## matlabtest01.m

listpX0 = 1;
doMatLabTest01 = 0;

## get 2014 data
oneBdata2014;  # funds, assets, adjclose

## funds
n = rows(funds);  # n = 243
tickers = funds(:, 1:4);
names = funds(:, 8 : columns(funds));

## adjusted closing prices and dates
M = rows(adjclose);  # M = 253
unixtime = adjclose(:, 1);
adjclose(:, 1) = [];
growth = adjclose(M, :) ./ adjclose(1, :);
date = zeros(0, 10);
for i = 1 : length(unixtime)
  date = [date; strftime("%Y-%m-%d", localtime(unixtime(i)))];
endfor

## normalized adjusted closing price differences
R0 = diff(adjclose) * diag(1 ./ adjclose(1, :));

## do rtndecomp and minnormy
pput = 252;  # market days per year
[E, F, f0] = rtndecomp(R0, 0, pput);
P = minnormy(F);
nP = columns(P);
EP = E * P;

## covariance and standard deviation of return
V = f0 ^ 2 + F' * F;
Sig = sqrt(diag(V))';
condition_V = cond(V);  # condition_V = 1.2734e+08

## get the efficient portfolio pX with 15% total return in 2014
eX = 0.15;
k0 = nP;
while EP(k0) >= eX
  k0--;
endwhile
k1 = k0 + 1;
t0 = (EP(k1) - eX)/(EP(k1) - EP(k0));
t1 = 1 - t0;
pX0 = P(:, k0) * t0 + P(:, k1) * t1;
JX = [1 : n](pX0 > 0);

## list efficient, 2013-12-31-close portfolio pX0
if listpX0
  printf("The efficient, 2013-12-31-close portfolio with return %.2f%% in 2014.\n", 100 * eX);
  printf("This portfolio was selected from 243 exchange traded funds/notes with\n");
  printf("at least $1 billion in assets under management at the end of 2014.\n");
  printf("The funds are listed in decreasing order of assets under management.\n");
  for j = JX
    printf("%3d.  %.5f  %-s\n", j, pX0(j), deblank(funds(j, :)));
  endfor
endif


#### MatLab test ####
# as per
# http://www.mathworks.com/help/finance/estimate-efficient-portfolios_bswmb3d-1.html
if doMatLabTest01
  pM = Portfolio;
  pM = setAssetMoments(pM, E', V);
  pM = setDefaultConstraints(pM);
  pMwgt = estimateFrontierByReturn(pM, eX);
endif
## The portfolio pMwgt should be (approximately) the same as pX0 above.