Modern_Portfolio_Theory_TRNS

Modern_Portfolio_Theory_TRNS - Modern Portfolio Theory...

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Modern Portfolio Theory Professor Gideon Saar Johnson School Cornell University Johnson School, Cornell University Outline Covariance and correlation coefficient. Two asset portfolio: – Diversification. Portfolio frontier and efficient portfolios. Systematic versus unsystematic risk. Incorporating the risk-free asset – Capital Allocation Line. Choice of optimal portfolios by investors. Copyright 2009, Prof. Gideon Saar, All rights reserved/Modern Portfolio Theory Numerical optimization in EXCEL.
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Optimal Risk/Return Tradeoff Modern portfolio theory provides a technology for optimally considering the tradeoff between risk and return when making investment decisions investment decisions. It has nothing to do with market efficiency. – These tools are extensively used to build actively managed portfolios. In other words, you can use them even if you do not think that prices of securities are informationally efficient. We will encounter it again when we discuss Strategic Asset Allocation. Copyright 2009, Prof. Gideon Saar, All rights reserved/Modern Portfolio Theory Covariance GOLD: r s p s IBM: r s p s 50% 0.20 -15% 0.20 40% 0.20 3% 0.20 -10% 0.35 14% 0.35 A measure of the co-movement of two random variables. Formula:     12 1 1 2 2 1, 1 2, 2 COV( , ) ( ) ( ) () ()* ss s s rr E r Er r Er rE rrE r p  10% -20% 0.25 40% 0.25 Copyright 2009, Prof. Gideon Saar, All rights reserved/Modern Portfolio Theory E(r GOLD )=0.5*0.2+0.4*0.2-0.1*0.35-0.2*0.25=9.5%, (r GOLD )=29.41% E(r IBM )=12.5%, (r IBM )=18.95% COV(r IBM ,r GOLD )=(-0.15-0.125)*(0.50-0.095)*0.2+ (0.03-0.125)*(0.4-0.095)*0.2+(0.14-0.125)*(-0.1-0.095)*0.35+ (0.4-0.125)* (-0.2-0.095)*0.25= -0.04938
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Correlation Coefficient Formula: The correlation coefficient is always between 1 and 1 12 COV( , ) (, ) () * () rr  The correlation coefficient is always between -1 and 1. – A negative correlation coefficient means that returns tend to move in opposite directions. A positive correlation coefficient means that returns tend to move in the same direction. (r IBM ,r GOLD )= -0.04938/(0.1895*0.2941)= -0.886 Copyright 2009, Prof. Gideon Saar, All rights reserved/Modern Portfolio Theory Two Asset Portfolio Formulas Portfolio weights (must sum to 100%): w 1 +w 2 =1 Portfolio realized return: r p =w 1 *r 1 +w 2 *r 2 Expected Return: –E ( r p )=E(w 1 *r 1 +w 2 *r 2 ) =w 1 *E(r 1 )+w 2 *E(r 2 ) (i.e., expected return on a portfolio is the weighted average of expected returns on stocks in the portfolio).
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This note was uploaded on 09/16/2009 for the course NBA 5420 taught by Professor Saar,gideon during the Spring '09 term at Cornell.

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Modern_Portfolio_Theory_TRNS - Modern Portfolio Theory...

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