copy of markowitz

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Markowitz

Model

Submitted to :

Dr. Daisy Sheby ThekkanalDr. Daisy Sheby Thekkanal

Submitted By : Vijay vaddoriya

Abhishek varshneyHimanshu atel

THE SURAT PEOPLES BANKCOLLEGE

OFBUSINESS ADMINISTRATION


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The Modern portfolio theory was developed by Dr. Harry M.

Markowitz in 1952. He generated a number of portfolios with

in agiven amount of investible funds. It is a model based ontheoretical frame work for analysis of risk and return. He used thestandard deviation for measurement of risk. He also utilised therelationship between securities for selection of better asset mix ina portfolio. His entire work lead to the concept of efficient

portfolio. An efficient portfolio is expected to yield highest returnfor low level of risk.

There are three important variables which are taken intoconsideration by Markowitz model. i.e. return, standard deviation,coefficient of correlation, Markowitz model is also called as full

covariance model.


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Assumptions of Markowitz model

The Markowitz model is based on the followingassumptions.a. Investors behave rationally.b. Investors know all the information about the market

situation.c. Investors choose higher returns to lower level of risk.d. The markets are efficient and they absorb

information quickly and perfectlye. Investors are risk aversef. Investors can reduce their risk by adding new

investments in the portfolio.

g. Investors will get a higher rate of return if they adoptthe efficient portfolio model.

h. By combining all the financial assets, the return onvarious securities as to be correlated to each other.

i. Investors decisions are based on expected returnand their variance.


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Parameters of Markowitz diversification

For building of efficient set of portfolio, weneed to look into these important

parameters. Expected return

Variability of returns as measured bystandard deviation.

Co-variance or variance of one securityreturn to other asset return.


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Definition of Risk

Risk : Risk is the potential for variability inreturns. The expected return is theuncertain return that an investor expects

to get from his investment. The realizedreturn is the certain return that aninvestor has actually obtained from hisinvestment at the end of the holding

period.


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Types of Risk ?

Total Risk=systematic risk +unsystematic risk


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Each security in a portfolio contributesreturns in the proportion of its investment

in security. Thus, the portfolio expectedreturn is the weighted average of theexpected returns from each of thesecurities, with weights representing the

proportionate share of the security in thetotal investment

Definition Return


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(Alpha) Alpha is the distance between the horizontal axis

and lines intersection with y axis.

Measure the unsystematic risk.

Beta

Beta

Alpha

Market return(OR Market Index)

Stock

return

It is the difference

between actual earnedreturn and expectedreturn at a level ofsystematic risk. If alphais positive return, thanthat scrip will havehigher returns. If alphais negative return, thanthat scrip will have

lower returns compare


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(beta)

Beta is used to describe the relationship betweenthe stocks return and market indexs return. Ifbeta=1 means 1% change in the market indexshows that it is on an average accompanied by a1% change in the stock price. Beta may be positive

or negative.

= % Price Change of a Scrip Return

% Price change of the market indexreturn

In short, if beta is 1, the scrip risk is the same asthe market risk. If beta is greater than 1, the scriprisk is more than the market risk and if beta is lessthan 1, the scrip risk is less than the market risk. If

beta is zero, stock price is unrelated to market


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How to calculate expected

Return :

W here, Rpis the return on theportfolio

Riis the return on

asset


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where ijis the correlation coefficientbetween the returns on assets i and j.


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For two assets portfolio :

Portfolio Return :

Portfolio Variance :


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For

Three assets portfolio :

Portfolio Return :

Portfolio Variance :


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