False Statements About Portfolio Theory

D

No security can plot above the theoretical CML. All risky securities must be contained within or lie upon the efficient frontier and the CML is tangent to the efficient frontier.

Let's analyze each statement to determine which one is false:

A. Total risk equals systematic risk plus unsystematic risk. This statement is true. In portfolio theory, total risk is composed of two components: systematic risk and unsystematic risk. Systematic risk refers to the risk that cannot be diversified away, such as market risk, interest rate risk, or inflation risk. Unsystematic risk, also known as specific risk, can be eliminated through diversification by holding a well-diversified portfolio. Therefore, statement A is true.

B. If a security plots above the SML, it is undervalued. This statement is false. The Security Market Line (SML) is a graphical representation of the Capital Asset Pricing Model (CAPM), which relates the expected return of a security to its systematic risk. The SML plots the expected return of a security on the y-axis and its beta (a measure of systematic risk) on the x-axis. According to the CAPM, securities that plot above the SML are considered overvalued because they offer a higher expected return than what is justified by their systematic risk. Therefore, statement B is false.

C. The risk measure associated with the CML is standard deviation (total risk). This statement is true. The Capital Market Line (CML) is another graphical representation of portfolio theory, specifically the efficient frontier. The CML represents a portfolio's expected return as a function of its standard deviation (total risk). The CML is derived by combining the risk-free rate with the market portfolio, which represents the optimal combination of risky assets in the market. Therefore, statement C is true.

D. If a security plots above the theoretical CML, it is undervalued. This statement is false. The theoretical CML represents the expected return and risk relationship for an efficient portfolio that consists of the risk-free rate and the market portfolio. Securities that plot above the CML are considered overvalued because they offer a higher expected return than what is justified by their risk level. Therefore, statement D is false.

In conclusion, the false statement is: B. If a security plots above the SML, it is undervalued.