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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 04:40, 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(RA) = 0.010, E(RB) = 0.013, Var(RA) = 0.0061, Var(RB) = 0.0046, and Cov(RA,RB) = 0.00062. We first want to minimize the variance of the portfolio. This will be:
