How Risky Is Your Series? Measured, Not Guessed

How it works

The series is ordered by date and rows sharing a date are averaged into one point. Whether the column holds levels or returns is decided arithmetically — returns straddle zero and are small in absolute size, levels are not — and the evidence for that decision is reported. Log returns are then used for volatility, the EWMA and the GARCH because they add across periods, which is what the square-root-of-time rule requires; simple returns are used for Value-at-Risk, expected shortfall and drawdown because those describe a percentage of capital. Rolling volatility is a standard deviation over a moving window, annualized by the square root of the observation rate, which is inferred from the dates and snapped to the nearest standard convention within 20%. Historical VaR is the empirical quantile of the simple returns; parametric VaR is the mean plus the normal quantile times the standard deviation; expected shortfall is the mean of the returns at or beyond the quantile and, parametrically, the normal closed form. The maximum drawdown is computed on the wealth index as the largest fall from a running peak, with its peak, trough and recovery dates. Volatility clustering is tested by the autocorrelation of squared returns and a Ljung-Box statistic. An EWMA decay is fitted by a one-dimensional likelihood search over the range 0.70 to 0.995, and a GARCH(1,1) is fitted by direct maximum likelihood with base R's optim on an unconstrained reparameterisation — omega through a log, the persistence and alpha's share of it through logistic transforms — so positivity and stationarity hold by construction; a likelihood-ratio test against a constant variance decides whether it earns its place. No volatility or finance package is used at any point.

Use it whenever you have a dated price, index, portfolio value or return series and need to know how risky it has been: how volatile, how bad a bad period is, how much worse the losses beyond that get, and how deep the worst fall was.

Not for forecasting the level or direction of the series (the conditional volatility describes width, not direction), not for comparing the risk of two series against each other, not for a cross-section of assets at a single date, and not as a risk limit on its own — every figure here describes the history supplied and none of them bounds what can happen next.

What data do you need?

One row per period with the date and the level (or the return). For example, daily closing prices:

Minimum 30 rows · Best with 250-5,000 periods (about one to twenty years of daily data)

What's in the report?

Standard-library analysis: how risky is this series? Map a date column and a price, value or return series and get the full risk picture — log and simple returns with each used where it belongs, rolling volatility with a stated window and annualization, historical and parametric Value-at-Risk at 95% and 99% with expected shortfall beside each one, the maximum drawdown with its peak date, trough date and recovery time, and a volatility-clustering diagnostic backed by an EWMA and a GARCH(1,1) fitted by direct maximum likelihood. The limits are computed rather than boilerplated: the excess kurtosis and the actual count of historical breaches beyond the normal model's prediction, the worst loss the sample has ever seen and the span it covers, and the measured gap between the first and second halves of the same history.