How this instrument works
Value at Risk answers one specific question: how much could a portfolio lose over a given period, at a stated level of confidence, before anything worse becomes the concern? The parametric (variance-covariance) version computed here assumes a portfolio's returns spread out in a bell-shaped, normal distribution around zero, so a single volatility figure — the standard deviation of returns — is enough to describe the whole range of outcomes. Multiplying that volatility by a z-score chosen for the confidence level, then by the portfolio's dollar value, turns a statistical spread into one dollar threshold.
Banks compute this figure because regulators require it — the Basel Committee's market-risk capital rules have tied the capital a trading desk must hold to VaR-style measures for decades. A corporate treasurer overseeing a bond ladder runs the same arithmetic before a board meeting; a hedge fund's risk manager runs it nightly across every book and reports the result up to a risk committee that sets position limits from it. None of them read a single figure as advice about what to hold — they read it as a gauge of how much capital or attention a given exposure currently demands.
The number is a threshold, not a ceiling. At 95% confidence, there is roughly a 5% chance — about one period in twenty, if volatility stays where it was measured — that the loss exceeds this figure, and parametric VaR says nothing about how far past it losses could run inside that tail; analysts who need that answer turn to Expected Shortfall or a historical-simulation model built from actual past returns instead of an assumed bell curve. The time horizon matters too: this figure covers whatever period the volatility percentage was measured over, so a volatility drawn from daily returns yields a one-day figure, and stretching that to a month or a year requires scaling the volatility first, not just relabeling the answer.
- Enter Portfolio value, $ — the total dollar value of the position or book being measured.
- Set Z-score (confidence level) to 1.65 for a 95% one-tailed confidence level, or 2.33 for 99%.
- Enter Portfolio volatility (std. dev.), % — the standard deviation of the portfolio's returns over the same period.
- Read Value at Risk, $ — the dollar loss threshold implied by those three figures together.
Worked example — the $1,000,000 portfolio
Take a $1,000,000 portfolio value with a Portfolio volatility (std. dev.) of 15% and a Z-score of 1.65, the standard figure for a 95% one-tailed confidence level. VaR = 1,000,000 × 1.65 × 15 ÷ 100 = $247,500 — the loss threshold this parametric method assigns to that combination of size, confidence, and volatility.
Raise the confidence level to 99% (z-score 2.33) on the same $1,000,000 book and VaR climbs to $349,500, because a stricter confidence level always demands guarding against a rarer, more extreme outcome. Double the volatility instead, to 30%, and VaR doubles too, to $495,000 — the formula is linear in both the z-score and the volatility, so either input moving proportionally moves the dollar figure by the same proportion.
Questions
What does the z-score in this formula actually mean?
It is the number of standard deviations from the mean that corresponds to your chosen one-tailed confidence level under a normal distribution. A z-score of 1.65 marks 95% confidence, and 2.33 marks 99% — higher confidence requires a larger z-score, which pushes Value at Risk up because you are now guarding against a rarer, more extreme loss.
Why doesn't VaR tell me the worst possible loss?
Because it is a threshold, not a ceiling. At 95% confidence, VaR marks the boundary that losses are expected to exceed only about one period in twenty — it says nothing about how severe losses get inside that remaining 5%. Teams who need that answer compute Expected Shortfall, sometimes called conditional VaR, which averages the losses beyond the threshold instead of stopping at it.
Who actually calculates VaR, and for what decision?
Bank trading desks compute it because Basel Committee capital rules tie required regulatory capital to VaR-style measures; hedge fund risk managers run it nightly across every book and report it to a risk committee that sets position limits from it; corporate treasurers use it to size the exposure in a bond or currency book before a board update. None of them treat a single figure as a buy or sell signal on its own.
What time period does this VaR figure actually cover?
Whatever period the volatility figure was measured over. Enter a volatility calculated from daily returns and the result is a one-day figure; enter an annualized volatility and the result covers a year. Mixing periods — a daily volatility fed in hoping for an annual answer — produces a number that is not economically meaningful without first scaling the volatility by the square root of time.
How does parametric VaR differ from historical simulation VaR?
Parametric VaR, computed here, assumes returns follow a normal distribution and needs only a single volatility figure. Historical simulation instead replays a portfolio's actual past returns and reads the loss at the desired percentile straight from that distribution, capturing skew and fat tails a bell curve smooths away, at the cost of needing a long, reliable history of real returns to draw from.
Why do volatility and VaR move by the same proportion?
Because the formula multiplies portfolio value, z-score, and volatility together with no other terms, VaR scales linearly with each one. Doubling volatility doubles VaR at a fixed confidence level, which is exactly why diversification — combining assets that do not move in lockstep to lower overall volatility — is the most direct lever available for reducing this figure without shrinking the portfolio itself.
References
- Bank for International Settlements — Basel Committee on Banking Supervision
- U.S. SEC Investor.gov — Investing basics and glossary
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.