Question

Using the properties of the Capital Market Line (CML) and the Security Market Line (SML), determine which of the following scenarios are consistent or inconsistent with the CAPM. Explain your answers. Let A and B denote arbitrary securities while F and M represent the riskless asset and the market portfolio respectively.

a) Scenario I:
Security E[R] β
A 25% 0.8
B 15% 1.2

(b) Scenario II:
Security E[R] σ(R)
A 25% 30%
M 15% 30%

(c) Scenario III:
Security E[R] σ(R)
A 25% 55%
F 5% 0%
M 15% 30%

(d) Scenario IV:
Security E[R] β
A 20% 1.5
F 5% 0
M 15% 1.0

(e) Scenario V:
Security E[R] β
A 35% 2.0
M 15% 1.0

Answer 1

The Capital Market Line (CML) and the Security Market Line (SML) are used to determine consistency with the CAPM. Scenarios I, III, IV are consistent with the CAPM, while scenarios II and V are inconsistent.

Step-by-step explanation:

The Capital Asset Pricing Model (CAPM) is based on the principle that investors are rewarded for taking on systematic risk, which is measured by the beta coefficient. The Capital Market Line (CML) represents portfolios of risky assets with varying levels of systematic risk. The Security Market Line (SML) represents the relationship between the expected return and beta of individual securities.

(a) Scenario I is consistent with the CAPM because security A has a higher expected return and lower beta compared to security B.

(b) Scenario II is inconsistent with the CAPM because security A has a higher expected return but the same beta as the market portfolio. Security M should have a higher expected return considering the level of risk.

(c) Scenario III is consistent with the CAPM as security A has a higher expected return and higher beta compared to the market portfolio. The riskless asset F has a lower expected return due to no systematic risk.

(d) Scenario IV is inconsistent with the CAPM because security A has a higher expected return and a higher beta compared to the market portfolio. The riskless asset F should have a lower expected return considering it carries no systematic risk.

(e) Scenario V is inconsistent with the CAPM because security A has a higher expected return and a higher beta compared to the market portfolio. The riskless asset M should have a lower expected return considering it carries no systematic risk.