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# Quant: Statistic

Geometric mean [(1+R )(1+R )........(1+R )]^(1/n) - 1
Population Mean m = Sum (Xi) / N
Sample Mean X = Sum(Xi) / n
Weighted Mean X = Sum(wiRi) = w1R1 + w2R2 +...+wnRn Where R , R , ..., R are the returns for assets 1,2,...,n and w , w , ...,w are the portfolio weights, so that w + w + ...+w = 1
Harmonic Mean N / (Sum (1/Xi)) where : N = number of purchases (equal \$ amounts) X = share price for each purchase
Variance SUM( Xi - mean)^2 / N
Standard deviation (Variance^2) ^ (1/2)
Sample Variance SUM( Xi - sample mean)^2 / n-1
Sample Standard deviation Sample Variance ^ (1/2)
Coefficient of Variation stdev / mean where: the lower the better
Sharpe Ratio (Rp - Rf) / stdev p where: the higher the better
Chebyshev’s Inequality 1- (1/k^2)
symmetrical distribution skew = 0
Leptokurtic kurtosis > 3 and more peaked with fatter tails
Kurtosis for a normal distribution 3.0
Excess kurtosis kurtosis - 3
Excess kurtosis for a normal distribution 0
Created by: thongkk