# AMPL Model by Vivek S. Mahanta
#
# Copyright (C) 2008 Drexel University
# All Rights Reserved
#
# Permission to use, copy, modify, and distribute this software and
# its documentation for any purpose and without fee is hereby
# granted, provided that the above copyright notice appear in all
# copies and that the copyright notice and this
# permission notice appear in all supporting documentation.                     

#   Source: 
#   Matthias Ehrgott, Rafail N. Gasimov',"Multiobjective Programming and 
#   Multiattribute Utility Functions in Portfolio Optimization"






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

param Ret default 0.05;
param M default 100;
param k default 5;
param Wmin default 0.05;

param R {T,A};
param P{A}; # Price of the assets
param u {j in A}
	:= (sum{i in T} R[i,j])/card(T);

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

var t >= 0;
var w{A} >= 0;
var d{A} binary;

#param uw
#	:= sum{j in A} u[j]*w[j];

#param wQw
#	:= sum{i in T} (sum{j in A} Rtilde[i,j]*w[j])^2/(card(T) - 1);

# param y {j in A} integer;

minimize risk: t;

subject to prob_const:
	(sum{j in A} u[j]*w[j]) - (sum{i in T} (sum{j in A} Rtilde[i,j]*w[j])^2/(card(T) - 1))^0.5 >= Ret;

subject to t_const:
	t >= (sum{i in T} (sum{j in A} Rtilde[i,j]*w[j])^2/(card(T) - 1))^0.5;

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

subject to w_d {j in A}:
	w[j] <= d[j];

subject to wmin_d {j in A}:
	Wmin*d[j] <= w[j];

subject to count_assets:
	sum{j in A} d[j] = k;


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  
;


param P:=
	US_3-MONTH_T-BILLS 100
	US_GOVN_LONG_BONDS 32
	SP_500 78
	WILSHIRE_5000 56
	NASDAQ_COMPOSITE 43
	LEHMAN_BROTHERS_CORPORATE_BONDS_INDEX 100
	EAFE 55
	GOLD 78;

solve;

display t,d, w;

printf: "Return = %10.7f \n", sum{j in A} u[j]*w[j]*P[j];