Sanity Checking Calculations

Medium2–3 hrsSanity CheckCross-ValidationOrders of MagnitudeDimensional Analysis

Overview

Sanity checking is the habit of running quick reality tests on any number before trusting it. In quant trading, this is essential: a model might output a 'fair value' that implies arbitrage that can't exist, or a risk system might report a VaR that's 100× what intuition suggests. The best practitioners treat every number as guilty until proven innocent. The core tools are: cross-validation from an independent direction, bounding with upper/lower limits, and dimensional analysis.

How to Recognize

→You've computed an answer and it feels suspiciously large or small
→Checking whether a model output is plausible before acting on it
→Validating a P&L attribution or risk number
→Any situation where 'does this make sense?' is the question

Step-by-Step Approach

1.Cross-validate from two completely independent angles
2.Bound the answer: what's the maximum it could possibly be? The minimum?
3.Check units: does the dimensional analysis work out?
4.Calibrate against a known comparable (revenue, population, physical constant)
5.If the two angles agree within 2–5×, the answer is plausible

Key Formulas

\text{Sanity: }\text{does } A \times B \times C \approx \text{known total?}

\text{Upper bound} = \text{everyone does it all the time}

\text{Lower bound} = \text{nobody does it, ever}

\text{Plausibility range: answer within 10× of both bounds}

Worked Examples

0Quick Example

Sanity check: 'US advertising market is

500 billion.' GDP ≈

25T. Ad spend/GDP ≈ 2%, which is historically normal. Cross-check: ~330M people ×

1500/person/year in ads ≈

495B. Both angles agree. Plausible. ✓

Problem

Your model estimates that trading 1 million shares of Apple (AAPL) will move the price by 0.1%. Is this plausible?

Solution

AAPL average daily volume: ~80M shares/day. Your trade is 1M/80M ≈ 1.25% of ADV.

Rule of thumb: market impact scales roughly as sqrt(participation rate). sqrt(0.0125) ≈ 0.11.

Volatility of AAPL: ~1.5% daily. Impact ≈ 0.11 × 1.5% ≈ 0.17%.

Your model says 0.1%. Roughly consistent with the square-root model. Plausible ✓.

If the model said 5% impact, that would be ~30× too high — flag as a bug.

Answer

0.1% impact for 1.25% of ADV is consistent with standard market impact models (sqrt(participation) × daily vol). Within range. ✓

Common Mistakes

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Accepting an answer because the math checked out — the math can be right but the inputs wrong. Always sanity-check inputs too.
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Using a circular sanity check (verifying the answer against itself with a rephrasing). Two checks must be genuinely independent.
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Not bounding. If you can't compute the answer quickly, at least bracket it: 'it must be between X and Y.'

Practice Problems

Click "Show Answer" to reveal

Your colleague says the US housing market is worth $50 trillion. Sanity check this.

Hint: Estimate from: number of housing units × average home price. Cross-check with fraction of total US wealth.

Back to Study Plan

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