And, now take you into a WORLD of……………..

A WOLRD OF PORTFOLIO

PORTFOLIO THEORY

PORTFOLIO ……??? …… A set of securities combined in some proportion is called portfolio.

Revisiting basic issues of… PORTFOLIO THEORY…

Basic Assumption of the Portfolio Theory… Portfolio reduces risk through diversification where diversification is understood as a process of accumulating various securities to reduce the risk.

BASIC OBJECTIVE BEHIND EVERY PORTFOLIO IS…... to improve upon the RISK - RETURN profile of one’s investment.

BASIC ISSUES IN CONSTRUCTION OF A PORTFOLIO What should be the security set from which securities are to be selected? In what proportion the securities are to be combined? How to evaluate a portfolio? How to select the optimum portfolio?

Our efforts to resolve these issues about portfolio takes us to the portfolio theories……

THE VERY FIRST SCIENTIFIC ATTEMPT TO ANSWER THESE QUESTIONS WAS MADE BY HARRY MARKOWITZ and Therefore, we start our Portfolio Theory with MARKOWITZ MODEL...

MARKOWITZ MODEL Markowitz is called father of Modern Portfolio Theory. He gave for the very first time a quantitative measurement of risk and return of a security as well as of a portfolio. He also suggested a methodology for constructing an optimum portfolio. He changed the whole character and the nature of the theory of Finance.

Markowitz said that since a security is evaluated in terms of Risk and Return parameters, a portfolio should also be evaluated in terms of Risk and Return.

Return and Risk of a Portfolio Where E(RP) = Expected Return of the Portfolio s(RP) = Standard Deviation of return on a portfolio ai = Proportion of ith security in the portfolio si2 = Variance of ith security E(Ri) = Return on ith security Cov(Ri,Rj) = Covariance between the return of ith security and the return of the jth security

Portfolio DIVERSIFY AWAY Risk ………????!!!!! Markowitz questioned NAÏVE DIVERSIFICATION - a diversification that is obtained by just adding a number of different securities into a portfolio. Can we really conclude that adding too many securities simply into a portfolio reduce risk?

Markowitz said - “… not necessarily. “ it may be or may not be “. Then, what determines whether risk in a portfolio can be reduced? Markowitz said - “it is the nature and the degree of covariances existing among securities that determine whether risk in a portfolio could be reduced”.

diversification gains!!! Diversification pays when the securities are having less degree of correlation and negative correlation. Expected Return r = -1 r = 1 Be clear about the diversification gains!!! Standard Deviation

Markowitz Model of Portfolio: (Journal of Finance : 1952) Assumptions: The investor is rational. The investor is risk averter. Securities and portfolios can be evaluated only in terms of two parameters - Mean and Variance. Security Market is perfectly competitive. Securities are perfectly divisible. Investors have complete information about Mean, Variance and Correlation of all securities. Investors have one period as holding period. Investors are not E(R) maximiser but E(U) maximiser and U = f(Risk and Return) Either Utility Function is quadratic or the returns are following normal probability distribution.

Are you searching for an OPTIMUM PORTFOLIO ……??? If YES!? Then, first, look for an efficient set of portfolios. A set of portfolios is called an efficient set if all the portfolios in it are non-dominated portfolios in the sense of mean-variance dominance principle. MEAN - VARIANCE DOMINANCE PRINCIPLE says that a portfolio is a dominating over the other portfolio if for the same or more expected return a portfolio is having same or less risk. for the same or less risk a portfolio is having more expected return.

Can we have a zero risk portfolio??? Yes! We can have it if we can find two securities having between them perfectly negative correlation.

MINIMUM VARIANCE SET OF PORTFOLIOS? It is a set of those portfolios which have minimum variance for a given expected return on a portfolio. It is usually referred as a BULLET because of its shape. If two or more portfolios from minimum variance set are combined, then the resultant portfolio also has minimum variance. Expected Return O Standard Deviation

MINIMUM VARIANCE PORTFOLIOS – TWO SECURITIES A portfolio with two shares will have minimum variance if the weight of one of the shares in the portfolio will be

EFFICIENT FRONTIER ……??? F Expected Return E Standard Deviation Y Expected Return A curve that shows non-dominated portfolios in terms of mean-variance dominance is called EFFICIENT FRONTIER. No portfolio on it is dominated by any one. It always have positive slope. It steepnees depends upon the degree of correlation that exists between portfolios. It is concave with respect to risk and convex with respect to expected return. X A B C E Standard Deviation

TWO - FUND SEPARATION THEOREM This theorem says that- all portfolios on the mean - variance efficient frontier can be formed as a weighted average of any two portfolios(or funds) on the efficient frontier.

OPTIMUM SELECTION OF A PORTFOLIO DEPENDS UPON RISK - RETURN TRADE - OFF!!! Expected Return P OPTIMUM PORTFOLIO E Standard Deviation

What are the most important contributions of Markowitz model? It has two important contributions: FIRST, it has provided tools of ‘quantification of ‘Risk and Return ’!!!

What are the most important contributions of Markowitz model? Second is the concept of ‘Efficient Portfolio’!!!

What are the most important contributions of Markowitz model? Third is the way through which ‘Optimum Portfolio’ is selected!!!

Is there anything in the Markowitz Model at which you would like to ‘ATTACK’?

ONE...

Large Volume of data required. I would become mad!!! I really do not know how many pieces of input data I need to generate my best portfolio?

Too much information required!!! This model requirement of information is huge and it increases exponentially with increase in the number of securities. Markowitz model requires (n (n+3))/2 pieces of input data.

TWO...

Have you ever wondered why returns of shares of companies from various industries are correlated?

What makes shares’ return to have correlation across the companies from the different industries? THINK!!!

Is there some underlying FACTOR which makes these correlations to exist?

But, are we in a position to identify that factor? If that factor exists, then your data requirement will also be considerably reduced!!!! But, are we in a position to identify that factor?

Yes!!!! We can identify that factor... And, this takes us to ...

SINGLE INDEX MODEL

SHARPE’S SINGLE FACTOR/INDEX MODEL It is ex-post relationship. It shows how a factor leads to generation of returns in a security. Its intercept represents unique return of a security which is independent of Market Index. The slope of the Single Index Model represents  which is a measure of SYSTEMATIC RISK. It is a linear relation between the return of a security and the underlying factor which is the MARKET INDEX.

Systematic Risk Vs. Unsystematic Risk Systematic Risk: Return on an asset is systemically influenced by return on market portfolio; hence if any variation in the return of an asset is explained by the variation in the market return, then such a variation is called SYSTEMATIC RISK. Such a risk is caused mainly by the macro factors; and it is non-diversifiable risk. Unsystematic Risk: Any variation in the return of an asset that is not explained by the variation in the market return and is independent of the market risk, or that resides within the asset itself is called UNSYSTEMATIC RISK. Such a risk is caused mainly by the micro factors; and it is diversifiable risk.

CHARACTERISTIC LINE A regression line fitted to the scatter plot of returns from the market portfolio and a security is called CHARACTERISTIC LINE. This is also a line that gives us the estimates of the parameters of the Single Factor Model. The slope of the characteristic line is called b that represents SYSTEMATIC RISK. It is called a characteristic line as its slope showing the risk characteristics of a security which is different for different securities.

CHARACTERISTICS LINE

COMPONENTS OF TOTAL RISK OF A SECURITY Total Risk of a security is determined by the variance of the returns. It is equal to Unsystematic Risk and Systematic Risk. That is--- TOTAL RISK = UNSYSTEMATIC RISK + SYSTEMATIC RISK. Where Total Risk of ith security = si2; Systematic Risk = bi2 sm2 ; and Unsystematic Risk = Total Risk - Systematic Risk = si2 - bi2 sm2.

It is R2. It represents proportion of total risk which is SYSTEMATIC. Is there any statistical measure that can tell us - out of total variation, how much per cent variation is due to systematic part and how much is due to unsystematic part? YES!!! It is R2. It represents proportion of total risk which is SYSTEMATIC. In what way, the information of R2 is useful for an investment manager?

ESTIMATION OF b The estimation of b of a security needs the following steps: First, identify a suitable MARKET INDEX. Collect information about the prices of the security and the Index. Fit the regression equation on the returns of the security and the Index where the security return will be taken as a dependent variable and the return on the Index will be taken as an independent variable.

b ESTIMATION [EXCEL output]

b ESTIMATION [EXCEL output]

b ESTIMATION [EXCEL output]

What next…?

INVESTORS’ ATTITUDE TOWARDS RISK ... Depending upon the attitude of investors towards risk, investors are classified as - RISK AVERSE RISK NEUTRAL RISK SEEKER

UTILITY CURVES… Risk Neutral Risk Averter RETURN Risk Lover RISK

Are investors really risk - averters …??? Yes, they are !!! It is indicated by the following facts observed by the researchers: Investors go for diversification. Investors buy insurance. Empirical relation between Risk and Return is found to be - high returns are found to be associated with high risk.