In the context of financial economics, if the returns of two firms are negatively correlated, which of the following statements is correct?

• A. It is possible for both firms to have positive betas.
• B. Neither firm can have a beta equal to zero.
• C. Both firms must have negative betas.
• D. One of the firms must have a negative beta.

Answer: (A)

Verified step by step guidance

1. Recall the definition of beta (\beta) in financial economics: it measures the sensitivity of a firm's returns to the returns of the overall market. A positive beta means the firm's returns move in the same direction as the market, while a negative beta means they move in the opposite direction.
2. Understand that beta is related to the covariance between the firm's returns and the market returns, normalized by the variance of the market returns: \(\beta_i = \frac{\text{Cov}(R_i, R_m)}{\text{Var}(R_m)}\)
3. Note that the correlation between two firms' returns (\rho_{12}) is different from their betas. Two firms can have returns that are negatively correlated with each other, but both can still have positive betas if both move in the same direction as the market overall.
4. Analyze the implications of negative correlation between two firms' returns: it means when one firm's return goes up, the other's tends to go down. However, this does not force either firm to have a negative beta or zero beta, because beta depends on the relationship with the market, not directly with each other.
5. Conclude that it is possible for both firms to have positive betas even if their returns are negatively correlated, because beta measures market sensitivity, not pairwise correlation between firms.