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FINANCE 260 - Does diversification always lower a portfolio’s beta?




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Fin 260

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FIN 260 2
Question 8
The CAPM assumes that I receive an expected return based on being in a diversified
portfolio even though I may only own one stock. Why?
The Capital Asset Pricing Model (CAPM) specifies the relationship between risk and
required rate of return on assets when they are held in well-diversified portfolios. The aim of
CAPM is to quantify the relationship between the beta of an asset and its resultant expected return.
CAPM uses the following formula to calculate the expected return of an individual
E [R
] = R
(risk free rate) + Risk Premium
John Lintner, Jack Treynor and Bill Sharpe, the developers of CAPM, included the aspect of
riskless assets while developing CAPM. They concluded that it is in the best interest for an investor
to hold more than one asset/stock. At every risk level an investor was currently in, there exists a
superior alternative. Combining a riskless asset with a super-efficient portfolio generates higher
expected returns for every risk level than holding a portfolio of risky assets.
The investors who are more risk averse will opt on investing super-efficient portfolio and
allocate the remainder to riskless assets. However, there are investors who are willing to take more
risks. These investors borrowed at riskless rates and invested the entire proceedings in the super-
efficient portfolio. This implies that each investor, regardless of their risk attitudes, should hold a
super-efficient portfolio. These portfolios are usually supremely diversified. This brings out the
market portfolio which includes all the individual assets traded in the stock market.

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FIN 260 3
CAPM, therefore, eliminates any possible rational for deciding against diversification. The
assumptions that the market lacks transaction costs and information asymmetry are used to justify
diversification. In a market where there are not transaction costs and the information is identical,
the need for diversification rather than holding a single stock/asset is intensified. The
rationalization behind CAPM implies that an investor holding less than the market portfolio has
not attained full diversification. Consequently, these investors bear the costs resulting from holding
less-than-the-market portfolio without receiving any offsetting benefit.
By extending the insight of Markowitz, CAPM explains the risk of an individual asset as a
function of the market portfolio. The formula illustrated below shows the relationship created by
CAPM between an individual asset and the market portfolio;
The assumption that all investors hold a diversified portfolio reflects why CAPM insists
on holding more than one stock. Investors are not rewarded for bearing risks that are
diversifiable. Consequently, the beta of each security can be established thus enabling the
calculation of the security’s expected return.

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