PORTFOLIO- MARKOWITZ MODEL AND SHARPE’S SINGLE INDEX MODEL

Introduction A portfolio involves the selection of

securities. Each individual investor puts his wealth in a combination of assets depending on his wealth, income and his preferences.

The traditional theory of portfolio postulates that selection of assets should be based on lowest risk, as measured by its standard deviation from the mean of expected returns.

But how to gain highest returns from the lowest risk?? is what led to the development of Markowitz model.

Harry Markowitz put forward this model in 1952.

It assists in the selection of the most efficient by analyzing various possible portfolios of the given securities. By choosing securities that do not 'move' exactly together, the HM model shows investors how to reduce their risk.

The HM model is also called Mean-Variance Model due to the fact that it is based on expected returns (mean) and the standard deviation (variance) of the various portfolios.

History of model

He started with the idea of risk aversion of average investors and their desire to maximise the expected return with the least risk.

Markowitz model is thus a theoretical framework for analysis of risk and return and their inter-relationships.

His framework led to the concept of efficient portfolios.

An efficient portfolio is expected to yield the highest return for a given level of risk or lowest risk for a given level of return.

1. Risk of a portfolio is based on the variability of returns from the said portfolio.

2. An investor is risk averse.3. An investor prefers to increase

consumption.4. Analysis is based on single period

model of investment.5. An investor either maximizes his

portfolio return for a given level of risk or maximizes his return for the minimum risk.

6. An investor is rational in nature.

Assumptions of the model

1. Expected return.2. Variability of returns as

measured by standard deviation from the mean.

3. Covariance or variance of one asset return to other asset returns.

Parameters for building up the efficient set of portfolio

How to determine the efficient portfolio?

In this figure, the shaded area PVWP includes all the possible securities an investor can invest in. The efficient portfolios are the ones that lie on the boundary of PQVW. This boundary PQVW is called the Efficient Frontier.

All portfolios that lie below the Efficient Frontier are not good enough because the return would be lower for the given risk.

Portfolios that lie to the right of the Efficient Frontier would not be good enough, as there is higher risk for a given rate of return.

The investor's optimal portfolio is found at the point of tangency of the efficient frontier with the indifference curve. This point marks the highest level of satisfaction the investor can obtain. R is the point where the efficient frontier is tangent to indifference curve C3, and is an efficient portfolio.

1. It requires lots of data to be included. An investor must obtain variances of return, covariance of returns and estimates of return for all the securities in a portfolio.

2. There are numerous calculations involved that are complicated because from a given set of securities, a very large number of portfolio combinations can be made.

3. The expected return and variance will also have to be computed for each of the securities in the portfolio.

Demerits of the HM Model

The extension of Markowitz model, overcoming of the defects, is this model.

Sharpe showed that there is along the efficient frontier a unique portfolio that, when combined with lending or borrowing at the pure interest rate, dominates all other combinations of efficient portfolios.

SHARPE’S SINGLE INDEX MODEL

Assumptions for Sharpe’s SIM(1)There exists a single pure

interest rate at which investors can lend and borrow in unlimited amounts

(2) Investors have homogeneous expectations regarding expected returns, variances and correlations.

Equation for SIMRi =αi + β*Rm +eiWhere, Ri = return on the stockαi = component of security that is

independentof market performanceβ =co-efficient in the market

expected change in Ri given a change in Rm

Rm =rate of return on market indexei =random elements of αi.

Criticism of SIMSingle index model has been

criticized because of its assumption that stock prices move together only because of common

co-movement with the market. Many researchers have found that there are influences beyond the

market like industry related factors that cause securities to move

together.

ConclusionIf investors are risk averse its suitable

for them to adopt Markowitz model, on the other hand, though SIM is criticized it is not possible by any other models to simplify calculations using empirical evidence.

Therefore, in choosing the portfolio of investments, one has to analyze carefully about the possibility of risk and return and adopt the suitable methods.

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