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An investor has a certain amount of dollars to invest into two stocks <math>IBM</math> and <math>TEXACO</math>. A portion of the available funds will be invested into | An investor has a certain amount of dollars to invest into two stocks <math>IBM</math> and <math>TEXACO</math>. A portion of the available funds will be invested into | ||
IBM (denote this portion of the funds with <math>x_A</math> and the remaining funds | IBM (denote this portion of the funds with <math>x_A</math> and the remaining funds | ||
| - | into TEXACO (denote it with <math>x_B</math>) - so <math>x_A+x_B=1 | + | into TEXACO (denote it with <math>x_B</math>) - so <math>x_A+x_B=1</math>. The resulting portfolio |
will be <math>x_A R_A+x_B R_B</math>, where <math>R_A</math> is the monthly return of <math>IBM</math> and <math>R_B</math> is the | will be <math>x_A R_A+x_B R_B</math>, where <math>R_A</math> is the monthly return of <math>IBM</math> and <math>R_B</math> is the | ||
monthly return of TEXACO. The goal here is to | monthly return of TEXACO. The goal here is to | ||
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<math> | <math> | ||
| - | \mbox{Minimize} \ \ mbox{Var}(x_A R_A+x_BR_B) | + | \mbox{Minimize} \ \ mbox{Var}(x_A R_A+x_BR_B) <br> |
\mbox{subject to} \ \ x_A+x_B=1 | \mbox{subject to} \ \ x_A+x_B=1 | ||
</math> | </math> | ||
Revision as of 04:37, 3 August 2008
Portfolio theory
An investor has a certain amount of dollars to invest into two stocks IBM and TEXACO. A portion of the available funds will be invested into IBM (denote this portion of the funds with xA and the remaining funds into TEXACO (denote it with xB) - so xA + xB = 1. The resulting portfolio will be xARA + xBRB, where RA is the monthly return of IBM and RB is the monthly return of TEXACO. The goal here is to find the most efficient portfolios given a certain amount of risk. Using market data from January 1980 until February 2001 we compute that $E(R_A)=0.010$, $E(R_B)=0.013$, $Var(R_A)=0.0061$, $Var(R_B)=0.0046$, and $Cov(R_A,R_B)=0.00062$. \\ We first want to minimize the variance of the portfolio. This will be:
