Pairs-trading Recap

Overview of Strategy:

Load the current price of A: XLK (tech ETF) and B: VTI (index ETF). note: ALPACA has a 15-min delay

Take a look-back window of 1 day minute-bar data

Calculate hedge-ratio \(\beta\) via OLS

\(\alpha = \beta*b\)

Define: \[spread = \alpha - \beta*b\] and

\[Z = \frac{spread - \mu_{spread}}{\sqrt{\sigma_{spread}}}\]

To manage risk if \(|Z|>3.5\) we exit the position

Long: buy XLK, short VTI

Short: sell XLK, buy VTI

if Z is too low we enter a long and if Z is too high we enter a short

The strategy lost around 1% of our portfolio value \(\approx\) $10,000

Theory behind the reasoning

Claim: the tech and overall economy are highly correlated

Pearson's rho: 0.8955 
 Kendall's tau:  0.7063 

Note: Kendalls’s \(\tau\) is a harsher measure of correlation than the traditional \(\rho\) from Pearson

Fitted Copulas to our ETF data:

The information criteria and Log-likelihood estimates indicate the tCopula is the best fit

         logLik      AIC
t       296.144 -588.289
normal  291.838 -581.677
frank   268.226 -534.451
clayton 199.637 -397.274
gumbel  285.921 -569.842
joe     236.099 -470.198

Estimated copulas superimposed with the empirical copula (making no distributional assumptions)

Our trading strategy implicitly made a normality assumption in the OLS regression of \(\beta\) and calculating Z. Given our t-Copula had the best fit it’s likely our model didn’t capture the behavior at the extremes (tails)