added lec3_4 & ex03

exercises/ex03/optriskreward.mod

+reset;
+
+set A;   		# asset categories
+set T := {1973..1994}; 	# years
+
+param lambda default 200;
+
+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:
+    lambda *
+    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  
+;
+
+#option solver snopt;
+#option solver ipopt;
+#option solver cbc;
+option solver cplex;
+#option solver gurobi;
+
+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 = %10.7f \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);