Beta Coefficient

The beta coefficient measures how strongly an asset's returns tend to move with the market as a whole.

The beta coefficient measures how strongly an asset’s returns tend to move with the returns on the market portfolio.

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Core formula

In the standard CAPM setup:

$$ \beta_i = \frac{\operatorname{Cov}(R_i, R_m)}{\operatorname{Var}(R_m)} $$

where (R_i) is the asset’s return and (R_m) is the market return.

This means beta is about systematic risk, not total risk. It asks how much the asset co-moves with market-wide shocks that cannot be diversified away.

Interpretation

  • (\beta = 1): moves roughly with the market
  • (\beta > 1): tends to amplify market moves
  • (0 < \beta < 1): tends to move with the market but less strongly
  • (\beta < 0): tends to move against the market

Why economists and investors care

In the capital asset pricing model, expected return depends on beta because investors are compensated for bearing market risk:

$$ E(R_i) = R_f + \beta_i \big(E(R_m) - R_f\big) $$

That makes beta central to asset pricing, portfolio design, and the cost of capital.

Knowledge Check

### What does beta mainly measure? - [x] Sensitivity of an asset's return to market-wide movements - [ ] The accounting profit of the issuer - [ ] The maturity of a bond - [ ] The inflation rate > **Explanation:** Beta captures co-movement with the market portfolio, which is why it is treated as a measure of systematic risk. ### Why is beta important in CAPM? - [x] Because expected return depends on the amount of market risk an asset carries - [ ] Because beta replaces all other forms of analysis - [ ] Because beta measures only idiosyncratic risk - [ ] Because CAPM assumes all assets have beta equal to one > **Explanation:** In CAPM, investors are compensated for systematic risk, and beta is the coefficient that measures that exposure. ### What does a beta greater than one usually imply? - [x] The asset tends to move more than the market in the same direction - [ ] The asset is risk free - [ ] The asset always outperforms the market - [ ] The asset has zero covariance with the market > **Explanation:** A beta above one means the asset's return tends to respond more strongly than the market to common shocks.