Value at Risk (VaR)

Value at Risk (VaR) is a “bad-day cutoff.” A 5% daily VaR answers: “What loss threshold marks the worst 5% of days?” If you land in that 5%, losses are at least that large (and often worse).

The most common misunderstanding is to read VaR as “the maximum loss.” It isn’t. It’s a percentile. If you’re in the unlucky 5%, VaR just tells you you’re past the threshold — not how far past.

The definition

At confidence level $\alpha$ (we use $0.05$), historical VaR is the left‑tail quantile:

$$\text{VaR}_{\alpha} = Q_{\alpha}(r)$$

Where $r$ is the daily return series.

How we calculate VaR at Gale Finance

1. Historical (empirical) VaR, not parametric. We compute VaR directly from the observed return distribution — no normality assumption.

2. Returns are daily log returns for tail-risk pages. In our tail risk section we use:

$$r_t = \ln\left(\frac{P_t}{P_{t-1}}\right)$$

Log returns add cleanly across multiple days and behave better statistically. For small daily moves, log and simple returns are very close.

3. Native calendars per asset. VaR is computed per asset on its own daily series (crypto includes weekends; equities/ETFs/metals are trading days). We don’t force everything onto a shared calendar for this metric.

4. 5% level. For one‑year windows, 5% corresponds to roughly ~13 (trading‑day assets) to ~19 (crypto) observations. That’s enough to be informative, but it’s still noisy — treat it as a descriptive statistic, not a forecast.

What VaR is good (and bad) for

Good:

• A quick “left‑tail cutoff” comparison across assets.
• A sanity check on whether an asset’s “bad day” behavior is mild or brutal.

Bad:

• Anything that needs to know what happens beyond the cutoff. For that, use Expected Shortfall.