Monday, November 16, 2015

Comment on Overnight SPY Anomaly

This post is in response to Michael Harris' Price Action Lab post, where he uses some simple R code to evaluate the asymmetry of returns from the day's close to the following day's open.  I'd like to respond to his 3 notes, which I've included below.
  1. The R backtest assumes fractional shares. This means that equity is fully invested at each new position. This is important because it affects drawdown calculations.
  2. When calculating the Sharpe ratio, the “geometric = FALSE” option must be used otherwise the result may not be correct. It took some time to figure that out.
  3. The profit factor result in R does not reconcile with results from other platforms or even from excel. PF in R is shown as 1.23 but the correct value is 1.17. Actually, the profit factor is calculated on a per share basis in R, although returns are geometric.
I completely agree with the first point.  I'm not sure Mike considers the output of  SharpeRatio.annualized with geometric=TRUE to be suspect (he doesn't elaborate).  The overnightRets are calculated as arithmetic returns, so it's proper to aggregate them using geometric chaining (i.e. multiplication).

I also agree with the third point, because the R code used to calculate profit factor is wrong.  My main impetus to write this post was to provide a corrected profit factor calculation.  The calculation (with slightly modified syntax) in Mike's post is:

getSymbols('SPY', from = '1900-01-01')
SPY <- adjustOHLC(SPY, use.Adjusted=TRUE)
overnightRets <- na.omit(Op(SPY)/lag(Cl(SPY)) - 1)
posRet <- overnightRets > 0
profitFactor <- -sum(overnightRets[posRet])/sum(overnightRets[!posRet])

Note that profit factor in the code above is calculated by summing positive and negative returns, when it should be calculated using positive and negative P&L.  In order to do that, we need to calculate the equity curve and then take its first difference to get P&L.  The corrected calculation is below, and it provides the correct result Mike expected.

grossEquity <- cumprod(overnightRets+1)
grossPnL <- diff(grossEquity)
grossProfit <- sum(grossPnL[grossPnL > 0])
grossLoss <- sum(grossPnL[grossPnL < 0])
profitFactor <- grossProfit / abs(grossLoss)

I'd also like to respond to Mike's comment:
Since in the past I have identified serious flaws in commercially available backtesting platforms, I would not be surprised if some of the R libraries have some flaws.
I'm certain all of the backtesting R packages have flaws/bugs.  All software has bugs because all software is written by fallible humans.  One nice thing about (most) R packages is that they're open source, which means anyone/everyone can check the code for bugs, and fix any bugs that are found.  With closed-source software, commercial or not, you depend on the vendor to deliver a patched version at their discretion and in their timing.

Now, I'm not making an argument that open source software is inherently better. I simply wanted to point out this one difference.  As much as I love open source software, there are times where commercial vendor-supported software presents a more appealing set of tradeoffs than using open source software.  Each situation is different.