Chapter 9 CAPM
Capital asset pricing model William Sharpe
•
Set of predictions concerning equilibrium expected returns on risky assets
•
Makes simplifying assumptions:
o
There are many investors with small wealth compared to the total wealth of all investors. They act as though their
individual trades have no affect
o
All investors plan for one identical holding period, ignores everything after holding period which is suboptimal
o
Investments are limited to publicly traded assets, they cannot invest in things like human capital or private enterprises, also
assumes they can borrow any amount at the risk free
o
Investors pay no taxes on returns and no transaction costs
o
All investors are rational mean variance optimizers, all use Markowitz
o
All investors analyze securities in the same way and share the same economic view of the world.
Homogeneous expectations
 given a set of security prices and the risk free rate, all investors use the same
expected returns and covariance matrix of security returns to generate the efficient frontier and the unique
optimal risky portfolio
•
Using the assumptions, the equilibrium that will prevail is
o
All investors will choose to hold a portfolio of risk assets in proportions that duplicate representation of the assets in the
Market portfolio
(M), which includes all traded assets
o
Not only will the market value be on the efficient frontier but it will be the tangency portfolio to the optimal capital
allocation line derived by every investor
As a result the CML, risk free through the market portfolio, is the best attainable CAL, all investors hold this
point, differing only in the amount invested in risk free
o
The risk premium on the market portfolio ill be proportional to its risk and the degree of risk aversion of the representative
investor.
o
The risk premium on individual assets will be proportional to the risk premium on the market portfolio, M, and the beta
coefficient of the security relative to the market portfolio. Beta measures the extent to which returns on the stock and the
market move together
Investors holding the market portfolio
•
The value of the aggregate risky portfolio will equal the entire wealth of the economy.
•
The proportion of each stock in the market portfolio, M, is the price/share times # of shares outstanding / total market value of all
stocks
•
All assets have to be included in the market portfolio, the only question is what price is acceptable to investors for them to include it in
their portfolio
The passive Strategy
•
The market portfolio that all investors hold is based on the common input list, thereby incorporating all relevant information about the
universe of securities
o
This means investors can kip the trouble of doing specific analysis and obtain efficient portfolio simply by holding the
market portfolio
•
Mutual fund theorem
:
a result associated with the CAPM asserting that investors will chose to invest their entire risky portfolio in a
market index mutual fund
o
Leads to the creation of mutual index funds, and the allocation in these funds vs. risk free
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 Fall '07
 MADIGAN,GE
 Capital Asset Pricing Model, Financial Markets, Modern portfolio theory, Market Portfolio

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