Beta in the single index model represents how responsive the individual stock is relative to changes in the market index.
True False
The correct answer and explanation is:
The correct answer is True.
In the single index model, Beta (β) measures the sensitivity or responsiveness of an individual stock’s returns relative to changes in the returns of the market index. This model assumes that the return on a stock can be explained by the return of the market, plus some firm-specific risk that is not explained by the market’s performance.
Beta is a key component in the Capital Asset Pricing Model (CAPM), which helps to assess the risk and expected return of an asset. The single index model simplifies the relationship between the stock’s return and the market’s return by using a linear relationship: Ri=αi+βiRm+ϵiR_i = \alpha_i + \beta_i R_m + \epsilon_i
Where:
- RiR_i is the return of the individual stock.
- αi\alpha_i is the stock’s intercept, which is the return of the stock that is not explained by the market.
- βi\beta_i is the stock’s sensitivity to the market return.
- RmR_m is the return of the market index.
- ϵi\epsilon_i is the random error term, representing company-specific factors.
Beta provides a measure of systematic risk, meaning it reflects the risk associated with general market movements. A Beta of 1 indicates that the stock’s return moves in perfect correlation with the market index. A Beta greater than 1 suggests that the stock is more volatile than the market, while a Beta less than 1 indicates that the stock is less volatile.
For example, if a stock has a Beta of 1.2, it is expected to move 1.2 times as much as the market. If the market goes up by 10%, the stock is expected to increase by 12%. Conversely, if the market declines by 10%, the stock would be expected to decline by 12%.
Beta is an important tool for investors to understand how much risk a stock adds to a diversified portfolio. Stocks with high Betas can offer higher potential returns but come with greater risk, while stocks with low Betas are seen as safer but offer more modest returns.