# When is a Backtest Too Good to be True? Part Two.

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In the previous post, I went through a simple exercise which, to me, clearly demonsrtates that 60% out of sample guess rate (on daily basis) for S&P 500 will generate ridiculous returns. From the feedback I got, it seemed that my example was somewhat unconvincing. Let’s dig a bit further then.

Let’s add Sharpe ratio and maximum drawdown to the CAGR and compute all three for each sample.

return.mc = function(rets, samples=1000, size=252) { require(PerformanceAnalytics) # The annualized return for each sample result = data.frame(cagr=rep(NA, samples), sharpe.ratio=NA, max.dd=NA) for(ii in 1:samples) { # Sample the indexes aa = sample(1:NROW(rets), size=size) # All days we guessed wrong bb = -abs(rets) # On the days in the sample we guessed correctly bb[aa] = abs(bb[aa]) # Compute the statistics of interest for this sample. result[ii,1] = Return.annualized(cc,scale=252) result[ii,2] = SharpeRatio.annualized(bb,scale=252) result[ii,3] = maxDrawdown(cc) } return(result) }

Let’s look at some summary statistics:

require(quantmod) gspc = getSymbols("^GSPC", from="1900-01-01", auto.assign=F) rets = ROC(Cl(gspc),type="discrete",na.pad=F)["1994/2013"] df = return.mc(rets, size=as.integer(0.6*NROW(rets))) summary(df,digits=2) # cagr sharpe.ratio max.dd # Min. :0.34 Min. :1.8 Min. :0.13 # 1st Qu.:0.45 1st Qu.:2.3 1st Qu.:0.22 # Median :0.48 Median :2.5 Median :0.26 # Mean :0.48 Mean :2.5 Mean :0.27 # 3rd Qu.:0.51 3rd Qu.:2.7 3rd Qu.:0.31 # Max. :0.67 Max. :3.5 Max. :0.63

The picture is clearer now. Lowest Sharpe ratio of 1.8 among all samples, and a mean at 2.5? Yeah, right.

The results were similar for other asset classes as well – bonds, oil, etc. All in all, in financial markets, like in a casino, a small edge translates into massive wealth, and most practitioners understand that intuitively.

The post When is a Backtest Too Good to be True? Part Two. appeared first on Quintuitive.

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