Difference between revisions of "SOCR EduMaterials Activities ApplicationsActivities Portfolio"
| Line 8: | Line 8: | ||
find the most efficient portfolios given a certain amount of risk. | find the most efficient portfolios given a certain amount of risk. | ||
Using market data from January 1980 until February 2001 we compute | Using market data from January 1980 until February 2001 we compute | ||
| − | that | + | that <math>E(R_A)=0.010</math>, <math>E(R_B)=0.013</math>, <math>Var(R_A)=0.0061</math>, <math>Var(R_B)=0.0046</math>, and |
| − | + | <math>Cov(R_A,R_B)=0.00062</math>. We first want to minimize the variance of the portfolio. This will be: | |
| − | We first want to minimize the variance of the portfolio. | ||
| − | This will be: | ||
<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 23:46, 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\[ \mbox{Minimize} \ \ mbox{Var}(x_A R_A+x_BR_B) <br> \mbox{subject to} \ \ x_A+x_B=1 \]
