... energy, consumer electronics, airlines, compute

1
Diversification and Portfolio Analysis

• Investments and Portfolio Management
• MB 72

2
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

3
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.

4

• Will diversification eliminate all our risk?
• It reduces risk to an undiversifiable level. It
  eliminates only company-specific risk.
• Simple diversificationrandomly selected stocks,
  equally weighted investments
• Diversification across industriesinvesting in
  stock across different industries such
  transportation, utilities, energy, consumer
  electronics, airlines, computer hardware,
  computer software, etc.

5
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 Markotwitzs Diversification
• The emphasis in Markowitzs Diversification is on
  portfolio expected return and portfolio risk

6
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)
• i1
• Where n is the number of securities in the
  portfolio
• Example

7
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?

8
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

9
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

10

• 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

11
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

12
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

13
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 investors 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.

14

• 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