In the March 1952 issue of Journal of Finance, Harry M. Markowitz published an article titled Portfolio Selection. In the article, he demonstrates how to reduce the risk of asset portfolios by selecting assets whose values aren't highly correlated. The following model implements these ideas in constructing a simple portfolio with three assets. A detailed discussion of this model may be found in Developing More Advanced Models.

MODEL:

! GENPRT: Generic Markowitz portfolio;

SETS:

 ASSET/1..3/: RATE, UB, X;

 COVMAT( ASSET, ASSET): V;

ENDSETS

DATA:

! The data;

!  Expected growth rate of each asset;

 RATE = 1.3   1.2  1.08;

!  Upper bound on investment in each;

 UB   = .75   .75   .75;

!  Covariance matrix;

 V    =   3     1   -.5

          1     2   -.4

        -.5   -.4     1;

!  Desired growth rate of portfolio;

 GROWTH = 1.12;

ENDDATA

 

! The model;

! Min the variance;

[VAR] MIN = @SUM( COVMAT( I, J):

             V( I, J) * X( I) * X( J));

! Must be fully invested;

[FULL] @SUM( ASSET: X) = 1;

! Upper bounds on each;

@FOR( ASSET: @BND( 0, X, UB));

! Desired value or return after 1 period;

[RET] @SUM( ASSET: RATE * X) >= GROWTH;

END

Model: GENPRT