Beta is defined as which of the following?

Beta is defined as which of the following?

• A. The covariance of the security's returns with the market's returns divided by the variance of the security's returns.
• B. The variance of the security's returns.
• C. The covariance between the security's returns and the market's returns divided by the variance of the market returns.
• D. The covariance between the security's returns and the market's returns divided by the variance of the market returns.

Answer: (D)

Beta measures how much a security’s returns move with the overall market. It is defined as the covariance of the security’s returns with the market’s returns divided by the variance of the market’s returns. This makes beta the slope of the regression of the security’s returns on the market’s returns, capturing the systematic (market-related) risk rather than the total risk of the security. In formula terms, beta = Cov(R_i, R_m) / Var(R_m). Because Cov(R_i, R_m) = ρ_i,m σ_i σ_m and Var(R_m) = σ_m^2, beta can also be expressed as ρ_i,m (σ_i / σ_m). A beta above 1 indicates greater sensitivity to market moves; a beta below 1 indicates less sensitivity. In CAPM, beta is used to scale the market risk premium when estimating expected return.

Beta measures how much a security’s returns move with the overall market. It is defined as the covariance of the security’s returns with the market’s returns divided by the variance of the market’s returns. This makes beta the slope of the regression of the security’s returns on the market’s returns, capturing the systematic (market-related) risk rather than the total risk of the security. In formula terms, beta = Cov(R_i, R_m) / Var(R_m). Because Cov(R_i, R_m) = ρ_i,m σ_i σ_m and Var(R_m) = σ_m^2, beta can also be expressed as ρ_i,m (σ_i / σ_m). A beta above 1 indicates greater sensitivity to market moves; a beta below 1 indicates less sensitivity. In CAPM, beta is used to scale the market risk premium when estimating expected return.