computation-patterns

name	computation-patterns
description	Python computation formulas for Treasury data analysis. Use for percent change, CAGR, stdev, kurtosis, VaR, regression, Theil index, and other statistical calculations.

Always use python3 -c for calculations.

Basic

• Percent change: ((new - old) / old) * 100
• CAGR: (end/begin)**(1/years) - 1
• Range: max(values) - min(values)

Statistics (import statistics)

• Sample stdev: statistics.stdev([...])
• Population stdev: statistics.pstdev([...])
• Mean: statistics.mean([...])
• Median: statistics.median([...])

Advanced

• Fisher kurtosis: m4/m2**2 - 3 (m2=variance, m4=4th central moment)
• Skewness (Fisher-Pearson): n/((n-1)*(n-2)) * sum(((x-mean)/stdev)**3)
• VaR (parametric 95%): mean - 1.645 * pstdev
• Expected Shortfall: mean of all values below VaR cutoff
• OLS slope: sum((x-xbar)*(y-ybar)) / sum((x-xbar)**2)
• OLS intercept: ybar - slope * xbar
• Arc elasticity: ((Q2-Q1)/((Q2+Q1)/2)) / ((P2-P1)/((P2+P1)/2))
• Theil index: (1/n) * sum((xi/mean) * ln(xi/mean))
• Macaulay duration: sum(t * CF_t / (1+y)^t) / sum(CF_t / (1+y)^t)
• Constant hazard rate: ln(V2/V1) / years