Diversification and Portfolio Analysis

Investments and Portfolio ManagementMB 72

OutlinePrinciples of Diversification

Simple DiversificationDiversification across industriesMarkowitz Diversification

Portfolio Analysis with Markowitz ModelExpected return and risk in Markowitz modelSignificance of correlation coefficient in portfolio analysisEfficient frontier

Portfolio Analysis with Negative weightsPortfolio Analysis with Riskless Asset

Principles of DiversificationWhy 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 investmentsDiversification across industries—investing in stock across different industries such transportation, utilities, energy, consumer electronics, airlines, computer hardware, computer software, etc.

Markowitz DiversificationCombining 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 diversificationExample of Markotwitz’s DiversificationThe emphasis in Markowitz’s Diversification is on portfolio expected return and portfolio risk

Portfolio Expected ReturnA weighted average of the expected returns of individual securities in the portfolio. The weights are the proportions of total investment in each security nE(Rp) = wi x E(Ri) i=1Where n is the number of securities in the portfolioExample:

Portfolio RiskMeasured by portfolio standard deviationNot a simple weighted average of the standard deviations of individual securities in the portfolio. Why?How to compute portfolio standard deviation?

Significance of CovarianceAn 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 timeExample:

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 doPerfect negative correlation

• Perfect inverse linear relationshipZero 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 portfolioCombining two securities with zero correlation reduces the risk of the portfolio. However, portfolio risk cannot be eliminatedCombining two securities with perfect negative correlation could eliminate risk altogether

Portfolio AnalysisJob 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 portfoliosSelect 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 portfoliosAs we change desired level of return, our efficient combination of securities in the portfolio will changeTherefore, we can get more than one efficient portfolio at different risk-return combinationsThe concept of “Efficient Frontier”

Efficient FrontierIs 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 returnPresents 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 returnAs 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 UtilityThe 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 riskIn 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 identicalWhich 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