CFA_PortfolioBasics - Portfolio Theory Basics

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Portfolio Theory Basics INTRODUCTION Major aim of modern  portfolio theory: to reduce risk without  reducing returns. Risk  is defined  as the uncertainty  associated  with the outcome of an event. The   variance   (or   standard   deviation)   measures   the   dispersion   of   returns   around   the  expected  return.  The standard  deviation  is the square  root of the variance. The idea is that   the   greater   the   dispersion   of   possible   outcomes   the   greater   the   variance   or   standard   deviation. Markowitz  Model  – indicates  that  the  proper  goal  of portfolio  construction  should  be to  generate  a portfolio  that  provides  the  highest  return  at  a given  level  of risk. A portfolio  having this characteristic is known  as an  efficient portfolio . Markowitz’s mean-variance frame work : the relevant  information  about  securities can be  summarized  by 3 measures: 1. Mean return 2. Standard Deviation of the returns 3. Correlation with other assets’ returns COVARIANCE OF RETURNS The   covariance of returns  indicates  how  the  rates  of return  of   two  assets  move  together  with  one  another  relative  to  their  means  over  a  period  of time.  A   positive  covariance  indicates that they move together in the same direction and  a  negative covariance  indicates  an opposite direction. A  covariance of zero  means there is no relationship  between  the two  variables.  Although  it indicates  direction, it does not  say much  about  the strength  of the  directional   movement,  since  magnitude  of  covariance  depends  on  the  variances  of  the  individual   returns as well as on the relationship  between  the series. More  information  about  the  strength  of  the  directional  movement  of  the  two  series  of  returns   can   be   obtained   by   standardizing   the   covariance   by   the   individual   standard   deviations – yielding the  correlation coefficient (r ij ). The  correlation coefficient  is the pure measure  of co-movement  between  the returns of two   assets. The correlation  coefficient  is unitless and  bounded  by +1 and  -1. When  r ij  is +1, the  returns  are perfectly  correlated.  They move  together  in the  same  direction. When  r ij  is –1,  Norman Cheung Portfolio Theory Basics 1 j i ij σ σ Cov = ij r
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the returns  move perfectly in opposite directions. When r ij  is 0, the return  are not correlated.  The key component in any diversification  strategy is the correlation of security returns. 
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This note was uploaded on 10/03/2010 for the course FINANCE 08FB40447 taught by Professor Raymond during the Spring '10 term at University of Manchester.

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CFA_PortfolioBasics - Portfolio Theory Basics

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