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Completed-session research

Beta & Market Model

How much of a listing's movement its exchange benchmark explains — and how much it does not.

Research Intelligence
252 ≈ one trading year.
Short government bill yield. Shifts alpha only — see below.
What this page is for
What this page separates

On any given day a listing moves partly because the whole market moved and partly because something happened to the company. This page regresses the listing's daily returns on its exchange benchmark's and splits the two apart: beta is how hard it responded to the market, R² is how much of its movement the market accounts for, and what is left over is the company's own.

What people use it for
  • Reading a move correctly. A 3% fall on a day the index fell 2% is a very different event at beta 1.5 than at beta 0.4.
  • Judging "outperformance". A high-beta listing beats the index in every rising market without doing anything clever.
  • Knowing what diversification can reach. The idiosyncratic share is the risk that holding more names on the same exchange did not remove.
  • Deciding whether index-level news matters. At a low R², the index tells you very little about this listing.
Risk-free rate — what to put in that box

It is the return you could have earned over the same period without taking market risk — in practice the yield on a short government bill in the listing's own currency (India: the 91-day T-bill, in recent years around 6–7%; the US 3-month Treasury bill is the equivalent).

The model asks because it compares excess returns: the listing's return above that rate against the benchmark's return above it. Both sides get the same subtraction, so beta and R² barely move — it shifts alpha, by roughly (1 − beta) × the rate. Choosing it is really a choice about how to read alpha.

Leave it at 0% to read alpha as plain performance against the benchmark with no financing assumption. This app does not fetch a live bill yield — the number is yours, and the result states back which one was used.

What each number means
Beta — how much the listing moved for each 1% the benchmark moved, over this window. 1.0 tracked the index one-for-one; above 1 amplified it, below 1 damped it; negative means it moved the other way. It is measured history, not a property of the company — it drifts, and changing the window changes it.
Alpha (annualized) — the part of the return the benchmark did not account for, scaled to a year. Positive means the listing did better than its beta relationship alone implied over this window. It is a leftover, not skill and not an expected return — and at a low R² the leftover is mostly noise.
R² — the share of the listing's movement the benchmark explains, from 0 to 1. 0.22 means about 22% of it tracked the index and roughly 78% was its own. Low R² also means beta and alpha are estimated loosely: a weak relationship measured precisely is still a weak relationship.
Total annualized volatility — how much the listing's own daily returns varied, scaled to a year. It bundles market-driven and company-driven movement together.
Idiosyncratic volatility — the part of that variation the benchmark could not explain — what owning more listings on the same exchange alongside it would not have diversified away.
Benchmark — the index the regression actually used, printed rather than assumed. Beta is always beta against something; against a different index the same listing has a different beta.
Sessions regressed / Window — the window you asked for versus the sessions where both the listing and the index traded — holidays, halts and a short listing history shorten it. Fewer sessions means a wobblier beta, so compare two windows before treating one number as the answer.
Enter an exact exchange listing to regress its returns on the exchange benchmark.

Alpha here is what the benchmark did not account for over the window measured. It is a description of the past, never an expected return, a target, or a recommendation.