New on FinoLib · Volume II: Capital Markets
I have added a new article to FinoLib, my finance education website: Value at Risk (VaR): How It Works and Its Limitations, part of Volume II: Capital Markets. This page gives you the core of the topic in expert but plain language; the full article goes much deeper.
5.5 Value at Risk (VaR) — Measuring Downside Risk
The idea in plain words
Value at Risk, or VaR, answers the question: how much could I lose on a bad day? It states a loss that should be exceeded only with a chosen probability over a chosen time. For example, a 1-day 99% VaR should be exceeded about 2.5 days a year. On a $100 million S&P 500 position, ten years of data give $2.65 million by formula and $3.28 million from history, because real returns have fat tails, meaning extreme moves happen more often than the bell curve says. Regulators are moving to expected shortfall, which measures the average size of tail losses.
Key points
■Parametric VaR = z × σ × position; 2.326 × 1.138% × $100 million = $2.65 million.
■Historical VaR reads the 1st percentile of actual returns: $3.28 million, 24% higher.
■A calm 250-day window cut the parametric figure to $1.91 million.
A closer look
Value at Risk (VaR) answers a specific, practical question: over a given time horizon, at a given confidence level, what loss should the portfolio exceed only rarely? A statement like “1-day 99% VaR of $10 million” means the portfolio is expected to lose no more than $10 million on 99 out of 100 trading days; equivalently, a loss above $10 million should occur on about 1 trading day in 100, or about 2.5 days a year (1% × 252 trading days ≈ 2.5). It is a threshold, not a worst case.
Decision rule
Compute VaR both ways. If historical VaR exceeds parametric VaR by more than about 20%, the return distribution is fat-tailed: set limits on the historical figure or on 97.5% expected shortfall, not on the normal-distribution number. Use a data window that contains at least one stress period, or add a stressed VaR calibrated to a crisis year (US bank rules require one).
The costliest mistake
Calibrating VaR to a calm window. On February 19, 2020, a parametric VaR based on the prior 250 days used a daily σ of 0.744%, giving 2.326 × 0.744% × $100 million = $1.73 million. In the next 22 trading days losses exceeded that figure 11 times, against 0.22 expected, and on March 16, 2020, the index fell 11.98%, an $11.98 million loss, 6.9 times the VaR. Limits set on the calm-window number would have allowed far more exposure than the firm could bear. Always check the figure against a window that includes a crisis.
5.6 VaR’s Limitations — What It Doesn’t Capture
The idea in plain words
VaR has three blind spots. It says nothing about how bad losses can get beyond its threshold. It relies on data from calm periods. And it assumes you can sell your positions within the time period. Backtesting exposes the first two: a rolling S&P 500 VaR was breached 13 to 15 times a year in 2018, 2020 and 2022, against 2.5 expected. The third showed up in the 2022 UK gilt crisis, when hedged pension funds ran out of cash to meet collateral calls after a 160 basis point move.
Key points
■US banks’ VaR capital multiplier rises from 3.00 (4 or fewer exceptions) to 4.00 (10 or more).
■LDI yield buffer = capital ÷ (exposure × duration): 250 bp at 2× leverage and duration 20, 125 bp at 4×.
■A +160 bp move wiped out a 4× fund and left a 2× fund needing new capital within days.
Decision rule
Never set a limit on VaR alone; pair it with three checks: a backtest (at 99%, more than 4 exceptions in 250 days means recalibrate, 10 or more means the model is wrong); a stress test using both the worst historical move and a hypothetical move at least twice that size; and a liquidity test: enough cash or eligible collateral to meet margin calls from the stress move until new capital arrives (the Bank of England used five days for LDI funds).
The costliest mistake
Sizing a buffer to history. In the LDI example, a 4× fund with a 125 basis point buffer passed a 100 basis point stress test and sat more than four times above the largest one-day move on record (29 basis points). A 160 basis point move then cost it 32 of its 25 of capital, 128% of its equity. The fix the Bank of England required, about 250 basis points of resilience, is roughly 2× leverage at a duration of 20. Size buffers to plausible shocks, not observed ones.
What the full article covers
In the full article I take you through these sections:
■5.5 Value at Risk (VaR) — Measuring Downside Risk
■5.6 VaR’s Limitations — What It Doesn’t Capture
It includes worked examples, a look under the hood at the mechanics, a clear decision rule, the one mistake that costs people the most, a recap, a reveal-on-click quiz and the official sources behind every figure.
Volume II: Capital Markets
Read the full article on FinoLib
The complete article, Value at Risk (VaR): How It Works and Its Limitations, with every worked example, diagram, quiz and source, is free to read in Volume II, Capital Markets on finolib.com.
Explore the Finance Education Series: Vol. II — Capital Markets · Vol. I — Global Economy · Vol. III — Finance Encyclopedia · Vol. IV — Finance Careers · Vol. V — Personal Finance