Testing for normal dist with Kolmogorov-Smirnov

Kolmogorov-Smirnov test- are your returns normally distributed? Why? Value at risk, Modern portfolio theory, CAPM assume returns of assets are normally distributed

Get the percent daily returns X [0.2,0.1,0.3 …]

Sort the returns B = Sorted(X) = [0.1,0.2,0.3 …]

enumerate the returns C = Enum(B) = [1,2,3, …]

Divide C by len(X) D = [1/300,2/300,3/300 …] D is called empirical distribution

Get Mean and Standard deviation of returns (B or C) Using mean , get normal distribution of B E = [normDist(0.1, 0.15, 0.01), normDist(0.2, 0.15, 0.01) …] E is called theoretical distrbution

We plot 2 series, B vs D, B vs E

Get difference of D and E F = D - E

Get maximum of differences aka max(F) supremum = max(F)

How bad does normal distribution fit the data Kolmogorov-Smirnov statistic = supremum * sqrt(len(X))

Critical value is 1%, if our Kolmogorov-Smirnov statistic > 1, then our data is not normally distributed