Co-Relation & Its Signification in Portfolio Analysis - Prasun & Group

8/6/2019 Co-Relation & Its Signification in Portfolio Analysis - Prasun & Group

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Co-relation & Its Signification

inPortfolio Analysis

Prasun Pandey : 32

Sajesh Nair : 30

Sunil Ledwani : 19

Bhavesh Mankani : 52

Sagar Vartak : 45

Nikesh Malhotra : 21


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Outline

Principles of Diversification

Simple Diversification

Diversification across industriesMarkowitz Diversification

Portfolio Analysis with Markowitz Model

Expected return and risk in Markowitz model

Significance of correlation coefficient in portfolio analysisEfficient frontier


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Principles of DiversificationWhy do people invest?

Investment positions are undertaken with the goal of earning someexpected return. Investors seek to minimize inefficient deviations from

the expected rate of returnDiversification is essential to the creation of an efficientinvestment, because it can reduce the variability of returnsaround the expected return.

A single asset or portfolio of assets is considered to beefficient if no other asset or portfolio of assets offers higherexpected return with the same (or lower) risk, or lower riskwith the same (or higher) expected return.


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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, computerhardware, computer software, etc.


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Markowitz DiversificationCombining assets that are less than perfectly positivelycorrelated in order to reduce portfolio risk withoutsacrificing portfolio returns.

It is more analytical than simple diversification andconsiders assets correlations. The lower the correlationamong assets, the more will be risk reduction throughMarkowitz diversification

Example of Markotwitzs DiversificationThe emphasis in Markowitzs Diversification is onportfolio expected return and portfolio risk


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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 eachsecurity

n

E(Rp) = wi x E(Ri)

i=1

Where n is the number of securities in the portfolio

Example:


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Portfolio Risk

Measured by portfolio standard deviation

Not a simple weighted average of the standarddeviations of individual securities in the portfolio.

Why?

How to compute portfolio standard deviation?


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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:


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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


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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 eliminatedCombining two securities with perfect negative

correlation could eliminate risk altogether


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Portfolio Analysis

Job of a portfolio manager is to use these risk and return statisticsin choosing/combining assets in such a way that will result in

minimum risk at a given level of return, also called efficientportfolios

Select investment weights in such a manner that it results in aportfolio that has minimum risk at a desired level of return, i.e.,efficient portfolios

As we change desired level of return, our efficient combination ofsecurities in the portfolio will change

Therefore, we can get more than one efficient portfolio atdifferent risk-return combinations

The concept of Efficient Frontier


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Efficient Frontier

Is the locus of points in risk-return space having themaximum return at each risk level or the least possible risk

at each level of desired returnPresents a set of portfolios that have the the maximumreturn for every given level of risk or the minimum risk fora given level of return

As an investor you will target a point along the efficientfrontier based on your utility function and your attitudetowards risk.

Can a portfolio on the efficient frontier dominate any otherportfolio on the efficient frontier?

Examples


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The Efficient Frontier and

Investor UtilityThe slope of the efficient frontier curve decreases steadily aswe 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-offsinvestor is willing to make between expected return and risk

In conjunction with the efficient frontier, these utility curvesdetermine which particular portfolio on the efficient frontier

best suits an individual investor.


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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


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Co-Relation & Its Signification in Portfolio Analysis - Prasun & Group