# Objective: convex quadratic 
# Constraints: linear 

set A;   		# asset categories
set T := {1973..1994}; 	# years

param mu default 2;

param R {T,A};

param mean {j in A}
    := ( sum{i in T} R[i,j] )/card(T);

param Rtilde {i in T, j in A}
    := R[i,j] - mean[j];

param Cov {j in A, k in A}
    := sum {i in T} (Rtilde[i,j]*Rtilde[i,k]) / card(T);

param Corr {j in A, k in A}
    := Cov[j,k]/sqrt(Cov[j,j]*Cov[k,k]);

var x{A} >=0; 

minimize lin_comb:
    mu *
    sum{i in T} (sum{j in A} Rtilde[i,j]*x[j])^2 / card{T}
    - 
    sum{j in A} mean[j]*x[j]
    ;

subject to tot_mass:
    sum{j in A} x[j] = 1;

data;

set A := 
    US_3-MONTH_T-BILLS US_GOVN_LONG_BONDS SP_500 WILSHIRE_5000 NASDAQ_COMPOSITE
    LEHMAN_BROTHERS_CORPORATE_BONDS_INDEX EAFE GOLD;   

param R:
US_3-MONTH_T-BILLS US_GOVN_LONG_BONDS SP_500 WILSHIRE_5000 NASDAQ_COMPOSITE 
LEHMAN_BROTHERS_CORPORATE_BONDS_INDEX EAFE GOLD :=
1973  1.075  0.942  0.852  0.815  0.698  1.023  0.851  1.677 
1974  1.084  1.020  0.735  0.716  0.662  1.002  0.768  1.722 
1975  1.061  1.056  1.371  1.385  1.318  1.123  1.354  0.760 
1976  1.052  1.175  1.236  1.266  1.280  1.156  1.025  0.960 
1977  1.055  1.002  0.926  0.974  1.093  1.030  1.181  1.200 
1978  1.077  0.982  1.064  1.093  1.146  1.012  1.326  1.295 
1979  1.109  0.978  1.184  1.256  1.307  1.023  1.048  2.212 
1980  1.127  0.947  1.323  1.337  1.367  1.031  1.226  1.296 
1981  1.156  1.003  0.949  0.963  0.990  1.073  0.977  0.688 
1982  1.117  1.465  1.215  1.187  1.213  1.311  0.981  1.084 
1983  1.092  0.985  1.224  1.235  1.217  1.080  1.237  0.872 
1984  1.103  1.159  1.061  1.030  0.903  1.150  1.074  0.825 
1985  1.080  1.366  1.316  1.326  1.333  1.213  1.562  1.006 
1986  1.063  1.309  1.186  1.161  1.086  1.156  1.694  1.216 
1987  1.061  0.925  1.052  1.023  0.959  1.023  1.246  1.244 
1988  1.071  1.086  1.165  1.179  1.165  1.076  1.283  0.861 
1989  1.087  1.212  1.316  1.292  1.204  1.142  1.105  0.977 
1990  1.080  1.054  0.968  0.938  0.830  1.083  0.766  0.922 
1991  1.057  1.193  1.304  1.342  1.594  1.161  1.121  0.958 
1992  1.036  1.079  1.076  1.090  1.174  1.076  0.878  0.926 
1993  1.031  1.217  1.100  1.113  1.162  1.110  1.326  1.146 
1994  1.045  0.889  1.012  0.999  0.968  0.965  1.078  0.990 
;

solve;

display Corr;

printf: "-------------------------------------------------------------------\n";
printf: "                                      Asset       Mean    Variance \n";
printf {j in A}: "%45s %10.7f %10.7f \n", 
    j, mean[j], sum{i in T} Rtilde[i,j]^2 / card(T);

printf: "\n";
printf: "Optimal Portfolio:                    Asset       Fraction \n";
printf {j in A: x[j] > 0.001}: "%45s %10.7f \n", j, x[j];

printf: "Mean = %10.7f, Variance = %10.5f \n",
    sum{j in A} mean[j]*x[j],
    sum{i in T} (sum{j in A} Rtilde[i,j]*x[j])^2 / card(T);