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

set T years   /1973*1994/;

parameter s_max # i.e. a 5.522 percent std. deviation on reward ;
s_max= 0.00305;

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 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  reward;

equation tot_mass,
         risk_bound ,
         defobj  ;

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

model optreward /all/;
solve optreward  using nlp minimizing reward;

file dem /output/;  put dem;
Put "reward  = ", reward.l:20:10; Put /;Put /;
Put "item         x       "; Put /;
Loop(A,put A.tl:8 Put x.l[A]:12:7  /;);
put "----------------------------------------------"; Put /;
put "              Asset          Mean    Variance "; Put /;

  loop(A,
put "           ",put A.tl:10,mean[A]:12:4,
 sum{T,(sqr(Rtilde[T,A])/card(T))}:12:4 ;
  Put /;); Put /;

put "Optimal Portfolio:    Asset             Fraction "; Put /;
loop(A$(x.l[A]>0.001),put "                      ",
put  A.tl:15, put x.l[A]:10:5, Put /;  );

Put /;
put "        Mean = ", sum{A,mean[A]*x.l[A]}:10:4,
    "    Variance = ",(sum{T,sqr(sum{A,Rtilde[T,A]*x.l[A]})}/card(T)):10:5;