Portfolio Theory – Covariance

Practice Question

Intro to Finance
Portfolio Theory
Covariance
Short Answer

The return on stock A has a covariance of 0.1 with the return on the market portfolio whereas the return on stock B has covariance of 0.3 with the market return. The return on which stock moves more closely with the return on the market portfolio?

Answer +
Final Answer: Insufficient information: we would need the standard deviation of both A and B.
Explanation +

To determine which stock moves more closely with the return on the market portfolio, we need to calculate the beta for each stock.

The formula for beta is:
\[ \beta_i = \frac{\text{Cov}(R_i, R_m)}{\text{Var}(R_m)} \] where \( \text{Cov}(R_i, R_m) \) is the covariance of the stock with the market and \( \text{Var}(R_m) \) is the variance of the market returns.

Given:
- Cov(RA, Rm) = 0.1
- Cov(RB, Rm) = 0.3
- Var(Rm) = unknown

Without the market variance, we cannot compute beta for either stock. Beta is the correct measure of co-movement, not raw covariance. Therefore, we lack the required information.

Conclusion: The correct answer is:
Insufficient information: we would need the standard deviation of both A and B.