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Data
• Time-series Regressions
• CAPM
R −R + (R −R ) +
it f i i mt f it
• FF3F Model
R −R + (R −R ) +s smb +h hml +
it f i i mt f i t i t it
Part I CAPM
% loading data
x = load('25_Portfolios_5x5.txt');
T1 = size(x,1);
labels = { 's1v5' 's1v4' 's1v3' 's1v2' 's1v1' ...
's2v5' 's2v4' 's2v3' 's2v2' 's2v1' ...
's3v5' 's3v4' 's3v3' 's3v2' 's3v1' ...
's4v5' 's4v4' 's4v3' 's4v2' 's4v1' ...
's5v5' 's5v4' 's5v3' 's5v2' 's5v1'};
x = load('F-F_Research_Data_Factors.txt');
x = x(st:st-1+size(r,1),:);
rmrf = x(1:en2,2);
smb = x(1:en2,3);
hml = x(1:en2,4);
rf = x(1:en2,5);
dates = x(1:en2,1);
dates = floor(dates/100)+(dates-100*floor(dates/100))*1/12; % turns
192603 in to 1926+3/12;
Part I CAPM
% loading data
T = length(rmrf);
N = size(r,2);
rx = r-rf*ones(1,N);
%CAPM
f = [rmrf];
[alpha, beta, R2, siga, sigb] = tsregress(rx,f);
Part I CAPM
• tsregress.m function:
function [alpha, beta, R2, siga, sigb] = tsregress(rx,f);
T = size(rx,1);
N = size(rx,2);
K = size(f,2);
if size(f,1) ~= size(rx,1);
disp('tsregress error: factors and returns must be of same
length');
end;
X = [ones(T,1) f];
b = X\rx;
u = rx-X*b;
s2 = var(u)'*(T-1)/(T-K-1); % produces a vector, variance of the
25 errors
Part I CAPM
• tsregress.m function( ):
mx = inv(X'*X);
dmx = diag(mx); % we're interested in standard errors, the
diagonals of the covariance matrix of bs
siga = (s2*dmx(1)).^0.5; % standard error
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