Running head: FOUR COMPONENTS OF AN INFORMATION SYSTEM
Four Components of an Information System
Name
Institutional Affiliation
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FOUR COMPONENTS OF AN INFORMATION SYSTEM
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Four Components of an Information System
People utilize both the information techno
set of asset markets: there exists a complete set of asset markets
if it is possible to construct $ distinct portfolios one for each
state such that each portfolio has a payoff of one unit of
account in precisely one state and zero in every other state.
T
Hj1j =1 1 pj Hj1j =1 Hj = pj 1j j=1(2($ (4.18) By construction,
the right-hand side of (4.18) is the same for every investor.
Hence, Hj is the same for every investor the result asserted at
the outset. Notice that (4.18) is a consequence of asset market
e
Fig. 4.3. Indifference curves in
P, P space In mean-variance analysis the investors preferences
can be expressed by indifference curves in the plane of expected
return,
P (a good), and standard deviation of return, P (representing
risk, a bad). Points to
the use of probabilities to express beliefs, and (b) characterizes
preferences about uncertain outcomes with a von Neumann
Morgenstern utility function that depends on the outcome (say,
the
level
of
wealth)
butthatisthesamefunctionforallstates.
TheEUHlead
about uncertainty. For rigorous analyses of uncertainty in
modern finance, see Lengwiler (2004, especially chaps. 25)
and Cvitanic and Zapatero (2004, chap. 4). The axiomatic
foundations of the EUH have been intensively researched for
many years. Concise
Mr0j j=1(2(n The term Gj measures the extent to which asset j
is overpriced (Gj < 0) or underpriced (Gj > 0) in comparison
with the prediction of the CAPM. Thus, non-zero Gj terms
signal the presence of CAPM disequilibrium. This is not the
only interpreta
u
W;=Ej =0(1(2(n which is the FVR for the one-period portfolio
problem.
Appendix 4.3: Implications of complete asset markets This
appendix shows that, if two conditions are satisfied, the H
random variable in the FVR does not depend on preferences;
that i
on its validity (for example, the model ignores skewed
distributions of asset returns). Even so, mean-variance analysis
provides the foundation for the capital asset pricing model
(studied in chapter 6), one of the most well-known (though
frequently dispa
jMj/M).
Inthecontextofequation(6.11),
theCAPMimpliesthatanassetsriskpremium is a function of its
beta-coefficient not its standard deviation. That is (rather
imprecisely),
theriskpremiumonanyassetcorrespondstothecorrelationbetween
its rate of return and t
include topics relevant for chapters 10 and 11. Among the many
contributions not specifically directed to finance, those by
Tversky and Kahneman (1974), Kahneman and Tversky (1979),
Loomes and Sugden (1982) and Starmer (2000) deserve careful
attention. Sh
ptimizesthesepreferences
i.e.choosetheportfoliothatreachesthehighestfeasibleindifferencec
urve. The practical importance of this approach is that it is often
reasonable to assume that the first stage is the same for all
investors who have the same informa
aj =1 Thus, the rate of return on the portfolio, rP, equals the
weighted sum of the rates of return on each asset, the weights
being the portfolio proportions. Note that the rate of return is
uncertain because rj, not aj, varies across states. Finally, su
j
for j=1(2(n (6.8) where K
Mr0 denotes the excess expected return on the market
portfolio. To make sense of equation (6.8), recall the case of
perfect foresight (see chapter 1)
The capital asset pricing model 149 for which pj =vj/
1+r0. This is the simpl
. The objective function then becomes 2 P, the maximization of
which is equivalent to minimizing risk, irrespective of expected
return.21
4.4.3 The FVR in the mean-variance model What form does the
FVR take in the mean-variance model? Appendix 4.5 shows
t
is constant in
P(P space (the indifference curves), are convex from below. See
figure 4.3.18 The justification for the convex-from-below shape
of the indifference curves can be made on several grounds: (a)
intuitive plausibility that it seems reasonable t
B
SML
Fig. 6.4. Disequilibrium in the CAPM
The mean rate of return on asset A is greater than predicted by
the CAPM given its beta-coefficient: the point A lies above the
SML. Hence, A is underpriced conditional on the validity of
the CAPM. Point B indica
equilibrium is attained will the set of prices (and hence rates of
return) be compatible with the planned portfolios of investors
and the stocks of assets. Strictly, the CAPM asserts nothing
about the equilibrating process; it is a theory of asset market