Difference between revisions of "SOCR EduMaterials Activities ApplicationsActivities Portfolio"
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We first want to minimize the variance of the portfolio. | We first want to minimize the variance of the portfolio. | ||
This will be: | This will be: | ||
| + | |||
<math> | <math> | ||
| − | \mbox{Minimize} Var(x_A R_A+x_BR_B) \\ | + | \begin{eqnarray*} |
| − | subject \ | + | \mbox{Minimize} \ \ \mbox{Var}(x_A R_A+x_BR_B) \\ |
| + | \mbox{subject to} \ \ x_A+x_B=1 | ||
| + | \end{eqnarray*} | ||
</math> | </math> | ||
| − | |||
| − | |||
<math>Insert formula here</math> | <math>Insert formula here</math> | ||
Revision as of 23:34, 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\[ \begin{eqnarray*} \mbox{Minimize} \ \ \mbox{Var}(x_A R_A+x_BR_B) \\ \mbox{subject to} \ \ x_A+x_B=1 \end{eqnarray*} \] \(Insert formula here\)
