portfolio management (1) - MPT Modern Portfolio Theory...

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1 K. Hartviksen MPT – Modern Portfolio Theory Business 2039
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2 K. Hartviksen Key Terms Harry Markowitz MPT Expected return required return portfolio systematic risk unsystematic risk diversification beta coefficient security market line market premium for risk capital asset pricing model cost of capital mean, variance, standard deviation correlation capital market line
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Harry Markowitz Modern portfolio theory was initiated by University of Chicago graduate student, Harry Markowitz in 1952. Markowitz showed how the risk of a portfolio is NOT just the weighted average sum of the risks of the individual securities…but rather, also a function of the degree of comovement of the returns of those individual assets.
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3 Risk and Return - MPT Prior to the establishment of Modern Portfolio Theory, most people only focused upon investment returns…they ignored risk. With MPT, investors had a tool that they could use to dramatically reduce the risk of the portfolio without a significant reduction in the expected return of the portfolio.
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10 Correlation The degree to which the returns of two stocks co-move is measured by the correlation coefficient. The correlation coefficient between the returns on two securities will lie in the range of +1 through - 1. +1 is perfect positive correlation. -1 is perfect negative correlation.
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11 Perfect Negatively Correlated Returns over Time Time 1994 1995 1996 Returns on Stock A 10% Returns on Stock B A two-asset portfolio made up of equal parts of Stock A and B would be riskless. There would be no variability of the portfolios returns over time. Returns on Portfolio Returns %
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145 K. Hartviksen Ex Post Portfolio Returns Simply the Weighted Average of Past Returns i R i x R x R i i n i i i p asset on return asset of weight relative : Where 1 = = = =
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145 K. Hartviksen Ex Ante Portfolio Returns Simply the Weighted Average of Expected Returns Relative Weight Expected Return Weighted Return Stock X 0.400 8.0% 0.03 Stock Y 0.350 15.0% 0.05 Stock Z 0.250 25.0% 0.06 Expected Portfolio Return = 14.70%
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Grouping Individual Assets into Portfolios The riskiness of a portfolio that is made of different risky assets is a function of three different factors: the riskiness of the individual assets that make up the portfolio the relative weights of the assets in the portfolio the degree of comovement of returns of the assets making up the portfolio The standard deviation of a two-asset portfolio may be measured using the Markowitz model: B A B A B A B B A A p w w w w σ ρ , 2 2 2 2 2 + + =
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Risk of a Three-asset Portfolio C A C A C A C B C B C B B A B A B A C C B B A A p w w w w w w w w w σ ρ , , , 2 2 2 2 2 2 2 2 2 + + + + + = The data requirements for a three-asset portfolio grows dramatically if we are using Markowitz Portfolio selection formulae.
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This note was uploaded on 03/21/2010 for the course KNOWLEDGE 5654 taught by Professor Mr.david during the Spring '10 term at IESE Business School.

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portfolio management (1) - MPT Modern Portfolio Theory...

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