Portfolio
Management
Basic assumption
• One basic assumption of portfolio theory is
that investors want to maximize the returns
from the total set of investments for a given
level of risk.
Risk Aversion
• Portfolio theory also assumes that investors are
basically risk averse, meaning that, given a choice
between two assets with equal rates of return, they
will select the asset with the lower level of risk.
• Investor will only accept high risk when there are
high returns.
• This combination of risk preference and risk
aversion can be explained by an attitude toward risk
that depends on the amount of money involved.
MARKOWITZ PORTFOLIO THEORY
• In 1960, there was no quantifiable risk management
approach.
• The basic portfolio model was developed by Harry
Markowitz (1952, 1959), who derived the expected
rate of return for a portfolio of assets and an
expected risk measure.
• Markowitz showed that the variance of the rate of
return was a meaningful measure of portfolio risk
under a reasonable set of assumptions
• The Markowitz model is based on several assumptions
regarding
• investor behavior:
• 1. Investors consider each investment alternative as being
represented by a probability distribution of expected returns
over some holding period.
• 2. Investors maximize one-period expected utility, and their
utility curves demonstrate diminishing marginal utility of
wealth.
• 3. Investors estimate the risk of the portfolio on the basis of
the variability of expected returns.
• 4. Investors base decisions solely on expected return and risk,
so their utility curves are a function of expected return and
the expected variance (or standard deviation) of returns only.
• 5. For a given risk level, investors prefer higher returns to
lower returns. Similarly, for a given level of expected return,
investors prefer less risk to more risk
Alternative Measures of Risk
• One of the best-known measures of risk is the
variance, or standard deviation of expected
returns.
• It is a statistical measure of the dispersion of
returns around the expected value whereby a
larger variance or standard deviation indicates
greater dispersion.
• Another measure of risk is the range of returns. It is
assumed that a larger range of expected returns,
from the lowest to the highest, means greater
uncertainty regarding future expected returns.
• Instead of using measures that analyze all
deviations from expectations, some observers
believe that investors should be concerned only
with returns below expectations, which means only
deviations below the mean value.
Expected Rates of Return
• The expected rate of return for a portfolio of
investments is simply the weighted average of the
expected rates of return for the individual
investments in the portfolio. The weights are the
proportion of total value for the individual
investment.
Variance (Standard Deviation) of Returns
for an Individual Investment
• The variance, or standard deviation, is a measure of
the variation of possible rates of return Ri from the
expected rate of return E(Ri) as follows.
Variance (Standard Deviation) of Returns
for an Individual Investment
• The variance, or standard deviation, is a measure of
the variation of possible rates of return Ri from the
expected rate of return E(Ri) as follows.
Variance (Standard Deviation) of Returns
for a Portfolio
• Covariance of Returns: Covariance is a measure of
the degree to which two variables move together
relative to their individual mean values over time.
• In portfolio analysis, we usually are concerned with
the covariance of rates of return rather than prices
or some other variable.
• A positive covariance means that the rates of return
for two investments tend to move in the same
direction relative to their individual means during
the same time period.
• In contrast, a negative covariance indicates that the
rates of return for two investments tend to move in
different directions relative to their means during
specified time intervals over time..
The Efficient Frontier
• The efficient frontier represents that set of
portfolios with the maximum rate of return for
every given level of risk, or the minimum risk for
every level of return
• Frontier will be portfolios of investments rather
than individual securities
– Exceptions being the asset with the highest return and
the asset with the lowest risk
Efficient Frontier
The efficient frontier represents that set of portfolios with the maximum rate of return for
every given level of risk, or the minimum risk for every level of return
Efficient frontier are portfolios of investments rather than individual securities except the
assets with the highest return and the asset with the lowest risk
Efficient Frontier & Investor Utility
• An individual investor’s utility curve specifies the trade-offs he
is willing to make between expected return and risk
• The slope of the efficient frontier curve decreases steadily as
you move upward
• The interactions of these two curves will determine the
particular portfolio selected by an individual investor
• The optimal portfolio has the highest utility for a given
investor
Efficient Frontier & Investor Utility
• The optimal lies at the point of tangency between the
efficient frontier and the utility curve with the highest
possible utility
• As shown in Exhibit 6.16, Investor X with the set of utility
curves will achieve the highest utility by investing the
portfolio at X
• As shown in Exhibit 6.16, with a different set of utility curves,
Investor Y will achieve the highest utility by investing the
portfolio at Y
• Which investor is more risk averse?
Efficient Frontier
Efficient Frontier & Investor Utility