Can a stock that is more volatile than the market have a negative beta?

Can a stock that is more volatile than the market have a negative beta?

• A. No, beta cannot be negative
• B. Only for micro-cap stocks
• C. Only if the company has negative earnings
• D. Yes, if it correlates inversely to the market

Answer: (D)

Beta reflects how a stock’s returns move in relation to the market, not how volatile the stock is on its own. The key idea is that the sign of beta comes from the direction of the relationship with the market, while the magnitude comes from how strongly it moves together with the market. A stock can be more volatile than the market and still have a negative beta if its returns tend to move in the opposite direction to market moves. The formula Beta = Cov(Ri, Rm) / Var(Rm) shows this clearly: Var(Rm) is positive, so the sign of beta is the sign of the covariance between the stock and the market. Covariance is negative when the stock’s returns are negatively correlated with the market, meaning it tends to rise when the market falls and fall when the market rises. The stock’s higher volatility affects how big its moves are (the beta’s magnitude), but not the sign by itself. So, if a stock is more volatile yet tends to move inversely to the market, its beta can indeed be negative.

Beta reflects how a stock’s returns move in relation to the market, not how volatile the stock is on its own. The key idea is that the sign of beta comes from the direction of the relationship with the market, while the magnitude comes from how strongly it moves together with the market.

A stock can be more volatile than the market and still have a negative beta if its returns tend to move in the opposite direction to market moves. The formula Beta = Cov(Ri, Rm) / Var(Rm) shows this clearly: Var(Rm) is positive, so the sign of beta is the sign of the covariance between the stock and the market. Covariance is negative when the stock’s returns are negatively correlated with the market, meaning it tends to rise when the market falls and fall when the market rises. The stock’s higher volatility affects how big its moves are (the beta’s magnitude), but not the sign by itself.

So, if a stock is more volatile yet tends to move inversely to the market, its beta can indeed be negative.