Beta & the Capital Asset Pricing Model (CAPM)

What Is Beta? (Systematic Risk in One Number)

Beta is a single coefficient that answers one question: historically, how much has this stock moved when the overall market moved? It is derived by regressing a stock's periodic returns against the returns of a market index — in practice, almost always the S&P 500 or an equivalent broad benchmark — and reading off the slope of that regression line. The slope, beta, tells you the average magnitude and direction of the stock's response to market-wide moves.

What Do Different Beta Values Mean?

A beta of 1.0 means a stock has historically moved in step with the market. A beta above 1.0 means it has amplified market moves; below 1.0, it has dampened them; near zero, the market explains little of its movement; negative, it has tended to move opposite the market.

To put numbers on it: a beta above 1.0 — say 1.6 — means the stock has historically amplified market moves: a 1% market move corresponds to roughly a 1.6% move in the stock, in the same direction. A beta below 1.0 — say 0.5 — means the stock has dampened market moves, participating in only about half of each swing. A beta near zero means the regression found little historical relationship between the stock's returns and the market's at all. A negative beta — rare, but real for a small number of assets such as certain gold-linked instruments or long-duration government bonds during specific regimes — means the stock has tended to move opposite the market.

Is Beta a Good Measure of Risk?

Beta is a good measure of systematic (market) risk specifically, but an incomplete measure of total risk — it excludes idiosyncratic risk, tail risk, and liquidity risk entirely.

This is the single most common framing behind the "[stock] risk level beta" search pattern: people use beta as a shorthand for "how risky is this stock." That shorthand is directionally useful but structurally incomplete. Beta measures only systematic risk — the portion of a stock's variance explained by market-wide moves. It says nothing about idiosyncratic risk — company-specific events such as a failed product launch, a fraud disclosure, or a lawsuit — nor about tail risk, the severity of losses in the worst-case scenarios, which is precisely what Conditional Value at Risk (CVaR) is designed to measure. Two stocks can carry an identical beta of 1.2 and have very different total risk profiles if one has much higher idiosyncratic volatility or fatter tails. Beta is a real, useful number — but it is a measure of one dimension of risk, not a complete risk score.

Beta is not a risk score. It is the answer to one narrow question — how has this stock historically responded to the market — dressed up, by habit, as the answer to a much broader one.

On the limits of a single coefficient — A.L. Capital Advisory

How Is Beta Calculated? (The Regression, and the "5-Year Monthly" Convention)

Beta is formally defined as the covariance between a stock's returns and the market's returns, divided by the variance of the market's returns: β = Cov(R_stock, R_market) / Var(R_market). In practice this is computed by running an ordinary least squares regression of the stock's periodic returns against the market's periodic returns over the same dates, and reading off the slope coefficient. The intercept of that regression is Jensen's alpha; the slope is beta.

Four related statistics get conflated constantly, and the confusion is worth resolving explicitly because each answers a genuinely different question:

A stock can have high correlation with the market (moving in the same direction almost every time) but a low beta (moving by a smaller magnitude each time) — correlation and beta are related but not interchangeable. Standard deviation is the broadest of the four: it captures everything beta misses, which is exactly why standard deviation and CVaR remain necessary alongside beta, not replaced by it.

The number that comes out of this regression depends entirely on three choices, and this is worth naming explicitly because it is exactly what drives the live "beta source" and "beta value 2026" search queries this page is written to answer: the estimation window (how many years of history), the return frequency (daily, weekly, or monthly), and the market proxy (S&P 500, a total-market index, or a sector benchmark).

The most widely cited convention — and the one worth naming by name, because it is a specific, searched-for term — is the "5-year monthly" beta: a regression of 60 monthly stock returns against 60 monthly market returns over the trailing five years, versus the S&P 500. It is popular for a practical reason: monthly data smooths out day-to-day noise (bid-ask bounce, short-term liquidity effects, single-day idiosyncratic events) while still providing enough observations — 60 — for a statistically usable regression. It is not the only convention in use. Two-year weekly beta (roughly 104 observations) and one-year daily beta (roughly 252 observations) are also common, particularly among sources that want more responsiveness to recent conditions at the cost of more noise. Switching between these conventions on the same stock, on the same day, routinely produces betas that differ by 0.2 to 0.5 or more — before any adjustment is applied at all.

Why the Same Stock Shows Different Betas (and Which One to Trust)

This is the question every serious beta user eventually asks, because it is the question the data forces on you: why does the same ticker show a beta of 1.6 on one screener, 1.9 on another, and 2.1 on a third — on the same day, for the same company? The answer is not that one source is wrong and the others are right. It is that raw regression beta is a noisy, estimation-error-laden statistic, and every one of the three inputs above — window, frequency, market proxy — moves it.

Consider a single stock with genuine, structural exposure to the market of roughly 1.7–1.8. A 5-year monthly regression might return 1.75. A 2-year weekly regression, more sensitive to a recent period of elevated volatility, might return 2.10. A 1-year daily regression, dominated by a handful of large single-day moves around earnings, might return 1.55. None of these is "the" beta. Each is a point estimate of an underlying, unobservable quantity, with its own standard error — and for many stocks, especially smaller-cap or newly listed names with limited history, that standard error is wide enough that the reported figure carries real estimation risk.

It is worth naming the actual defaults, because "why does my screener disagree with Bloomberg" is a real, specific, and answerable question: Bloomberg's own default beta setting is 2 years of weekly returns against the S&P 500, reported alongside a Blume-adjusted figure — not the 5-year monthly convention most textbooks lead with. Many free retail-facing screeners default closer to 5-year monthly, unadjusted. Neither is "the" correct beta; they are two different, equally legitimate methodological choices that will not agree on the same stock.

A stock can legitimately show three different betas across these four rows, on the same day, with no error anywhere in the calculation — the disagreement is entirely a function of which convention was used.

Professional practice does not treat any single raw figure as ground truth. Instead, it adjusts beta before using it in a cost-of-equity calculation, using one of two well-established methods:

Blume adjustment (1971). Marshall Blume found that measured betas exhibit a statistical tendency to drift toward 1.0 over time — extreme betas in one period tend to be less extreme in the next. The Blume adjustment builds this mean-reversion directly into the number used for valuation: Adjusted Beta = (2/3) × Raw Beta + (1/3) × 1.0. It is simple, transparent, and widely used by data providers (this is why "adjusted beta" figures from major terminals often sit closer to 1.0 than a raw regression would suggest).

Vasicek shrinkage (1973). Oldrich Vasicek's Bayesian approach improves on Blume by making the amount of shrinkage depend on estimation uncertainty: a beta estimated with a small standard error (a large, liquid, long-history stock) is shrunk less; a beta estimated with a large standard error (a small, thinly-traded, or newly-listed stock) is shrunk more, toward the cross-sectional average beta of comparable stocks. This is precisely the same logic this site's Ledoit-Wolf shrinkage framework applies to covariance matrix estimation: raw sample estimates are noisy, and optimal shrinkage — weighted by how much noise is actually present — produces a more reliable input than either the raw estimate or a crude fixed rule.

Thin-trading adjustments (Scholes-Williams, Dimson). A less commonly discussed but academically well-established source of bias affects illiquid or infrequently-traded stocks specifically: when a stock doesn't trade at the exact moment the market index is priced, its recorded return is stale relative to the market's, which biases the regression beta — typically downward for thinly-traded names. Scholes and Williams (1977) and Dimson (1979) independently proposed corrections that add lagged and leading market-return terms to the regression and sum the resulting coefficients, producing a beta that corrects for this "nonsynchronous trading" bias. In practice this matters most for small-cap, low-float, or newly-listed stocks where daily trading volume is genuinely thin — precisely the names where raw beta is already least reliable for the reasons above.

The A.L. Capital Beta Reliability Grade

Every raw beta comes with an implicit confidence level that the number itself doesn't disclose — a beta of 1.6 with a standard error of 0.15 and a beta of 1.6 with a standard error of 0.55 look identical on a screener but should not be trusted equally. To make that estimation uncertainty visible before it silently distorts a valuation, I use a simple four-tier grading heuristic on every beta before it goes into a client cost-of-equity calculation:

This is a practitioner heuristic developed at A.L. Capital for triaging beta inputs quickly, not a published academic standard — it operationalises the same estimation-uncertainty principle behind Vasicek (1973) shrinkage into thresholds that are fast to apply by eye before a number ever reaches a DCF model. When the three criteria disagree — a stock with strong R² but a wide standard error, for instance — the rule is to take the lowest (most conservative) of the three indicated grades, not an average. A stock graded C or D should never be the sole basis for a cost-of-equity figure regardless of how clean the point estimate looks.

Levered vs Unlevered Beta (and Why It Matters for Valuation)

Levered beta — also called equity beta — is the beta observed directly from a regression of a stock's returns, and it reflects the company's actual capital structure, debt included. Debt increases the volatility of equity returns relative to the volatility of the underlying business, because fixed interest obligations amplify the swings in what's left over for equity holders. Two companies with identical operating businesses but different debt loads will show different levered betas — the more leveraged company will show the higher one.

Unlevered beta — also called asset beta — strips out the effect of financial leverage, isolating the risk of the underlying business itself. This is the number to use when comparing companies with different capital structures, or when building a target company's cost of equity from a peer group that carries different average leverage. The standard conversion is the Hamada equation:

In practice, this matters most when using an industry or peer-group beta as a starting point for a company that doesn't yet have a long, clean trading history — a recent IPO, a spin-off, or a private company being valued for the first time. The correct procedure is to take several comparable companies' levered betas, unlever each using its own capital structure, average the resulting unlevered (asset) betas, and then relever that average using the target company's own capital structure. Skipping the unlever/relever step and simply averaging raw levered betas across peers with different debt loads embeds their capital-structure differences into a number that is supposed to represent business risk alone.

CAPM: From Beta to Cost of Equity

The Capital Asset Pricing Model, developed independently by William Sharpe (1964), John Lintner (1965), and Jan Mossin, building on Harry Markowitz's mean-variance portfolio theory, answers a specific question: what return should an investor require to hold a risky asset, given that asset's exposure to market-wide (systematic) risk? The answer is additive and intuitive — compensation for time, plus compensation for risk:

Each input carries its own estimation choices, but as of July 2026, reasonable illustrative figures are a risk-free rate — proxied by the 10-year US Treasury yield — near 4.3%, and an equity risk premium near 5.0%, consistent with the range Aswath Damodaran's implied-ERP methodology has produced through recent years. These inputs move with market conditions and should be re-sourced at the time of use rather than treated as fixed constants; what matters for this framework is the mechanism, not the specific decimal.

Plugging in an adjusted beta of 1.50 gives a cost of equity of 4.3% + 1.50 × 5.0% = 11.8%. Plugging in the same stock's raw, unadjusted 2-year weekly beta of 2.10 instead gives 4.3% + 2.10 × 5.0% = 14.8% — a difference of exactly the kind the estimation-window instability shown in Figure 2 will produce if left unadjusted. A 3-percentage-point difference in the discount rate is not a rounding error in a DCF model; it is frequently the difference between a stock looking cheap and looking expensive.

How Beta Drives DCF Valuation (The Chain to Intrinsic Value)

Beta does not stop at cost of equity. It is the first link in a chain that runs all the way to intrinsic value, and each link inherits the estimation error of the one before it:

Because a DCF discounts cash flows that extend many years into the future, small changes in the discount rate compound into large changes in present value — especially for long-duration growth businesses where more of the value sits in cash flows five, ten, or fifteen years out. A 0.3 difference in beta, at a 5.0% equity risk premium, moves cost of equity by 1.5 percentage points. Holding everything else in the model constant, moving WACC by roughly that amount can move a growth stock's DCF intrinsic value by well over 10–15% — frequently more than the swing produced by realistic changes in the terminal growth rate or near-term revenue assumptions that receive far more analyst attention. Beta is, in practice, one of the highest-leverage and least-scrutinized inputs in the entire DCF chain.

import numpy as np


def regression_beta(stock_returns: np.ndarray, market_returns: np.ndarray) -> tuple:
    """
    Raw regression beta via covariance / variance, plus standard error and R².

    Parameters
    ----------
    stock_returns, market_returns : ndarray (T,) — aligned periodic returns

    Returns
    -------
    beta, se_beta, r_squared : float, float, float
    """
    cov_matrix = np.cov(stock_returns, market_returns)
    beta = cov_matrix[0, 1] / cov_matrix[1, 1]
    alpha = np.mean(stock_returns) - beta * np.mean(market_returns)

    fitted = alpha + beta * market_returns
    resid = stock_returns - fitted
    n = len(stock_returns)

    ss_res = np.sum(resid ** 2)
    ss_tot = np.sum((stock_returns - np.mean(stock_returns)) ** 2)
    r_squared = 1 - ss_res / ss_tot

    # standard error of the slope estimate
    resid_var = ss_res / (n - 2)
    se_beta = np.sqrt(resid_var / np.sum((market_returns - np.mean(market_returns)) ** 2))

    return beta, se_beta, r_squared


def blume_adjusted_beta(raw_beta: float) -> float:
    """Blume (1971): shrink two-thirds of the way toward 1.0."""
    return (2/3) * raw_beta + (1/3) * 1.0


def vasicek_shrunk_beta(
    raw_beta: float, se_beta: float,
    prior_mean: float, prior_var: float,
) -> float:
    """
    Vasicek (1973): Bayesian shrinkage toward a cross-sectional prior,
    weighted by relative estimation precision.
    """
    w = prior_var / (prior_var + se_beta ** 2)
    return w * raw_beta + (1 - w) * prior_mean


def capm_cost_of_equity(beta: float, rf: float, erp: float) -> float:
    """CAPM: Cost of Equity = Rf + beta × ERP."""
    return rf + beta * erp


# ── Example: illustrative high-beta semiconductor stock, 5-yr monthly ──
np.random.seed(7)
n_months = 60
market_r = np.random.normal(0.008, 0.045, n_months)
true_beta = 1.95
stock_r = true_beta * market_r + np.random.normal(0.002, 0.07, n_months)

raw_beta, se, r2 = regression_beta(stock_r, market_r)
adj_beta = blume_adjusted_beta(raw_beta)
vasicek_beta = vasicek_shrunk_beta(raw_beta, se, prior_mean=1.0, prior_var=0.09)

rf, erp = 0.043, 0.05
coe_raw = capm_cost_of_equity(raw_beta, rf, erp)
coe_adj = capm_cost_of_equity(adj_beta, rf, erp)

print(f"Raw beta:            {raw_beta:.2f}  (SE {se:.2f}, R² {r2:.2f})")
print(f"Blume-adjusted beta:  {adj_beta:.2f}")
print(f"Vasicek-shrunk beta:  {vasicek_beta:.2f}")
print(f"Cost of equity (raw beta):     {coe_raw:.2%}")
print(f"Cost of equity (adjusted beta): {coe_adj:.2%}")

Raw beta:            2.10  (SE 0.18, R² 0.70)
Blume-adjusted beta:  1.73
Vasicek-shrunk beta:  1.81
Cost of equity (raw beta):     14.80%
Cost of equity (adjusted beta): 12.97%