Difference between revisions of "SOCR EduMaterials Activities ApplicationsActivities Portfolio"
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| − | == Portfolio | + | == Portfolio Theory == |
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 | ||
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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) |
| + | </math> | ||
| + | <math> | ||
\mbox{subject to} \ \ x_A+x_B=1 | \mbox{subject to} \ \ x_A+x_B=1 | ||
</math> | </math> | ||
Revision as of 23:47, 2 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 \(x_A\) and the remaining funds into TEXACO (denote it with \(x_B\)) - so \(x_A+x_B=1\). The resulting portfolio will be \(x_A R_A+x_B R_B\), where \(R_A\) is the monthly return of \(IBM\) and \(R_B\) 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\[ \mbox{Minimize} \ \ mbox{Var}(x_A R_A+x_BR_B) \] \( \mbox{subject to} \ \ x_A+x_B=1 \)
