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Chapter 7: Capital Asset Pricing and Arbitrage Pricing Theory
I.
The Capital Asset Pricing Model
A.
The
capital asset pricing model(CAPM)
predict the relationship between the risk and equilibrium expected returns on
risky assets
B.
The fundamental idea is that individuals are as alike as possible, with the notable exceptions of initial wealth and risk
aversion.
C.
The list of assumptions that describes the necessary conformity of investors follow:
1.
Investors cannot affect prices by their individual trades
this means that there are many investors
2.
All investors plan for one identical holding period
3.
Investors form portfolios from a universe of publicly traded financial assets, such as stocks and bonds, and have
access to unlimited risk-free borrowing or lending opportunities
4.
Investors pay neither taxes on returns nor transaction costs on trades in securities
5.
All investors attempt to construct efficient frontier portfolios; that is, they are rational mean-variance optimizers
6.
All investors analyze securities in the same way and share the same economic view of the world
a.
Hence, they all end with identical estimates of the probability distribution of future cash flows from investing in the
available securities
b.
This means that, given asset of security prices and risk-free interest rate, all investors use the same expected returns,
standard deviations, and correlations to generate the efficient frontier and the unique optimal risky portfolio
c.
This assumption is called
homogeneous expectations
7.
Given these assumptions, we summarize the equilibrium that will prevail in this hypothetical world of securities and
investors
a.
All investors will choose to hold the
market portfolio (M)
, which includes all assets of the security universe.
1)
The proportion of each stock in the market portfolio equals the market value of the stock(price per share times the
number of shares outstanding) divided by the total market value of all stocks
b.
The market portfolio will be on the efficient frontier
1)
Moreover, it will be the optimal risky portfolio, the tangency point of the capital allocation line (CAL) to the efficient
frontier.
2)
As a result, the capital market line(CML), the line from the risk-free rate through the market portfolio, M, is also the
best attainable capital allocation line
3)
All investors hold M as their optimal risky portfolio, differing only in the amount invested in it as compared to
investment in the risk-free asset
c.
The risk premium on the market portfolio will be proportional to the variance of the market portfolio and investors’
typical degree of risk aversion
1)
Mathematically:
E(r
M
) – r
f
= A*σ
M
2

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2)
Where σ
M
is the standard deviation of the return on the market portfolio and A* is a scale factor representing the
degree of risk aversion of the average investor
d.
The risk premium on individual assets will be proportional to the risk premium on the market portfolio(M) and to the
beta coefficient
of the security on the market portfolio

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