diversification and portfolio analysis@ bec doms

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Diversification and portfolio analysis@ bec doms


  • 1.Diversification and Portfolio Analysis

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.


  • 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(R p ) =w ix E(R i )
  • i=1
  • 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


  • 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.


  • 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