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Lesson 04 of 08 · published

Beta — covariance / variance, in plain words

~30 min · beta

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The single number that captures market sensitivity

From last lesson: CAPM's central input is β. Beta measures a stock's sensitivity to overall market moves. Mathematically:

Beta is the covariance of the stock's returns with the market's returns, divided by the variance of the market's returns. The covariance / correlation language from Track 3 lesson 3, applied to stock vs. market.

What it means in plain words: if the market goes up X%, by how much does this stock go up on average? β answers that.

Beta intuitions by range

  • β = 1.0: moves with the market. Index funds have β ≈ 1 by definition.
  • β > 1: amplifies market moves. Tech stocks often β = 1.2-1.6. Speculative or leveraged plays can be 2+.
  • β < 1: dampens market moves. Utilities, consumer staples, healthcare often β = 0.5-0.8.
  • β = 0: uncorrelated with market. Pure cash, gold sometimes.
  • β < 0: moves opposite to market. Rare for stocks; gold or VIX-related instruments sometimes.

Beta values are estimated from historical data. They're noisy (a stock's beta can change over time) and vary by methodology (which market index, what time period, daily vs. weekly returns). Different sources can give different betas for the same stock.

Why beta matters

Three reasons:

1. CAPM expected returns. Beta is the input. Higher β = higher expected return per CAPM.

2. Portfolio sensitivity to market. If your portfolio's weighted-average beta is 1.3, expect your portfolio to move 1.3x what the market does, on average. A 10% market drop suggests roughly a 13% portfolio drop. Useful for sizing positions.

3. Hedging. If you want to hedge a long position, knowing your beta tells you how much short index exposure you need to neutralize market risk.

Limitations and refinements

Real-world beta is noisy. Common limitations:

  • Time-varying. A stock's beta in 2020 isn't necessarily its beta in 2025.
  • Regime-dependent. Beta during normal times may differ from beta during crises (correlations spike up in panics).
  • Doesn't capture all risk. A stock's full risk includes idiosyncratic factors that beta-relative-to-market ignores.

Multi-factor models (Fama-French 3-factor, 5-factor, etc.) extend the framework — adding "value" factor, "size" factor, and others to better capture cross-sectional return variation. Useful for serious quantitative analysis; CAPM-with-just-beta is fine for most retail purposes.

The takeaway

Beta = stock's sensitivity to the market. Cov(R, R_m) / Var(R_m). β = 1 moves with market; > 1 amplifies; < 1 dampens. Used as the input to CAPM and as a portfolio-level sensitivity measure. Noisy and time-varying in practice. Multi-factor models extend the framework. The polymorphic "shake" base class from Track 1 — same shape, applied to "shake of one stock relative to shake of the market."

Exercise

  1. If a stock has β = 1.5 and the market drops 10%, approximately how much does the stock drop?
  2. You hold a portfolio with weighted-average β = 1.2 worth ₩100M. The market drops 8%. Estimate your loss.
  3. If a stock has β = 0.3, what does that say about its sensitivity to broad market moves?
  4. Why might beta be unreliable as a predictor during a crisis (correlations spike)?

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