Three families of quant reasoning for investing
| Family | Mechanic | Investing application |
|---|---|---|
| Market sizing (Fermi build-up) | Build the answer from a chain of rough estimates (population x penetration x price), each within 2x of the right answer; the chain converges to an order-of-magnitude bound | Independent TAM check on a memo's revenue runway claim; sanity-check on a sell-side analyst's bull-case revenue projection; quick disqualification of impossibly-large TAM claims |
| Probability reasoning (base rates + expected value) | Translate a qualitative claim into a base rate from the relevant reference class; compute expected value across outcomes; size the position by the asymmetry rather than the headline upside | Position-sizing for binary catalysts (FDA approvals, M&A announcements, earnings beats); evaluation of "is this an outlier?" claims; identification of when the market is mispricing a clear probability |
| Valuation by inspection | Compress a multi-step DCF, comp, or earnings-power calculation into a single mental shortcut (e.g., "15% earnings yield + 5% growth = 20% expected return, ignoring multiple compression") | 30-second cross-check on a price target; rapid go/no-go screen on whether a stock is worth deeper analysis; defense against narrative-driven bull cases that don't survive a coarse arithmetic check |
| Reverse Fermi (decomposition) | Take a stated number and decompose it into the build-up chain implied; ask whether each component of the implied chain is plausible | Stress-testing a TAM claim, a margin assumption, or a growth-rate projection by reverse-engineering what would have to be true at each component level for the headline number to make sense |
The customer-times-spend market-sizing chain
The single most useful Fermi-build pattern for investors is the customer-x-spend market-sizing chain. Mechanic: estimate the population of potential customers in the relevant reference class (US small businesses, US households, global enterprises), estimate the penetration rate (what fraction find this product relevant), estimate the average annual spend per customer, and multiply. Even if each estimate is off by 50%, the product is off by at most 3-4x, which is still useful for order-of-magnitude bounding. Apply the chain to any memo's TAM claim and immediately notice whether the analyst's TAM number is plausibly within the order of magnitude of the build-up or whether it requires heroic assumptions to reach. The chain is also the right discipline for evaluating your own ideas: if your investment thesis assumes a $20B revenue opportunity and your Fermi build-up arrives at $2B, you have to confront the gap before committing capital.
Why base rates are consistently underweighted
Base rates are the most consistently underweighted input in retail-investor probability reasoning. Mechanic: when evaluating a claim ("this management team will turn the business around," "this catalyst will trigger a re-rating," "this binary event will resolve favorably"), look up or estimate the base rate of similar claims being correct in the relevant reference class. Turnarounds in this industry succeed roughly 25-35% of the time historically; FDA approvals at this stage of trial succeed at roughly the published rate; M&A premiums at this size and sector cluster around a specific median. A specific claim that asks the reader to project above the base rate is a claim that requires specific evidence for why this case differs from the average. Investors who anchor to vivid recent narratives (the company that did pull off the turnaround, the FDA approval that did clear) instead of the base rate consistently overpay for low-probability outcomes. The discipline of starting with the base rate and then asking what specific evidence justifies deviating from it is one of the highest-ROI mental moves in probabilistic thinking.
Fermi-check a memo's TAM claim
Expected value and position sizing for a binary catalyst
Why expected value alone does not size a position
Compute the expected value AND let the asymmetry size the position. EV = 0.70 x $120 + 0.30 x $60 = $84 + $18 = $102, vs current price $80, giving $22 of expected value (27.5% expected return). The single-step EV calculation is not the hard part; the discipline is letting the binary-tail risk constrain the position size despite the favorable expected return. A 25% drawdown if the deal breaks is meaningful even at a 30% probability of break; concentration in a single binary catalyst is the classic place where 'high expected value' positions destroy track records because the EV captures the average outcome but the realized outcome is binary (either +50% or -25%, never +27.5%). The Kelly-style adjustment: position size scales with edge (expected return) and inversely with the squared downside, so a 1.5:1 to 2:1 bull-bear asymmetry at 70% probability typically supports a 2-5% portfolio position, not a maximum-conviction sizing. The discipline of computing EV then constraining for downside is the correct probabilistic framework; option A treats high probability as license to over-size, option C ignores the downside arithmetic and computes only the upside-weighted return, and option D abandons the math entirely. The discipline is to compute the number AND let the asymmetry constrain the sizing -- both moves are required.
Fast cross-checks that catch order-of-magnitude errors
Earnings yield plus growth as a return shortcut
Four pathologies in brainteaser reasoning
Going deeper (optional). Up next: four pathologies in brainteaser-style reasoning that compromise its usefulness — an advanced aside you can skip on first pass and come back to anytime. Continue when you're curious.
Going Deeper -- four pathologies in brainteaser-style reasoning that compromise its usefulness. (1) False precision: treating a Fermi estimate as if it were a model output rather than an order-of-magnitude bound; the right use is "$1-3B TAM" not "$1.8B TAM." (2) Skipping the chain: jumping to an answer without building the chain ("the TAM is huge") foregoes the discipline that catches errors at each component step. (3) Base-rate neglect on novel narratives: a story that sounds genuinely unprecedented ("AI will reshape this industry") tempts the reader to skip the base-rate check, but the relevant reference class still exists (previous industry-reshaping technologies have produced specific cross-sectional return patterns worth knowing). (4) Valuation-by-inspection without constancy check: the earnings-yield + growth shortcut depends on multiple-constancy; applying it without checking whether the current multiple is structurally defensible produces a number that looks rigorous but rests on a hidden assumption. AI prompt for self-review: "Given this memo's TAM claim, growth-rate assumption, and price target, build an independent Fermi check on each, identify the largest divergence between the memo's number and the Fermi bound, and assess whether the divergence is a sign the analyst knows something I don't or a sign the analyst is stretching." These mental shortcuts make every memo faster to evaluate; the discipline is using them as cross-checks rather than as substitutes for the deeper analytical work.
Sit with the ideas.
A company sells a single SaaS product to small-and-medium-sized US businesses at $200/month per seat. Without any market-research input, what is the disciplined Fermi-estimation order-of-magnitude bound on the company's plausible US revenue if it captured 5% of the addressable market?