Beta and CAPM — how the market prices risk
The answer
Beta measures how much a share has moved compared with its market index in the past. A beta of 1 means it moved with the index. A beta of 1.6 means it moved about 1.6 times as far, up and down.
The capital asset pricing model, or CAPM, uses beta to estimate the return an investor should require from that share. It is a model of how risk is priced, and it describes the world less well than its popularity suggests.
Why this costs you money
The expensive belief is that beta measures risk. It does not measure risk. It measures co-movement with an index, which is a different thing, and the gap between them is where people get hurt.
Consider what a low beta actually says. It says the share has not moved much with the index over the measurement window. It does not say the business is safe. A company with steady quarterly results and a slow-moving share price can have a beta of 0.7 while carrying a balance sheet that will not survive a credit event. When the event arrives, the share does not fall 0.7 times as much as the index. It falls 90% while the index falls 20%, and the beta calculated from 3 quiet years described nothing about the situation you were in.
The second cost affects long-term investors. Beta is used inside almost every valuation model to set the discount rate — the return an investor requires. A higher beta produces a higher required return, which produces a lower calculated value. Analysts feed a beta measured over 2 years into a model that forecasts 15 years of cash flows, then present the answer to 2 decimal places. Small changes in that beta move the answer enormously. The precision is invented, and decisions get made on it.
The third cost is a habit. Somebody decides to lower their portfolio's risk, so they sell high-beta holdings and buy low-beta ones. What they have reduced is their exposure to index movement. They may have increased their exposure to a single industry, or to one interest rate, or to a promoter's borrowing. They lowered the number they were watching and raised the risk they own.
How it works
Beta comes from a straight line fitted through a scatter of points.
Take the weekly return of a share for the last 2 years. Take the weekly return of the index over the same weeks. Plot one against the other. Fit the best straight line through the points. The slope of that line is beta.
Beta = how far the share tends to move for each 1% move in the index.
A second number falls out of the same calculation and it is more useful than beta itself. R-squared tells you how much of the share's movement the index explains, from 0 to 1. An R-squared of 0.7 means index movement accounts for about 70% of what this share did. An R-squared of 0.15 means the index explains almost nothing, and the beta calculated alongside it is close to meaningless.
Almost nobody looks at the R-squared. It is printed next to the beta on most data services.
What CAPM is for
CAPM answers one question: what return should an investor require for holding this asset, given that some of its risk can be removed by diversification and some cannot?
That is the idea underneath it. If you hold 40 different shares, the events specific to each company mostly cancel out. What does not cancel is the movement common to all of them, which is the market. So, in the model, an investor should be paid only for the risk that cannot be diversified away, and beta measures how much of that risk an asset carries.
Expected return = Risk-free rate + Beta × (Expected market return − Risk-free rate)
The bracketed term is the equity risk premium: the extra return investors expect for owning shares rather than government bonds.
The risk-free rate is the yield on a government bond, because a government borrowing in its own currency is assumed not to default in that currency. Use a bond whose maturity roughly matches your holding period, and use the government of the currency your cash flows are in.
The model was developed independently by Jack Treynor in 1961 and 1962, William Sharpe in 1964, John Lintner in 1965 and Jan Mossin in 1966, building on Harry Markowitz's work on portfolio selection. Sharpe shared the 1990 Nobel Memorial Prize in Economic Sciences for it.
Where it stops being true
Every assumption in CAPM fails in the real world, and it is worth knowing which failure matters.
The model assumes no transaction costs and no taxes. It assumes you can borrow and lend without limit at the risk-free rate, which no individual can. It assumes every investor holds the same expectations. It assumes the "market" is every asset in existence, including property, private businesses and human capital — and Richard Roll pointed out in 1977 that this portfolio cannot be observed, so the model cannot be properly tested at all. What gets tested instead is a share index, which is a small and unrepresentative sample of it.
Then the evidence. Eugene Fama and Kenneth French found the relationship between beta and returns to be far weaker than the model requires, and in 2004 concluded that the failure of CAPM in empirical tests means most applications of the model are invalid. Separately, a large body of work has documented the low-volatility anomaly: low-beta shares have historically delivered returns as good as or better than high-beta shares, the exact opposite of the model's central prediction.
CAPM is still taught, still used in every corporate finance department, and still the standard way regulators set an allowed return. Know it because it is the common language. Do not mistake fluency for truth.
What it tells you, and what it does not
Beta tells you how much of your share's past movement came from the index. That is genuinely useful, and it is the same idea as subtracting the index move before interpreting a single day.
Beta does not tell you the chance of permanent loss. It does not tell you whether the company can pay its debts. It does not tell you anything about the future except by assuming the past window repeats.
Beta is also unstable in ways people forget. It depends on the window — 1 year of daily returns and 5 years of monthly returns produce different numbers for the same share. It depends on the index — beta against the Nifty 50 and beta against a broad market index are different. It changes when the company changes, and a company that has just taken on large debt has a higher true beta than its history shows.
The decision rule
Treat beta as a question, not a measurement. The question is: how much of this holding's movement does the index explain, and is index movement the risk I actually care about?
If the R-squared is high and you invest for 10 years, beta tells you how bumpy the ride will be and nothing about whether you will arrive.
If the R-squared is low, ignore the beta entirely. The share is being driven by something the index does not contain, and that something is what you should be studying.
Unless the company's financing has changed recently — new debt, a large acquisition, a rights issue — in which case the historical beta describes a company that no longer exists.
Try this now
Five minutes, and the goal is not a number. The goal is to find out whether the number describes anything you care about.
- Open your holdings. For each one, find beta — it is on the fundamentals or key statistics tab of most brokers, and on free data sites. Write the list down.
- Beside each beta, write what percentage of your portfolio that holding is.
- Multiply each beta by its percentage weight, and add up the results. That is your portfolio beta. A portfolio beta of 1.15 means your portfolio has historically moved about 15% more than the index, in both directions.
- Now the part that matters. For each holding, write down in 6 words the thing that would actually damage this investment permanently. A lost contract. A regulator. A promoter's borrowing. A technology change. A single large customer.
- Read your 2 columns side by side.
What you should see. For most portfolios, the beta column and the damage column have nothing to do with each other.
Your highest-beta holding is usually not your riskiest one. It is your most volatile one, which is a statement about how the price behaves on ordinary days. Your riskiest holding is often something with a modest beta and a specific, nameable problem.
You should also find that your portfolio beta is close to 1. Most retail portfolios are, because they hold large index constituents. If you have been reducing risk by selling volatile shares, check whether the beta actually moved. Usually it has moved very little, and the risk you were worried about was never in that number.
Three real cases
1. Fama and French, 1992 and 2004 (United States) — the model tested and found wanting Eugene Fama and Kenneth French examined the relationship between beta and realised returns across US shares over long periods. They found that beta had little power to explain the differences in return between shares, while company size and the ratio of book value to market value had considerable power. Revisiting the question in 2004, they concluded that CAPM's empirical record is poor enough to invalidate most of the ways the model is used. Both men are among the most cited researchers in finance, and Fama received the Nobel Memorial Prize in 2013. This is not a fringe objection. It is the mainstream finding.
2. The low-volatility anomaly, documented through 2011 (global) — the prediction reversed CAPM predicts that higher beta earns higher return. Malcolm Baker, Brendan Bradley and Jeffrey Wurgler, writing in the Financial Analysts Journal in 2011, documented the opposite over decades of data: portfolios of low-volatility and low-beta shares delivered returns at least as good as high-beta portfolios, with much smaller swings. Their explanation was institutional — professional managers are measured against a benchmark, which discourages them from holding low-beta shares even when those shares are attractive. Whatever the cause, a model whose central prediction runs backwards for decades is a model to be used with caution.
3. Yes Bank, March 2020 (India) — the beta described the wrong thing Yes Bank was one of India's larger private banks and a widely held share. On 5 March 2020 the Reserve Bank of India superseded its board and imposed a moratorium, and a reconstruction scheme followed, under which the bank's additional tier 1 bonds were written down entirely and the equity was heavily diluted. Whatever beta had been calculated from the previous 2 years of weekly returns, it did not describe this. The risk that mattered was the loan book, the capital position and the regulator — none of which appears in a regression against the index. Investors who thought of their bank exposure in terms of beta were measuring the wrong thing with real precision.
The question that resolves it
A novice looks at a beta of 0.6 and asks: is this a safe stock?
An expert looks at the same 0.6 and asks: what fraction of this stock's movement does the index explain, and what is the thing that could destroy it permanently?
Beta answers a question about ordinary days. Permanent loss happens on the other kind.
What would make this wrong
If beta captured the risk that gets paid for, then over long periods high-beta portfolios would out-earn low-beta portfolios. Repeatedly and across markets, they have not. That single finding is enough to reject the strong form of the model, and it is the finding this article is built on.
The honest limits run the other way too.
Beta is not useless. For a diversified portfolio measured over years, it describes reasonably well how much the whole thing swings relative to the market. It is a fair tool at the portfolio level even where it is weak at the individual share level.
CAPM is not useless either. It gives a disciplined structure for thinking about required return, it forces you to state a risk-free rate and a premium out loud, and it is the accepted method in regulation and company finance. Rejecting it entirely leaves you with no framework at all, which is worse.
And a low R-squared is not a defect in the share. It means the index does not drive it, which can be exactly what a diversifying investor wants.
In India
Betas for Indian shares are typically calculated against the Nifty 50 or the S&P BSE Sensex, using 1 to 3 years of daily or weekly returns. Different data providers use different windows, so 2 sources will show 2 different betas for the same share. Neither is wrong. They answer slightly different questions.
The risk-free rate used in India is the yield on Indian government securities, usually the 10-year G-Sec, published by the Reserve Bank of India and the Clearing Corporation of India. It has generally sat well above US Treasury yields, largely because Indian inflation has been higher. A higher risk-free rate flows straight into every valuation done with CAPM, which is one reason the same business is valued lower in India than in the United States by the same method.
The equity risk premium for India is estimated rather than observed, and published estimates vary. The estimate you choose changes the answer materially, which tells you how much confidence the final number deserves.
One structural point matters. The Nifty 50 is concentrated: a small number of large companies, and financial services in particular, account for a large share of it. A beta calculated against it is partly a measurement of how much your share moves with a handful of banks. For a small or mid-sized company in an unrelated industry, that regression can be close to noise.
In the United States
Betas are typically calculated against the S&P 500, and the convention on most data services is 5 years of monthly returns. Some providers apply an adjustment that pulls the raw beta toward 1, on the reasoning that betas drift toward 1 over time. So a published US beta may not be the raw regression slope at all.
The risk-free rate is the yield on US Treasury securities: the 10-year note for long-horizon valuation, short Treasury bills for short horizons. Yields are published daily by the US Treasury.
CAPM is embedded in American corporate practice more deeply than in most markets. It sits inside the weighted average cost of capital used to approve factory investments, inside fairness opinions in takeovers, inside impairment tests for goodwill, and inside the rates utility regulators allow. When you read that a company's cost of equity is 9.4%, you are almost always reading a CAPM output. Aswath Damodaran of New York University publishes free annual estimates of equity risk premiums and industry betas, which is the reference most practitioners use.
Where they differ, and what that tells you
The risk-free rate is not a global number, and this is the most common mistake made by Indian readers of American material.
A US valuation uses a Treasury yield because the cash flows are in dollars. An Indian valuation must use a rupee government bond yield, because the cash flows are in rupees and the rupee has had higher inflation. Mixing them produces a value wrong by a wide margin, always in the direction of making Indian assets look cheaper than they are.
The second difference is what the index contains. The S&P 500 spreads across many industries, so a beta against it is closer to a beta against the economy. The Nifty 50 is concentrated, so an Indian beta is measured against a narrower reference.
What that tells you is where beta is worth using. For a large Indian company in a sector heavily represented in the index, beta and R-squared carry real information. For a small or mid-sized Indian company outside those sectors, check the R-squared, and if it is low, stop using the number rather than adjusting it.
Carry this
- Beta measures co-movement with an index, not the chance of permanent loss.
- Read the R-squared beside every beta. A low R-squared makes the beta noise.
- The risk-free rate must match the currency of the cash flows. Never import one.