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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.

- 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.
- 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.
- 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:

require(quantmod)

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])

*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)

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.

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