Unformatted text preview: stors for the risk of holding the market portfolio.
E(rM)-rf = also known as the market price of risk for individual assets, as market portfolio has a beta =1. S ECURITY MARKET LINE
The Security Market Line (SML) shows diagrammatically the equilibrium return of a risky asset for each level
of beta. If an asset is expected to offer a return larger than that predicted by CAPM, all investors are assumed
to be aware of this info and will rush to buy the asset, and push up the price until its expected return falls to
the equilibrium level as suggested by CAPM. Thus, an asset above the SML is said to be under priced. Beta of 0.5 means that it
contributes half of the risk of an
average asset and gets half the
rewards in expected returns
Beta of 2 means that it contributes
double the risk of an average asset
and gets twice the rewards ***A stock’s alpha = expected return of a stock – expected return predicted by CAPM 11 Cheryl Mew FINS2624 – Portfolio Management Semester 1, 2011 T HE BLACK (1972) CAPM WITH RESTRICTED BORROWING AT R F
As noted earlier, CAPM is built upon some unrealistic assumptions. In practice, investors cannot borrow at the
same risk-free rate since they are restricted from issuing risk free assets, e.g. treasury notes to the public. To
explore this restriction, Black developed an alternative version of the CAPM with restricted borrowing.
Black (1972) show that any portfolio constructed by combining efficient portfolios is itself on the efficient
frontier. Black also showed that every portfolio on the efficient frontier has a companion portfolio on the
bottom half of the minimum variance set with which it is not correlated. The companion portfolio, denoted ZP
is typically located by drawing a tangent from point P on the efficient frontier to the y axis, and then drawing a
horizontal line to meet the efficient frontier again.
The companion portfolio of the market portfolio, ZM, is given a unique name, the minimum variance zero beta
portfolio, because it: Lies on the minimum variance set so that among all the portfolios of risky assets with the same level
of expected return as ZM, it has the smallest variance
Is not correlated with M. Thus the beta of ZM is cov(rZM, rM)/variance of M = 0 Despite having a zero beta this does not...
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