Value at Risk Calculator
The formula
What the value at risk tells you
The bank regulator's favorite one-liner: with confidence X over horizon t, losses will not exceed this amount — under normal markets and a Gaussian model. J.P. Morgan's RiskMetrics made it the industry standard in 1994.
Calculation: VaR = W × z × σ × √t. Enter your inputs and every substitution is shown below the result.
Reading the result
Never read VaR as "the most you can lose" — it says nothing about the tail beyond the cutoff. Two books with identical VaR can have wildly different crash exposure; pair it with stress tests.
Rules of thumb: Major banks run 1-day 99% VaR near 1–2% of tier-1 capital; a retail portfolio above ~4% VaR per month is aggressive
Limitations and best practice
The 2008 crisis was the textbook indictment: VaR collapsed because correlations went to 1 and volatility doubled exactly when models estimated it low. VaR calibrated on calm data is a promise broken at the worst moment.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
What does 95% VaR actually mean?
Why do regulators prefer expected shortfall now?
Can VaR be right and still blow up a fund?
Source & methodology
Jorion, P. (2007) Value at Risk, 3rd ed.; RiskMetrics Technical Document (1996); Basel III FRTB.
Value at Risk: the number, the method and the caveats
You are here because you need a specific number, and you want to see how it was produced before you rely on it. Searchers land on a Value at Risk page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
The number itself is the easy part. What takes judgement is knowing which inputs are facts in your situation and which are guesses wearing a decimal point — a distinction this page makes explicit for every field above.
A calculation like this one is worth roughly as much as a careful sentence: it forces several vague considerations into one comparable quantity. Once Value at Risk is on the table, the argument can stop being about impressions.
Nothing below is stock text pasted around a number: the worked example computes value at Risk = $3,504 from this tool’s own defaults, and the sensitivity section ranks the inputs that move the result — Position value first, at ≈10.0 % of the headline for a ten-percent error either way in that input. Work down the page and by the end you could re-derive the result in a spreadsheet from memory.
The Value at Risk formula, explained
The engine implements a single stated model: VaR = W × z × σ × √t. There is no hidden coefficient and no login-gated precision — the formula printed is the formula executed, which is also what makes the result citable.
Position value ($) (example value 177,500) is a measured number in the unit named by the label; the formula does not convert for you. Replace the example with the figure from your own records — the tool recomputes instantly and the printed steps follow your numbers.
Daily volatility (%) (example value 1) is a measured number in the unit named by the label; the formula does not convert for you. Check the convention first: if the source says “6.5 % per year”, type 6.5 and let the formula do the rest.
Confidence level (example value 95%) is a selector, not a measurement: the engine follows a different route for each option. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
Horizon (days) (example value 1) is a measured number in the unit named by the label; the formula does not convert for you. Be precise about the boundary (exact date, start of month); time inputs decide the exponent in most formulas.
What each “Confidence level” choice actually does: 90% → $2,730 · 95% → $3,504 · 97.5% → $4,175 · 99% → $4,955 — each value above is the model’s own output for that option, so the choice can be made on evidence rather than on what a category feels like it means.
Value at Risk on the example inputs: the complete substitution
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Position value ($), Daily volatility (%), Confidence level, Horizon (days). Run to the end, the value at Risk resolves to $3,504 — At 95% confidence you could lose about $3,504 over 1 day on the bands this tool uses.
- VaR = $177,500 × 1.6449 × 0.0120 × √1
- = $3,504 — expected to be exceeded in roughly 0 of every 100 similar 1-day windows
z-multiplier used — 1.645. If your inputs change, this is usually the first companion figure to move.
VaR as % of position — 1.97 %. This is the number experienced users quote when the headline alone would mislead.
1-day 95% VaR (for reference) — $3,504. If your inputs change, this is usually the first companion figure to move.
Expected shortfall (≈ VaR × 1.25 at 95%) — $4,380. Compare it against the main result of $3,504 before drawing conclusions.
Re-running with your own figures is instant; re-running by hand once is the best way to know the tool is telling you the truth.
How far Value at Risk can reasonably move
Single-point answers invite false confidence, so the same engine was run across a band around the input that matters most here. Each row is a full recalculation of Value at Risk, not an interpolation.
| Position value setting | Value at Risk |
|---|---|
| 80 % of the example value | $2,803 |
| 90 % of the example value | $3,153 |
| example inputs | $3,504 |
| 110 % of the example value | $3,854 |
| 120 % of the example value | $4,204 |
Across 5 settings of Position value, the result spans $2,803 to $4,204. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Position value alone; the substitution steps will follow your figures exactly.
What actually moves your Value at Risk
Nobody should have to guess which input matters. The engine was re-run once per field below — ten percent up, ten percent down, everything else frozen — and the results ranked by how far they moved the value at Risk. For Value at Risk the ranking is measured rather than guessed, and it belongs to these defaults: shift the starting point and the order can shift with it.
- Nudge Position value by ±10 % and Value at Risk lands between $3,153 and $3,854 (sensitivity ≈10.0 %)
- Nudge Daily volatility by ±10 % and Value at Risk lands between $3,153 and $3,854 (sensitivity ≈10.0 %)
- Nudge Horizon by ±10 % and Value at Risk lands between $3,324 and $3,675 (sensitivity ≈5.1 %)
Position value is the dominant lever here: ten percent either way moves the result by about 10.0 %, from $3,153 to $3,854. Measure that input from a document rather than from memory, and Daily volatility is effectively tied with it (≈10.0 % for the same nudge), so verify the pair together. The remaining fields can sit at safe defaults without materially changing the answer — knowing which is which is what separates a careful calculation from an anxious one.
Is your Value at Risk good — reading the result bands
Nobody acts on a bare figure — they act on a figure with a comparison attached. The default case lands in the “At 95% confidence you could lose about $3,504 over 1 day” band, and bands are deliberately wide because real situations overlap. How much of that band is luck? On Position value alone ten percent either way covers $3,153 to $3,854. The practical reading rules: compare against your own history before comparing against other people; treat band boundaries as zones, not walls — one point on the wrong side of a threshold rarely changes a real outcome; and when a companion output contradicts the headline, believe the pair.
The comparison worth making is not with somebody else’s Value at Risk but with the version of your own situation measured last quarter — same formula, same conventions, different inputs.
Common mistakes with Value at Risk (and the fix)
The 2008 crisis was the textbook indictment: VaR collapsed because correlations went to 1 and volatility doubled exactly when models estimated it low. VaR calibrated on calm data is a promise broken at the worst moment. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Reading Value at Risk as a promise rather than a conditional. Every number here is of the form “if these inputs, then this result”; when an input moves, the honest response is to recompute rather than to defend the old figure.
Attention is also misallocated between fields. Having measured this engine, we can say where it belongs: Position value first, everything else second.
A final trap is presentation: reporting Value at Risk to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
A quick check for any Value at Risk figure
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Note the date and the inputs beside the number so the figure can be audited later.
- Re-verify Position value against a source document — ten percent of error there moves the headline by ≈10.0 %.
- Confirm the example values are plausible for your own situation before replacing them.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
A routine for decision-grade Value at Risk
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Value at Risk takes a minute to learn and applies to every input above.
Step 1 — start from evidence. The inputs behind Value at Risk are position value ($), daily volatility (%), confidence level, horizon (days). Write them down with their source next to each one; if you cannot name where a figure came from, that is the input most likely to be wrong. A figure nobody can reproduce is a figure nobody will act on twice.
Step 2 — enter the conservative case first. Resist the flattering scenario. Type the inputs you would defend in front of a sceptical reader, read the Value at Risk ($3,504 for the example values), and note the verdict band. Numbers are cheap to produce and expensive to retract; the extra minute is the cheapest insurance available.
Step 3 — play with the inputs on purpose. Ten percent up, ten percent down, one field at a time. Within a few minutes you will know this calculation better than most people who quote its results. Most surprises in numbers are surprises about inputs, not about formulas.
Step 4 — stress before you commit. A decision that survives a ten-percent squeeze on its two biggest inputs needs no luck to be sound. One that does not survive is a decision about hope, not about arithmetic. When two sources disagree, it is almost never the arithmetic that differs.
Step 5 — record the context, not just the number. Note today’s date and the inputs alongside the $3,504 output. Six months from now the context is what turns this figure into a trend. If the verdict changes with a ten-percent nudge, report the nudge alongside the number.
Who actually uses Value at Risk — and when
In Portfolio Management the figure computed here is usually the first one somebody asks to see. Having it — with the formula behind it — changes your position in the conversation from participant to reference. A figure with a date beside it becomes evidence; without one it stays an anecdote.
The audience for this page is people who need one trustworthy number before their next decision. In professional Portfolio Management practice the pattern is always the same — screen with Value at Risk, then invest slow analysis only in whatever survives the screen. Rounding early is the quietest way to introduce a permanent error.
There is a personal-administration use people overlook: periodic self-checking. Value at Risk quietly drifts as life changes — rates move, bodies change, costs compound — and re-running it a few times a year catches drift while correction is still cheap. Comparisons are cheap: run the identical calculation for the alternative and look at the gap.
Quick answers: what searchers ask about Value at Risk
What affects Value at Risk the most?
Value at Risk is driven above all by Position value. Perturbing only that field by ten percent either way produced $3,854 against the $3,504 baseline — a ≈10.0 % response, while Daily volatility manages ≈10.0 %.
Do daily volatility and position value matter equally?
Effectively. Measured on this engine they land at ≈10.0 % and ≈10.0 % for the same ten-percent nudge, so the honest advice is to get both right; chasing precision in only one of them buys almost nothing.
How much does the “Confidence level” choice change the answer?
The spread is not cosmetic: this choice alone takes Value at Risk from $2,730 to $4,955 with every other input frozen, which is more influence than most of the numeric fields on this page can claim.
What is a typical Value at Risk?
With the example inputs on this page the result is $3,504, labelled “At 95% confidence you could lose about $3,504 over 1 day”. “Typical” varies with situation, which is why every result here ships with its verdict band and its sensitivity list: they turn one figure into a range you can locate yourself inside.
How do I calculate Value at Risk by hand?
Three steps: write the formula (VaR = W × z × σ × √t), insert your values, and simplify. The worked example section shows exactly that chain for the default inputs; replicating it once on paper teaches you more about Value at Risk than any number of calculator runs.
What happens to Value at Risk if position value changes by 10 %?
On these inputs a ±10 % change in position value takes Value at Risk to $3,854 against the $3,504 example — around 10.0 % of the headline. The same test on every other field is in the sensitivity section.
Is the Value at Risk result of $3,504 good or bad?
Good and bad are comparisons, so the honest test is three questions: where does your own Value at Risk sit against the $3,504 reference above, how far would a plausible input error move it (≈10.0 % per ten percent on Position value), and what does the alternative option compute to?
Does Value at Risk account for fees and taxes?
Only what you put in. Fees belong inside Position value ($) where they shrink returns before compounding touches them; taxes are outside the scope of a pre-tax Value at Risk and should be layered on top before decisions.
Can Value at Risk be negative or empty?
Yes, and that is informative rather than broken: a negative Value at Risk usually means the inputs encode an outflow or a shortfall, and the verdict band above labels exactly that situation instead of hiding it.
What does 95% VaR actually mean?
If you repeat the period many times under similar conditions, losses exceed the VaR figure about 5% of the time. It does not bound the size of those exceedances.
Why do regulators prefer expected shortfall now?
Basel III moved to CVaR/expected shortfall because VaR is not subadditive — it can reward dangerous diversification illusions and ignores tail depth.
Can this tool see the numbers I type?
It cannot. There is no submission step: the calculation happens in your browser and the result disappears when you close the page. Treat the fields above as a scratchpad rather than a form.
What the labels on this page mean
- z-multiplier used
- 1.645 on the example inputs — a companion figure printed beside the headline of Value at Risk so that no result is read in isolation.
- VaR as % of position
- 1.97 % for the Value at Risk worked case; it sits next to the main result because it carries context the headline leaves out.
- 1-day 95% VaR (for reference)
- $3,504 on the example inputs — a companion figure printed beside the headline of Value at Risk so that no result is read in isolation.
- Value at Risk
- The primary output of this tool: $3,504 for the default inputs, computed exactly from VaR = W × z × σ × √t.
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- The interpretation attached to a result (“At 95% confidence you could lose about $3,504 over 1 day” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Value at Risk moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Where the Value at Risk model comes from
The model is published arithmetic implemented exactly as written: VaR = W × z × σ × √t. Source of record: Jorion, P. (2007) Value at Risk, 3rd ed.; RiskMetrics Technical Document (1996); Basel III FRTB. Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
Treat the output as a precise answer to the question you typed: exact arithmetic, transparent formula, published source, no hidden rounding. What that buys you is reproducibility — two people, two browsers, the same arithmetic, and a printed trail from inputs to result that either of them can audit.
Next steps after the calculation
Save the number together with its inputs and today’s date; a Value at Risk figure without context is unusable the moment an input changes.
This page was written for people who need one trustworthy number before their next decision, and the promise is that nothing above required trust. Bookmark the tool, re-run it whenever an input moves by more than a few percent, and keep the date with the number.