Which of the following statements about security market line (SML) is least likely to be true?
Click on the arrows to vote for the correct answer
A. B. C.A
The correct answer is option B: The SML measures risk using the standardized covariance of the stock with the market.
The security market line (SML) is a graphical representation of the relationship between the expected return and the systematic risk (beta) of an individual security. It helps investors assess whether a security is fairly valued, overvalued, or undervalued in relation to its risk.
Let's analyze each statement to understand why option B is least likely to be true:
A. The SML must be graphed using the standard deviation of the market portfolio. This statement is true. The SML is constructed by plotting the expected return of a security on the vertical axis and its systematic risk (beta) on the horizontal axis. The systematic risk is usually measured by the standard deviation of the market portfolio, which represents the overall market's risk. By using the standard deviation of the market portfolio, the SML captures the relationship between risk and expected return in the market.
B. The SML measures risk using the standardized covariance of the stock with the market. This statement is least likely to be true. The SML does not measure risk using the standardized covariance of the stock with the market. Instead, it measures risk using beta, which is a standardized measure of the stock's sensitivity to market movements. Beta represents the covariance of the stock's returns with the market returns divided by the variance of the market returns. Therefore, beta captures the systematic risk of the stock, which cannot be diversified away.
C. Securities plotting above the SML are undervalued. This statement is true. The SML acts as a benchmark for evaluating securities. If a security's expected return is higher than what the SML predicts based on its beta, it is considered undervalued because it offers a higher expected return for its level of systematic risk. Conversely, securities plotting below the SML are considered overvalued because they offer a lower expected return for their level of systematic risk.
In summary, option B is least likely to be true because the SML measures risk using beta, not the standardized covariance of the stock with the market.