Post on 06-May-2015
description
Diversification and Portfolio Analysis
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