How to use Returns Distribution Analyzer
Paste a returns CSV. The page renders a histogram with normal-overlay, QQ plot, skewness, excess kurtosis, the Jarque-Bera test, and a tail-weight index — the visual case for why Sharpe alone misleads on non-Gaussian returns.
What It Does
Use the calculator with intent
Paste a returns CSV. The page renders a histogram with normal-overlay, QQ plot, skewness, excess kurtosis, the Jarque-Bera test, and a tail-weight index — the visual case for why Sharpe alone misleads on non-Gaussian returns.
Quants who suspect the returns distribution has fatter tails than Gaussian and need the visual evidence before tear-sheet review.
Interpreting Results
QQ plot is the headline. Heavy tails show as deviation from the diagonal at both ends. Jarque-Bera p-value below 0.05 means the return distribution is statistically non-normal — Sharpe and VaR assumptions need adjustment.
Input Steps
Field by field
- 1
Upload data
Upload a return series (daily, weekly, or monthly returns).
- 2
Read outputs
Read the four moments: mean, std, skew, excess kurtosis. Excess kurtosis above 3 = fat tails.
- 3
Read outputs
Read the distribution-fit comparison (Normal vs. Student-t vs. Skewed-t vs. GED). Student-t with low ν typically wins for return series.
- 4
Read outputs
Read VaR and CVaR at 95% and 99%. CVaR > VaR by definition; the gap shows tail severity.
- 5
Use result
Use the QQ plot to spot tail behavior visually. Heavy upper-right tail = positive skew; heavy lower-left tail = negative skew.
Common Scenarios
Use realistic starting points
Trend-following daily returns
Frequency
daily
Span
5 years
Right-skewed, occasional very large positive days. Sharpe undersells this kind of distribution; Sortino captures it better.
Short-vol strategy daily returns
Frequency
daily
Span
3 years
Negative skew, fat left tail. Sharpe oversells this kind of distribution; tail-risk metrics (CVaR) tell the real story.
Try These Tools
Run the numbers next
Risk-Adjusted Returns Calculator
Paste a returns CSV. Sharpe, Sortino, Calmar, Omega, alpha, beta, tracking error, information ratio, max drawdown, and tail moments — plus.
Sharpe vs Sortino Calculator
Paste daily returns; get Sharpe, Sortino, Calmar, and Omega side-by-side with a recommendation on which ratio fits your distribution.
VaR Backtest — Kupiec & Christoffersen
Paste P&L + VaR series and run Kupiec POF, Christoffersen independence, and joint conditional-coverage tests. Likelihood-ratio χ² p-values.
FAQ
Questions people ask next
The short answers readers usually want after the first pass.
Related Content
Keep the topic connected
Volatility
Volatility as the standard deviation of returns: realized vs implied, the annualization gotcha, and why volatility-of-volatility matters.
Sharpe vs Sortino
Sharpe vs Sortino: when the gap between the two tells you something real about a strategy's tail behaviour — and when it's just noise from a small sample.
Value at Risk (VaR)
Value at Risk: the loss threshold you'll exceed with probability α. Why historical VaR is brittle and what it doesn't tell you about the tail.
Expected Shortfall (CVaR)
Expected shortfall: the average loss given a VaR breach. Why regulators are migrating from VaR and what ES catches that VaR misses.