set A asset categories
/   US_3_MONTH
    US_GOVN
    SP_500
    WILSHIRE
    NASDAQ
    LEHMAN
    EAFE
    GOLD  / ;

set T years   /1973*1994/;

table R[T,A]
      US_3_MONTH   US_GOVN   SP_500   WILSHIRE  NASDAQ  LEHMAN   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
;
parameter r_min  i.e., at least 10 percent return;  r_min=1.10;
parameter mean[A];     mean[A]=sum{T,R[T,A]}/card(T);
parameter Rtilde[T,A]; Rtilde[T,A]=R[T,A] - Mean[A];

alias (A,A1);
parameter Cov[A,A1];   Cov[A,A1]=sum{T,(Rtilde[T,A1]*Rtilde[T,A1])}/card[T];
parameter Corr[A,A1];  Corr[A,A1]=Cov[A,A1]/sqrt(Cov[A,A1]*Cov[A,A1]);

positive variable  x(A);
         variable  risk;

equation tot_mass,
         reward  ,
         defobj  ;

defobj..     risk        =e= sum{T,sqr(sum{A,Rtilde[T,A]*x[A]})/card[T]};
reward..     r_min       =l= sum{A,mean[A]*x[A]};
tot_mass..   sum{A,x[A]} =e= 1                  ;

model optrisk /all/;
solve optrisk  using nlp minimizing risk;