Question

How to compute Optimal Portfolio Selection ?

Explain in details, please

Answer 1

Feasible set of Portfolios

With a limited number of securities an investor can create a large number of portfolio with different proportion of securities.These consitutes feasible set of protfolio in which an investor can invest . Its also known as Portfolio opportunity set. Each portfolio is portfolio opportunity set characterised by an expected returns & risk . Investors are not interested in all portfolio in opportunity set. Some portfolios are dominated by others either if Higher returns & same risk or Lower risk & same returns. Portfolio domintaed by others is known as inefficient portfolio.

Efficent Frontier

It can be illustrated with following graph of XY where x represents Risk & Y represents Returns . Each portfolio has its own risk and return are deplected by asingle point in the risk return space enclosed within two axis of the graph. Graph shows set of portfolio created with given securities and its shape is concave because it consist of securities that are lessthan perfectly correlated to each other.

While comparing each portfolis as follws ;

1 . E & F - E is selected

2. C & E - E is selected (High returns and low risk)

3. C & A - C is selected (Lower risk) C is lowest risky portfolio compared to all others , C in this graph represent Global Minimum Variance Portfolio

4 . A & B - (same risk) B is selected because it has High returns .

ie , Portfolio lying on North west boundary of shaped area is more efficent than others. This boundary of shaped area is called as Efficent Frontier because it contain more efficent portfolio set.

Optimal portfolio

Optimal portfolio is a term used in portfolio theory to refer to the one portfolio on the Efficient Frontier with the highest return-to-risk combination given the specific investor's tolerance for risk.

Rational investors prefers to invest in efficient Portfolio. Investors prefers to ionvest in portfolios within efficient Frontier dependence on investors degree of risk averses. If they arfe high risk averses they prefers lower left hand side of efficient frontier. If they are too much risk averses and they prefers Higher portions of Efficient Frontier.

Selection of optimal portfolio depends on investors risk aversion or risk tolerance. This can be graphically represented by risk return utility curve or indiffernece curve.

* Each curve represents combination of risk and return , all of which equally satisfactory to investors.

* Investors will indifferent to successive points in curve

* Each sucessive curve moves upward left , represent, high level of satisfaction

" Optimum portfolio is one at the point of tangency between Efficent Frontier and Indifference Curve"

Markowitz Model

Markowitz used the technique of quardratic programming to determine efficent portfolio.Using the risk and return of each security he can calculate covariance estimates of each pair of securities and calculated using Risk & return for all possible portfolio.. For a specific estimated portfolio return he determine Least risk portfolio using   quardratic programming. For another specific estimated portfolio return he again repeat the same procedure and give minimum risk portfolio.This process repeated and different values of expected returns and resulting minimum risk portfolio constitute Optimum portfolio or set of efficient portfolio.