Capital Asset Pricing Model
Question (2010/2011 Exam – Q7 (section B)): The Capital Asset Pricing Model holds in economies satisfying a certain set of conditions. State four of these conditions and identify why they are essential for the model to hold (you are not expected to derive the entire model but you must identify the steps in the theory where these conditions play an important role).
Under 7 sets of key assumptions, we know that all agents will hold a particular market portfolio, which consists of the same proportion of risky assets. Moreover, there exists a linear relationship (pricing model) between market price of risk and the return of all efficient portfolios, which consist of one riskless asset and the market portfolio of risky assets described previously. This relationship is the slope of the Capital Markets Line which connects the riskless asset with the market portfolio of risky assets. The formula of the Capital Markets Line is as follows:
where E(rm) is the return on the market portfolio rf is the return on the riskless asset while σm is the risk of the market portfolio (described by its variance)
All points of the efficient frontier - which is defined as the set of un-dominated portfolios of risky assets in the absence of the riskless asset - will be dominated by the Capital Markets Line except for the market portfolio ‘M’. This is referred to as the Two-fund separation theorem. Therefore, the agents will hold a combination of the market portfolio and the riskless asset, along the line of the Capital Markets line, where they can reach a high level expected return, while bearing the cost of a higher risk, through either consuming less of the riskless asset or even short-selling the riskless asset and buy more of the market portfolio from the proceeds, given their degree of risk aversion. This is demonstrated in the following diagram:
where agent I is the most risk averse holding a combination of the market portfolio and the riskless asset, agent II is only holding
Under 7 sets of key assumptions, we know that all agents will hold a particular market portfolio, which consists of the same proportion of risky assets. Moreover, there exists a linear relationship (pricing model) between market price of risk and the return of all efficient portfolios, which consist of one riskless asset and the market portfolio of risky assets described previously. This relationship is the slope of the Capital Markets Line which connects the riskless asset with the market portfolio of risky assets. The formula of the Capital Markets Line is as follows:
where E(rm) is the return on the market portfolio rf is the return on the riskless asset while σm is the risk of the market portfolio (described by its variance)
All points of the efficient frontier - which is defined as the set of un-dominated portfolios of risky assets in the absence of the riskless asset - will be dominated by the Capital Markets Line except for the market portfolio ‘M’. This is referred to as the Two-fund separation theorem. Therefore, the agents will hold a combination of the market portfolio and the riskless asset, along the line of the Capital Markets line, where they can reach a high level expected return, while bearing the cost of a higher risk, through either consuming less of the riskless asset or even short-selling the riskless asset and buy more of the market portfolio from the proceeds, given their degree of risk aversion. This is demonstrated in the following diagram:
where agent I is the most risk averse holding a combination of the market portfolio and the riskless asset, agent II is only holding