% Fichier estim.m
% auteur: Pascal St-Amour, février 2001
% objectif: test du CAPM, alpha de Jensen.
% données CRSP
%	monthly, 1959:1 1992:12
%
%              SICC_1    SICC_2    SICC_3    SICC_4    SICC_5        M2


load DATA;
r1 = DATA(:,1); r2 = DATA(:,2); r3 = DATA(:,3);
r4 = DATA(:,4); r5 = DATA(:,5); rm = DATA(:,6);
n = length(r1);
Y = [ ...
    r1;
    r2;
    r3;
    r4;
    r5];
% Modele non-contraint
x = [ones(n,1), rm];
X = [ ...
        x zeros(n,2) zeros(n,2) zeros(n,2) zeros(n,2);
        zeros(n,2) x zeros(n,2) zeros(n,2) zeros(n,2);
        zeros(n,2) zeros(n,2) x zeros(n,2) zeros(n,2);
        zeros(n,2) zeros(n,2) zeros(n,2) x zeros(n,2);
        zeros(n,2) zeros(n,2) zeros(n,2) zeros(n,2) x;
    ];
beta = (X'*X)\(X'*Y);   beta_u = beta;
e_u = Y - X*beta;
sig_u = var(e_u);
STD = sqrt(diag(sig_u*inv(X'*X)));
TSTAT = beta./STD;
warning off
SSR_u = sum(e_u.^2);
disp('Modele non-contraint')
disp('  beta    STD     TSTAT')
disp([beta STD TSTAT])
[b,bint,r,rint,stats] = regress(Y,X);
disp('  beta    beta_min    beta_max')
disp([b,bint])
% Modele contraint
x = [rm];
X = [ ...
        x zeros(n,1) zeros(n,1) zeros(n,1) zeros(n,1);
        zeros(n,1) x zeros(n,1) zeros(n,1) zeros(n,1);
        zeros(n,1) zeros(n,1) x zeros(n,1) zeros(n,1);
        zeros(n,1) zeros(n,1) zeros(n,1) x zeros(n,1);
        zeros(n,1) zeros(n,1) zeros(n,1) zeros(n,1) x;
    ];
beta = (X'*X)\(X'*Y);   beta_r = beta;
e_r = Y - X*beta;
sig_r = var(e_r);
STD = sqrt(diag(sig_r*inv(X'*X)));
TSTAT = beta./STD;
SSR_r = sum(e_r.^2);
disp('Modele contraint')
disp('  beta    STD     TSTAT')
disp([beta STD TSTAT])
[b,bint,r,rint,stats] = regress(Y,X);
disp('  beta    beta_min    beta_max')
disp([b,bint])
F = ((SSR_r - SSR_u)/5) /(SSR_u / (n-10))
p_value = finv(F,5,n-10)
save estim_out
plot(beta_r,mean([r1,r2,r3,r4,r5])','.')
xlabel('beta')
ylabel('rendement espere')
% Output
% Modele non-contraint
%   beta    STD     TSTAT
%     0.0011    0.0011    0.9942
%     0.9360    0.0257   36.4008
%     0.0001    0.0011    0.1005
%     1.0317    0.0257   40.1224
%     0.0008    0.0011    0.7258
%     0.7230    0.0257   28.1188
%     0.0012    0.0011    1.0198
%     1.1123    0.0257   43.2573
%     0.0003    0.0011    0.2964
%     1.0642    0.0257   41.3886
% 
%   beta    beta_min    beta_max
%     0.0011   -0.0011    0.0034
%     0.9360    0.8854    0.9865
%     0.0001   -0.0021    0.0024
%     1.0317    0.9811    1.0822
%     0.0008   -0.0014    0.0031
%     0.7230    0.6725    0.7736
%     0.0012   -0.0011    0.0034
%     1.1123    1.0617    1.1628
%     0.0003   -0.0019    0.0026
%     1.0642    1.0137    1.1148
% 
% Modele contraint
%   beta    STD     TSTAT
%     0.9384    0.0256   36.6611
%     1.0319    0.0256   40.3129
%     0.7248    0.0256   28.3158
%     1.1148    0.0256   43.5510
%     1.0650    0.0256   41.6037
% 
%   beta    beta_min    beta_max
%     0.9384    0.8882    0.9887
%     1.0319    0.9816    1.0822
%     0.7248    0.6745    0.7751
%     1.1148    1.0645    1.1651
%     1.0650    1.0147    1.1152
% 
% 
% F =
% 
%     0.1035
% 
% 
% p_value =
% 
%     0.3271