Page 276 - DCOM504_SECURITY_ANALYSIS_AND_PORTFOLIO_MANAGEMENT

Unit 11: Capital Market Theory

But, since the weight of the asset will be relatively low, w 2 a Notes
i.e. additional risk = [2w w ]
m a am a m
Return = (w E(R ) + [w E(R )])
m m a a
Hence additional return = [w E(R )]
a a
(b) If an asset, a, is correctly priced, the improvement in risk to return achieved by
adding it to the market portfolio, m, will at least match the gains of spending that
money on an increased stake in the market portfolio. The assumption is that the
investor will purchase the asset with funds borrowed at the risk-free rate, R ; this is
f
rational if E(R ) > R .
a f
Thus
[w (E(R ) – R )]/[2w w ] = [w (E(R ) – R )]/[2w w ]
a a f m a am a m a m f m a m m
i.e. : [E(R )] = R + [E(R ) – R ] * [ ]/[ ]
a f m f am a m m m
i.e. : [E(R )] = R + [E(R ) – R ] * [ ]/[ ]
a f m f am mm
[ ]/[ ] is the “beta”, — the covariance between the asset and the market
am mm
compared to the variance of the market, i.e. the sensitivity of the asset price to
movement in the market portfolio.
2. Assumptions:
Because the CAPM is a theory, we must assume for argument that:
(a) All assets in the world are traded.

(b) All assets are infinitely divisible.
(c) All investors in the world collectively hold all assets.
(d) For every borrower, there is a lender.

(e) There is a riskless security in the world.
(f) All investors borrow and lend at the riskless rate.
(g) Everyone agrees on the inputs to the Mean-STD picture.
(h) Preferences are well described by simple utility functions.
(i) Security distributions are normal, or at least well described by two parameters.

(j) There are only two periods of time in our world.
This is a long list of requirements, and together they describe the capitalist’s ideal world.
Everything may be bought and sold in perfectly liquid fractional amounts even human
capital! There is a perfect, safe haven for risk-averse investors i.e. the riskless asset. This
means that everyone is an equally good credit risk! No one has any informational advantage
in the CAPM world. Everyone has already generously shared all of their knowledge
about the future risk and return of the securities, so no one disagrees about expected
returns. All customer preferences are an open book risk attitudes are well described by a
simple utility function. There is no mystery about the shape of the future return
distributions. Last but not least, decisions are not complicated by the ability to change
your mind through time. You invest irrevocably at one point, and reap the rewards of
your investment in the next period at which time you and the investment problem cease
to exist. Terminal wealth is measured at that time i.e. he who dies with the most toys wins!
The technical name for this setting is “A frictionless one-period, multi-asset economy
with no asymmetric information.”

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