Diversification and Portfolio
Analysis
Investments and Portfolio
Management
MB 72
Outline
Principles of Diversification
Simple Diversification
Diversification across industries
Markowitz Diversification
Portfolio Analysis with Markowitz Model
Expected return and risk in Markowitz model
Significance of correlation coefficient in portfolio
analysis
Efficient frontier
Portfolio Analysis with Negative weights
Portfolio Analysis with Riskless Asset
Principles of Diversification
Why do people invest?
Investment positions are undertaken with the goal of
earning some expected return. Investors seek to minimize
inefficient deviations from the expected rate of return
Diversification is essential to the creation of an
efficient investment, because it can reduce the
variability of returns around the expected return.
A single asset or portfolio of assets is considered
to be efficient if no other asset or portfolio of
assets offers higher expected return with the
same (or lower) risk, or lower risk with the same
(or higher) expected return.
Will diversification eliminate all our risk?
It reduces risk to an undiversifiable level. It
eliminates only company-specific risk.
Simple diversification—randomly selected
stocks, equally weighted investments
Diversification across industries—investing in
stock across different industries such
transportation, utilities, energy, consumer
electronics, airlines, computer hardware,
computer software, etc.
Markowitz Diversification
Combining assets that are less than perfectly
positively correlated in order to reduce portfolio
risk without sacrificing portfolio returns.
It is more analytical than simple diversification
and considers assets’ correlations. The lower
the correlation among assets, the more will be
risk reduction through Markowitz diversification
Example of Markotwitz’s Diversification
The emphasis in Markowitz’s Diversification is
on portfolio expected return and portfolio risk
Portfolio Expected Return
A weighted average of the expected returns of
individual securities in the portfolio.
The weights are the proportions of total investment
in each security
n
E(Rp) =  wi x E(Ri)
i=1
Where n is the number of securities in the portfolio
Example:
Portfolio Risk
Measured by portfolio standard
deviation
Not a simple weighted average of the
standard deviations of individual
securities in the portfolio. Why?
How to compute portfolio standard
deviation?
Significance of Covariance
An absolute measure of the degree of
association between the returns for a
pair of securities.
The extent to which and the direction in
which two variables co-vary over time
Example:
Why Correlation?
What is correlation?
Perfect positive correlation
• The returns have a perfect direct linear relationship
• Knowing what the return on one security will do allows
an investor to forecast perfectly what the other will do
Perfect negative correlation
• Perfect inverse linear relationship
Zero correlation
• No relationship between the returns on two securities
Combining securities with perfect positive
correlation or high positive correlation does
not reduce risk in the portfolio
Combining two securities with zero correlation
reduces the risk of the portfolio. However,
portfolio risk cannot be eliminated
Combining two securities with perfect
negative correlation could eliminate risk
altogether
Portfolio Analysis
Job of a portfolio manager is to use these risk and
return statistics in choosing/combining assets in such
a way that will result in minimum risk at a given level
of return, also called efficient portfolios
Select investment weights in such a manner that it
results in a portfolio that has minimum risk at a
desired level of return, i.e., efficient portfolios
As we change desired level of return, our efficient
combination of securities in the portfolio will change
Therefore, we can get more than one efficient
portfolio at different risk-return combinations
The concept of “Efficient Frontier”
Efficient Frontier
Is the locus of points in risk-return space having
the maximum return at each risk level or the
least possible risk at each level of desired return
Presents a set of portfolios that have the the
maximum return for every given level of risk or
the minimum risk for a given level of return
As an investor you will target a point along the
efficient frontier based on your utility function
and your attitude towards risk.
Can a portfolio on the efficient frontier dominate
any other portfolio on the efficient frontier?
Examples
The Efficient Frontier and
Investor Utility
The slope of the efficient frontier curve decreases
steadily as we move upward (from left to right) on
the efficient frontier
What does this decline in slope means?
• Adding equal increments of risk gives you diminishing
increments of expected return
An individual investor’s utility curves specify the
trade-offs investor is willing to make between
expected return and risk
In conjunction with the efficient frontier, these
utility curves determine which particular portfolio
on the efficient frontier best suits an individual
investor.
Can two investors will choose the same
portfolio from the efficient set?
• Only if their utility curves are identical
Which portfolio is the optimal portfolio
for a given investor?
• One which has the highest utility for a given
investor given by the tangency between the
efficient frontier and the curve with highest
possible utility