Portfolio Beta Calculator
Portfolio beta is the weighted average of each holding's beta, describing how much the portfolio tends to move when the market moves. It is measured on past data and used to describe the future, which is the assumption that fails when correlations change.
How much market you are carrying
Defaults hold 50% at a beta of 1.10, 30% at 0.85 and 20% at 1.40, against a 10% market fall.
Check the weights sum to 100 before reading the beta — the formula does not normalise them, so weights that sum to 80 produce a beta that is 20% too low and no error appears.
Runs entirely in your browser. Nothing you type is sent anywhere or stored.
How the number is built
Multiply each holding’s weight by its beta, add them up, divide by a hundred. The arithmetic is trivial and what it reveals usually is not.
Portfolio beta = Σ (weight × beta) ÷ 100
Weights do the work. A small holding with a beta of 2.5 barely moves the answer; a large one with a beta of 1.2 moves it a great deal.
A worked example
Take the defaults: 50% at 1.10, 30% at 0.85 and 20% at 1.40.
That is (50 × 1.10) + (30 × 0.85) + (20 × 1.40) = 55 + 25.5 + 28 = 108.5.
Divided by 100, the portfolio beta is 1.0850.
Against a 10% market fall that implies −10.85%, which on 100,000 is −10,850.
A beta of 1.0850 means about 8.5% more market exposure than simply holding the index. That is a deliberate choice if you made it and an accident if you did not, and most portfolios arrive there by accident.
Diversification is not a count
Owning twenty things is not owning twenty bets. If they all have betas near 1.2, the portfolio has one exposure — the market — at 20% more than full size, and the count of holdings tells you nothing about that.
Beta also understates what happens in a crisis. Holdings that behave independently in ordinary conditions tend to move together in a severe fall, so the realised beta in the event that matters most is usually higher than the measured one.
Which is the central limitation of this number: it is an average of ordinary days used to predict extraordinary ones.
Backwards measurement, forwards use
Every beta you can look up is a regression on history, usually a few years of it. A company that has changed what it does, or grown enough to change its relationship with the index, carries a number describing something it no longer is.
Two published betas for the same company often disagree, because the providers used different windows, different frequencies and different benchmarks. None of them is wrong; they answered different questions.
What leverage does to it
Leverage multiplies beta directly, and the returns do not follow. On this site’s shared series, the unleveraged run returned 3.61% with a worst drawdown of 3.76%. At 2x it returned 6.61% against a naive 7.22%, with a drawdown of 7.45%. At 3x it returned 8.93% against a naive 10.83%, with a drawdown of 11.08%.
The drawdown scaled almost exactly with the multiple and the return fell short of it every time.
The figures are in research/series-measurements.json.
Changing a portfolio’s beta means trading. On this site’s shared series a round trip measures about 2% of the median bar range of 0.493, so an adjustment made for a view about the next month is paying a certain cost for an uncertain benefit.
Steering the number
Three levers move a portfolio beta and they are not equally sensible. Change the weights, change what you hold, or hold cash — and only the last is reliable.
Cash has a beta of zero, so it dilutes arithmetically. Adding a 20% cash holding to the default portfolio takes the beta from 1.0850 to 0.8680, without selling anything for a view about direction.
Reweighting toward lower-beta holdings works and is slower. Moving the 20% at 1.40 into the 0.85 holding takes the portfolio to 0.9750, at the cost of two trades and whatever tax they trigger.
Trading in and out to time the market’s beta is the lever that usually loses. It requires being right about direction, and it pays a certain cost each way against an uncertain benefit — so each adjustment has to avoid enough adverse movement to cover both round trips before it has helped at all.
The original data
Of the 24,971 unique videos in research/search-study-corpus.jsonl, 4 have an instruction-shaped
title about portfolio beta, at a median of 313 views across 4 channels — and 0% are
calculator-shaped. Correlation appears in 5 at 1,162 and the Sharpe ratio in 5 at 26,440. The counts
come from site/rank_tools2.py, which deduplicates by video id.
Four videos at a 313 median is the second-lowest figure in the tool study. Beta is quoted on every fund page and almost nobody explains how to combine several of them, which is the only form in which it is actually useful.
The answer to the question above depends on whether 1.4 was chosen. A beta of 1.4 in a portfolio built deliberately for growth over decades is doing its job; the same 1.4 arrived at by drift, in a portfolio someone will need to draw on in three years, is a mismatch nobody decided on. Beta is not good or bad — it is a description, and the only failure is not knowing what yours is.
When it fails
The failure is concentrated in exactly the event beta is used to prepare for. In a severe fall, correlations converge toward one and everything drops together, so a portfolio measured at 1.08 in calm conditions behaves closer to 1.3 in the week it matters. The number is not wrong about ordinary weeks; it is systematically optimistic about the ones that decide outcomes.
The second failure is weights that do not sum to 100. The formula will not tell you.
A third is using betas from different providers. They measured different windows.
A fourth is applying it to something with a short history. A beta needs data to regress.
A fifth is treating it as a risk measure. It measures co-movement, not the chance of loss.
And a sixth is ignoring what the benchmark is. A beta against a sector index says nothing about the market.
Related
Beta covers the individual measure and how the regression works. Diversification is what a high portfolio beta quietly undermines. And correlation is what changes when it matters most.
The reason I compute this at all is that a portfolio can feel diversified and carry a single number that says otherwise. Six holdings across four sectors sounds spread out; if every one of them has a beta near 1.3, the portfolio has one position in the market and it is 30% larger than it looks.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.