Utility Theory Continued .
Optimizing a Portfolio
In the first two examples we assumed that the investor had only two options: do nothing or invest
all of his money in a risky asset. In this example we use the same kind of utility functions as
in examples

CAPM and Factor Models
Systematic Risk
CAPM imposes a structure on the expected return of an asset and so also imposes a structure on
the random return of the asset. We can write the random return of an asset i as
e
ri = r f + i e
rm r f + ei
Applying CAP

Inclusion of a Risk-Free Asset
A risk-free asset has a return that is deterministic and therefore has = 0. The inclusion of a riskfree asset in a portfolio corresponds to lending or borrowing cash at the risk-free. Lending (e.g.
purchase of a bond) corres

Utility Theory
Utility functions give us a way to measure investors preferences for wealth and the amount of
risk they are willing to undertake in the hope of attaining greater wealth. This makes it possible
to develop a theory of portfolio optimization.

Stochastic Dominance
First Order Stochastic Dominance
Stochastic dominance is a theory of decision making under uncertainty with general applicability.
Stochastic dominance allows one to determine the preference of an expected utility maximizer
between in

The Efficient Markets Hypothesis
Market Efficiency
Origins of the Efficient Markets Hypothesis (EMH) can be traced back to the pioneering theoretical contributions of Bachelier (1900) and the empirical research of Cowles (1933). The modern
literature begi

Portfolio Theory: Risky Assets Only
Feasible Set
Suppose there are n basic assets. We can plot them on the mean-standard deviation diagram.
We can form portfolios of these n assets, using every possible weighting scheme, by letting the
coefficients wi ran

Arbitrage Pricing Theory (APT)
CAPM
relies on mean-variance framework
strong version of equilibrium i.e. everyone uses the mean-variance framework
APT
does not require assumption than investors evaluate portfolios on the basis of means and
variances
w

Utility Theory Continued .
Utility Theory and Real life Investors
What kind of utility function is the best kind to use? What kind of utility function is typical of
most investors? What kind best describes the mythical average investor? There do not appea

Mean Variance Portfolio Theory
Introduction
Portfolio theory was first discovered and developed by Harry Markowitz in the 1950s. His work
forms the foundation of modern Finance. The resulting theory as modified and extended by many
researchers is often ca

Factor Models
Application of mean-variance theory and CAPM to the design of a portfolio of stocks is not
straightforward
must use indirect and subtle methods to obtain information required
information required by the mean-variance approach grows substan

Journal of Economic PerspectivesVolume 17, Number 1Winter 2003Pages 59 82
The Ef cient Market Hypothesis and Its
Critics
Burton G. Malkiel
A
generation ago, the ef cient market hypothesis was widely accepted by
academic nancial economists; for example, se

Portfolio Theory: Risky Assets Only
In the main lecture notes to find a minimum-variance portfolio we fix the mean value at a specified value r p . Then we find the feasible portfolio of minimum variance that has this mean. Hence
we formulate the problem

Value-at-Risk (VaR)
Introduction
Risk measures such as variance, standard deviation, beta, factor loadings, duration and convexity and option Greeks (see next semester for more on duration, convexity and option Greeks)
provide valuable information for the