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Statistics for finance · level 2

Beta two ways

Beta is the slope of the stock on the market. Given covariance, divide by market variance; given correlation, scale the sigma ratio by ρ. Same number.

Theory: Portfolio Theory

Worked example: Cov(stock, market) = 72, Var(market) = 90. Beta?

covariance72
market variance90
β0.8

Step by step

  1. 1

    Beta is a regression slope

    β = Cov(i, m) / Var(m)

  2. 2

    Divide

    72 / 90 = 0.8

  3. 3

    Interpret

    The market moves 1%, this stock moves about 0.8%.

Cov(stock, market) = 72, Var(market) = 90. Beta? = 0.8

The theory behind it

Intuition

Beta is covariance with the market divided by market variance — equivalently correlation times the ratio of volatilities.

Common pitfalls

  • ×Using total volatility as a proxy for beta.
  • ×Estimating beta from too short a window.

In the interview

Cost-of-equity rounds.