How to Calculate CAPM Alpha and Beta with Regression in Python

May 14, 2026

What’s the question?

The Capital Asset Pricing Model (CAPM) predicts that a stock’s expected return is a linear function of its sensitivity to the overall market. Beta measures that sensitivity: a beta of 1.5 means the stock is expected to move 1.5% for every 1% move in the market. Alpha is the residual — the portion of a stock’s return that CAPM cannot explain through market exposure alone. Positive alpha means the stock outperformed what its market sensitivity would predict; negative alpha means it lagged. The question is: for a set of major U.S. stocks, how much of their return is explained by market exposure (beta), and how much is genuine idiosyncratic outperformance or underperformance (alpha)?

The approach

CAPM is estimated via ordinary least squares (OLS) regression. For each stock, daily excess returns (stock return minus the risk-free rate) are regressed against the market’s daily excess returns (SPY return minus the risk-free rate). The slope of the regression line is beta, the intercept is daily alpha (annualized by multiplying by 252 trading days), and R-squared measures the fraction of the stock’s return variance explained by market movements. A 5% annualized risk-free rate is assumed, consistent with prevailing Treasury yields.

Eight stocks spanning multiple sectors are tested: AAPL, MSFT, NVDA, AMZN, META, XOM, JNJ, and JPM. The interpretation threshold is set at +/-5% annualized alpha: above +5% is classified as OUTPERFORM, below -5% as UNDERPERFORM, and within the range as FAIR.

import xfinlink as xfl
import pandas as pd
import numpy as np
from scipy import stats

xfl.set_api_key("your_key")  # free at https://xfinlink.com/signup

RF_DAILY = 0.05 / 252
tickers = ["AAPL", "MSFT", "NVDA", "AMZN", "META", "XOM", "JNJ", "JPM"]
df = xfl.prices(tickers + ["SPY"], period="1y", fields=["return_daily"])
returns = df.pivot_table(index="date", columns="ticker", values="return_daily").dropna()
market_excess = returns["SPY"] - RF_DAILY

for ticker in tickers:
    stock_excess = returns[ticker] - RF_DAILY
    slope, intercept, r_value, p_value, std_err = stats.linregress(market_excess, stock_excess)
    alpha_ann = intercept * 252
    print(f"{ticker}: beta={slope:.2f} alpha={alpha_ann:+.1%} R2={r_value**2:.3f}")

Output:

=== CAPM Regression: Alpha, Beta, R² (1Y vs SPY, Rf=5%) ===

Ticker    Beta   Alpha (ann)      R²   Ann Return        Interpretation
----------------------------------------------------------------------
JNJ       0.06       +39.4%   0.002      +55.5%            OUTPERFORM
XOM      -0.25       +35.3%   0.017      +38.7%            OUTPERFORM
NVDA      1.75       +22.3%   0.397      +74.2%            OUTPERFORM
AAPL      0.98       +12.5%   0.278      +40.6%            OUTPERFORM
AMZN      1.43        -3.7%   0.341      +27.9%                  FAIR
JPM       0.99        -8.6%   0.318      +14.2%          UNDERPERFORM
MSFT      0.87       -29.3%   0.198       -9.8%          UNDERPERFORM
META      1.47       -33.7%   0.261       -6.0%          UNDERPERFORM

What this tells us

JNJ is the most striking result in this analysis. It delivered +55.5% with a beta of 0.06 and an R² of 0.002 — meaning virtually none of its return is explained by market movements. Its +39.4% alpha is almost entirely idiosyncratic, driven by company-specific factors (product approvals, litigation outcomes, spin-off activity) rather than broad market direction. For practical purposes, JNJ behaved as a market-neutral stock this year.

XOM’s negative beta (-0.25) indicates that energy moved inversely to the broader market during this period. Despite this contrarian behavior, XOM still delivered +38.7% in absolute returns, producing +35.3% in alpha. A negative-beta stock with positive alpha is the theoretical ideal for portfolio diversification: it contributes returns while hedging market drawdowns.

Nvidia’s alpha of +22.3% is notable because it exists on top of already-high market exposure (beta of 1.75). NVDA returned +74.2% for the year; CAPM attributes approximately 52 percentage points of that to its amplified market sensitivity, leaving 22.3% as genuine outperformance. Its R² of 0.397 is the highest in the group, confirming that market exposure is a meaningful driver of NVDA returns — but not the only one.

META and MSFT show large negative alphas (-33.7% and -29.3%), indicating significant underperformance relative to what their market betas would predict. META’s beta of 1.47 implies it should have captured amplified market gains, yet it returned -6.0% — a substantial shortfall that reflects company-specific headwinds.

The low R² values across the board (ranging from 0.002 to 0.397) indicate that the single-factor CAPM explains a minority of these stocks’ return variance. Multi-factor models (Fama-French three-factor, Carhart four-factor) would likely explain more of the variance by incorporating size, value, and momentum factors.

So what?

Alpha and beta decomposition separates skill (or luck) from market exposure. A portfolio manager who delivered +74% by holding NVDA at 1.75x beta took substantially more market risk than one who delivered +55% with JNJ at 0.06x beta. The alpha metric makes this comparison explicit. When evaluating stock performance or portfolio manager returns, always decompose the total return into its beta-driven and alpha-driven components — raw returns alone conflate market participation with genuine outperformance.