ewaAdj
3.809 1.194
This provides us with an intercept of α = 3.809 and a β = 1.194. Similarly for EWC as the
independent variable:
> comb2
Call:
lm(formula = ewaAdj ~ ewcAdj)
Coefficients:
(Intercept) ewcAdj
-1.638 0.771
This provides us with an intercept α = −1.638 and a β = 0.771. The key issue here is that
they are not equal to the previous regression coefficients. Hence we must use the ADF test
statistic in order to determine the optimal hedge ratio. For EWA as the independent variable:
> adf.test(comb1$residuals, k=1)
Augmented Dickey-Fuller Test
data: comb1$residuals
Dickey-Fuller = -3.6357, Lag order = 1, p-value = 0.02924
alternative hypothesis: stationary
Our test statistic gives a p-value less than 0.05 providing evidence that we can reject the null
hypothesis of a unit root at the 5% level. Similarly for EWC as the independent variable:
> adf.test(comb2$residuals, k=1)
Augmented Dickey-Fuller Test
data: comb2$residuals
Dickey-Fuller = -3.6457, Lag order = 1, p-value = 0.02828
alternative hypothesis: stationary
Once again we have evidence to reject the null hypothesis of the presence of a unit root,
leading to evidence for a stationary series (and cointegrated pair) at the 5% level.
The ADF test statistic for EWC as the independent variable is smaller (more negative) than
that for EWA as the independent variable and hence we will choose this as our linear combination
for any future trading implementations.
12.7.2 RDS-A and RDS-B
A common method of obtaining a strong cointegrated relationship is to take two publicly traded
share classes of the same underlying equity. One such pair is given by the London-listed Royal
Dutch Shell oil major, with its two share classes RDS-A and RDS-B.