Question

1. Explain 3 methods which can be used for portfolio selection and structuring

2. List and explain 4 concentration management techniques.

Answer 1

1)

The goal of portfolio construction is be to generate a portfolio that provides the highest return and lowest risk. Such portfolio would be known as optimal portfolio. The process of finding the optimal portfolio is described as portfolio selection.

1) Markowitz model

The conceptual framework and analytical tools for determining the optimal portfolio in disciplined and objective manner have been provided by Harry Markowitz in his pioneering work on portfolio analysis described in 1952, in Journal of Finance article and subsequent book in 1959. His method of portfolio selection has come to be known as the Markowitz Model.

Assumptions of Markowitz model

Investors are risk averse and thus have preference for expected return and dislike for risk.

Investor measures their preference and dislike for investment through the expected return and variances about security return.

Efficiency frontier

The Markowitz model of portfolio analysis generates an efficiency frontier, which is a set of efficient portfolios.

A portfolio is said to be efficient if it offers the maximum expected return for a given level of risk or if it offers the minimum risk for a given level of expected return.

An efficient portfolio is one that has higher return for the same risk or lower risk for same return.

The locus of efficient set of portfolios is called an efficient frontier

Risk Return Profile Of 2-asset Portfolio

Feasible Portfolios And Efficient Frontier

Feasible portfolios is the set of portfolios formed by combination of securities that can be obtained by adjusting the proportions of the amount invested in each security.

Limitations of Markowitz model

One of the main problems of the Markowitz model is large number of input data required for calculations.

If there are N securities in the portfolio he would need N return estimates, N variance estimates and N(N-1)/2 covariance estimates resulting in 2N + N(N-1) /2 estimates.

Another difficulty with the Markowitz model is the complexity of  computation required.

2) Capital Asset Pricing Model

The CAPM was developed in mid 1960s. The model has generally been attributed by William Sharpe, but John Lintnerand Jan Mossinalso made similar independent deviations. Consequently, the model is often referred to as Sharpe-Lintner-Mossin(SLM) Capital Asset pricing model.

Capital market theory extends portfolio theory and develops a model for pricing all risky assets and it helps in identifying under and overvalued securities, it is also applicable in measuring portfolio performance, testing of market efficiency.

CAPM concerns  with two types of risk namely unsystematic and systematic risks. CAPM is an equation that expresses the equilibrium relationship between security’s or portfolio expected returns and its systematic risk.

The central principle of the CAPM is that, systematic risk, as measured by beta, is the only factor affecting the level of return.

Security market line

Each asset may be viewed as a combination of risk free asset and market portfolio.

Under equilibrium, all the assets are plotted on SML i.e. all the assets which are priced correctly, lie on SML.

E(Rp) = Rf+ βp[E(Rm)-Rf]

The relationship between risk and return established by the SML is known as the Capital Asset Pricing Model.

The higher the value of Beta, higher would be the risk of the security and larger would be the return expected by the investors.

3) Single Index Model

In Markowitz model; 2N+N(N-1) /2input data have to be estimated.

If a financial institution buys 150 stocks, it has to estimate 11,175 i.e.,N(N-1) /2correlation coefficients.

Sharpe developed a simplified model to analyze portfolio.

Sharpe assumed that the return of a security is linearly related to a single index like the market index.

Casual observation of the stock prices over a period of time reveals that most of the stock prices move with the market index.

When the Nifty increases, stock prices also tend to increase and vice – versa.This indicates that some underlying factors affect the market index as well as the stock prices.

Stock prices are related to the market index and this relationship could be used to estimate the return of stock.

Ri= i+ βiRm+ ei

Where

Ri- expected return on security i

i- intercept of the straight line or alpha co-efficient  or return independent of the market

βi-  slope of straight line or beta co-efficient

Rm-  the rate of return on market index

ei- error term

According to this equation, the return of a stock can be divided into two components, the return due to the market and return independent of the market.

βi indicates the sensitiveness of the stock return to changes in market return.

The single index model is based on the assumption that stocks vary together because of the common movement in the stock market. There are no effects beyond the market that account for the stock co-movement.

The variance of the security has two components namely, systematic risk and unsystematic risk. The variance is explained by index is referred to as systematic risk.

Systematic Risk = β2ix Variance of the market

The unexplained variance is called as residual variance or unsystematic risk.

Unsystematic Risk = Total Variance – Systematic Risk

2ei= 2i– Systematic Risk

Thus,

Total Risk = Systematic Risk + Unsystematic Risk

2i= β2i.2m+ 2ei

From this, the portfolio variance can be derived

2p   = Variance of the portfolio

2m= Variance of the market

2ei= Variation in a security’s return not related to the market

Wi  = The portion of stock iin the portfolio

2)

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