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(New page: \begin{center} Portfolio theory \end{center} \noindent An investor has a certain amount of dollars to invest into two stocks ($IBM$ and $TEXACO$). A portion of the available funds will b...) |
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| - | + | == Portfolio theory == | |
| - | Portfolio theory | + | |
| - | + | An investor has a certain amount of dollars to invest into two stocks (<math>IBM</math>I and $<math>TEXACO</math>. A portion of the available funds will be invested into | |
| - | + | IBM (denote this portion of the funds with <math>x_A</math> and the remaining funds | |
| - | ( | + | into TEXACO (denote it with <math>x_B</math>) - so <math>x_A+x_B=1$</math>. The resulting portfolio |
| - | IBM (denote this portion of the funds with | + | |
| - | into TEXACO (denote it with | + | |
will be $x_A R_A+x_B R_B$, where $R_A$ is the monthly return of $IBM$ and $R_B$ is the | 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 | monthly return of $TEXACO$. The goal here is to | ||
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\mbox{subject to} \ \ x_A+x_B=1 | \mbox{subject to} \ \ x_A+x_B=1 | ||
\end{eqnarray*} | \end{eqnarray*} | ||
| + | <math>Insert formula here</math> | ||
| + | <math>Insert formula here</math> | ||
Revision as of 04:22, 3 August 2008
Portfolio theory
An investor has a certain amount of dollars to invest into two stocks (IBMI 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 $x_A R_A+x_B R_B$, 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*} Insertformulahere Insertformulahere
