Markowitz Portfolio Theory Dr. Lokanandha Reddy Irala (www.irala.org) 1

Probability distribution of returns Finite Holding Period Probability distribution of returns Risk of an asset - Variability (SD) of expected returns. Decisions - Based on the risk and return Assumption of Non satiation Investors prefer higher levels of terminal wealth to lower levels of terminal wealth – Given two portfolios with the same SD, the investor would choose the one with higher expected return Dr. Lokanandha Reddy Irala (www.irala.org) 2

Lokanandha Reddy Irala 3 Markowitz Portfolio Theory MPT - The Assumptions Finite Holding Period Probability distribution of returns Risk of an asset - Variability (SD) of expected returns. Decisions - Based on the risk and return Assumption of Non satiation Investors prefer higher levels of terminal wealth to lower levels of terminal wealth – Given two portfolios with the same SD, the investor would choose the one with higher expected return Lokanandha Reddy Irala 3 Markowitz Portfolio Theory

Assumption of Risk aversion Maximizing utility of wealth, but not wealth itself No transaction costs and taxes while buying and selling the securities Investments are infinitely divisible. Dr. Lokanandha Reddy Irala (www.irala.org) 4

MPT - The Feasible /Opportunity Set All the portfolios that could be formed from a given numbers of securities RP Rb B Rc C Rd E D A Ra p a e d b Lokanandha Reddy Irala 5 Markowitz Portfolio Theory

MPT - The Feasible /Opportunity Set RP Rb B Rc C Sub Optimal ??!! Rd E D A Ra Principle of Dominance – Efficient portfolios Efficient Frontier p a e d b Lokanandha Reddy Irala 6 Markowitz Portfolio Theory

MPT - The Optimal portfolio Which is the optimal portfolio for me ? A , E, C or B ? RP Rb B Rc C Rd E D A Ra Selection of optimal portfolio – Indifference Curves p a e d b Lokanandha Reddy Irala 7 Markowitz Portfolio Theory

MPT - The Indifference Curve RP C1 Rr R Rq Q Rp P p p q r Lokanandha Reddy Irala 8 Markowitz Portfolio Theory

MPT - The Indifference Map A set of Indifference curves represent the Indifference map of an Investor The steepness of the curve is dependent upon the degree of risk aversion of the investor The higher the risk aversion, the steeper is the curve RP C3 C2 C1 p Lokanandha Reddy Irala 9 Markowitz Portfolio Theory

MPT – The Optimal Portfolio Which is the optimal portfolio for me ? A , E, C or B ? C3 RP Optimal portfolio C2 C1 Rb B Rc C Rd E D A Ra p a e d b Lokanandha Reddy Irala 10 Markowitz Portfolio Theory

MPT- The Concavity Of The Efficient Set 1 2 3 6 4 5 7 8 9 10 Q S Portfolio S (3, 6+) efficient than R (when  = < +1) T R Portfolio R (3,6) with equal invest. in P and Q when  = +1 P Portfolio T (3-, 6) efficient than R (when  = < +1) Lokanandha Reddy Irala 11 Markowitz Portfolio Theory

Markowitz Portfolio Theory Thank You Questions? Lokanandha Reddy Irala 12 Markowitz Portfolio Theory