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Summary

VaR compresses a whole portfolio's market risk into one number — "we are X% certain we will not lose more than V over N days" — and is the natural aggregate counterpart to TOMIC's per-trade rules. Margin regimes determine how much capital the broker demands for the same book: Reg-T stacks per-position requirements, while portfolio margin stress-tests the combined book. VaR and portfolio margin are both scenario/percentile-based, so both need stress testing to catch what the percentile hides; Reg-T, by contrast, is a simple per-position summed rule with no scenario component.1

VaR and Expected Shortfall

The essentials from Hull:1

Measure Question it answers Caveat
VaR (99%, 10-day Basel parameters) Worst loss at the 1st percentile Says nothing about losses beyond the percentile; not coherent
Expected shortfall (C-VaR) Expected loss given we are in the tail Coherent; answers "how bad is bad?"
Stressed VaR (post-2008 Basel) VaR calibrated to a crisis window (e.g., 2008) Conservative; catches calm-data blindness
  • Estimation choices: historical simulation replays past moves on today's book (robust, slow); the model-building approach uses volatilities/correlations with delta–gamma approximations (fast, normality-dependent). For short-option books the quadratic model matters: positive gamma overstates linear VaR, negative gamma understates it — the classic short-premium blind spot.1
  • Inputs must be current: EWMA (λ = 0.94 daily) or GARCH(1,1) updating materially raises VaR in stressed markets, as the September 2008 four-index example shows.1
  • Back testing: actual losses should exceed 1-day 99% VaR on ~1% of days; a persistent excess flags a broken model.1

Reg-T vs Portfolio Margin

TOMIC's infrastructure guidance:2

Regime Method Character
Reg-T Margin per position, summed Simple, conservative, no portfolio credit for hedges
Portfolio margin Stress-test the entire portfolio; margin = worst-case scenario move Capital-efficient; requires genuine portfolio-level risk understanding
  • Example from the book: an AAPL married put requires $17,300 under Reg-T but ~$1,000 under portfolio margin — a massive capital liberation that is only safe if the trader can actually measure total portfolio risk.2
  • TOMIC's explicit recommendation: beginners stay on Reg-T until adept at portfolio risk management. Portfolio margin turns every trader into their own risk department, and its margin relief expands exactly when stress scenarios shrink — i.e., margin calls arrive after vol has spiked, not before.2
  • Margin is a liquidity risk, distinct from max loss: a defined-risk position's mark can stay within its max loss while interim margin/variation demands force liquidation at the worst point. The post-2012 clearing and margin regime that shaped these dynamics is covered in the wiki's case studies — see Volmageddon, COVID Crash, and August 2024 Spike rather than this page.

Stress Testing Complements VaR

A 99% daily VaR is silent about the 1% — which is where option books live or die:1

  • Replay the extreme moves of the last 10–20 years (Hull: the October 19, 1987 S&P move was 22.3 standard deviations; such moves should occur once in 7,000 years under normality, yet markets produce one or two per decade).
  • Add brainstormed scenarios: correlation → 1, VIX doubling, overnight gap with no repricing window, margin-call cascade.
  • For this wiki's purposes, the three case studies — Volmageddon, COVID Crash, August 2024 Spike — serve as pre-built historical stress scenarios for any short-premium book.

How It Fits TOMIC

TOMIC's own limits (2% per trade, 6% monthly, sector caps) are a simplified, rule-based surrogate for VaR/expected shortfall at retail scale; the VaR toolkit (EWMA vol inputs, correlation matrix, stress replays) is the professional version of the same idea. The two layers complement: rules cap behavior mechanically; VaR/stress measurement catches aggregate and correlation risk the rules miss.3 1

Links

Source Notes

  1. Hull bundle, topic Value at Risk. ↩↩↩↩↩↩↩

  2. TOMIC bundle, topic Trading Infrastructure. ↩↩↩

  3. TOMIC bundle, topic Risk Management. ↩