Loop with Time series

Dear all, I'm currently trying to build a Global minimum Variance Portfolio that changes over time. I have a timetable of several daily returns of 8 assets, and I want lo calculate the global minimum variance portfolio for that given month. I tried with imposing 21 as the number of days in a month, however this is not optimal, since months also have 22 and 23 days. Is it possible to create a loop where I link the groups to the belonging month?

Brief example: I have 5208 daily returns, assuming that every month has 21 days the output should be a 248x8 matrix

Thank you all

Answer 1

[Voss]

You can use the month and year functions, along with findgroups, to group the timetable by year and month. Then splitapply to perform some function (e.g., your method to "calculate the global minimum variance portfolio") on each month's data.

% construct a timetable like yours, containing (random)
% daily returns of 8 assets over 5208 days:
n_days = 5208;
n_assets = 8;
temp = num2cell(randn(n_days,n_assets),1);
t = timetable(datetime(now()-(n_days-1:-1:0).', ...
    'ConvertFrom','datenum','Format','dd-MMM-yyyy'),temp{:})

t = 5208×8 timetable
       Time          Var1         Var2         Var3         Var4        Var5        Var6        Var7        Var8   
    ___________    _________    _________    _________    ________    ________    ________    ________    _________

    24-Jun-2009      -0.8481      0.71243       0.5571     -1.0396      1.4287    0.060597      1.9732      0.73235
    25-Jun-2009      0.17632    -0.099614      -1.3244       1.597      1.2128     -2.7768      1.1392    -0.031456
    26-Jun-2009      -1.1902      -2.3053      -0.1268     0.47073     0.54342     0.93671    -0.77996       1.9441
    27-Jun-2009      -1.3209       1.4919    -0.058169     -3.1413     0.29271     0.67738    -0.41053      -1.9958
    28-Jun-2009       1.1728      -0.7338       1.5726     -0.1833     0.46258      1.1811    -0.14591      -2.6423
    29-Jun-2009     -0.61775     -0.67265      -1.3583     -1.0131     -1.8862     0.86179     0.77355     -0.77497
    30-Jun-2009       1.6884    -0.072801       0.5692      1.3678    -0.89934     0.09098      1.1243      -2.0821
    01-Jul-2009       2.0786      0.26348      0.58298     0.14293      1.0838    -0.68792     -1.3042       1.1386
    02-Jul-2009      -1.0093      0.76961       0.3776     0.89128    -0.82922    -0.67901     0.53186     -0.81903
    03-Jul-2009      -1.1324      0.24465      -1.2842    0.052565      2.3662      1.7737      1.5313       1.4701
    04-Jul-2009       1.6285      0.20871      0.75007     0.14514    -0.52201      1.8578     0.45132      0.66033
    05-Jul-2009    -0.076449      0.59771     -0.11854     -1.9007    -0.10417    -0.24515    -0.79338      0.47538
    06-Jul-2009     -0.34889      0.76339    -0.058678     -0.8654     -0.6213     0.84136     0.61626      0.54069
    07-Jul-2009      0.48528      0.42656      -2.5592    0.026154     0.19026     0.30093       2.256      -2.0029
    08-Jul-2009      0.67997      0.98076      -1.0043      1.4066     0.11917    -0.53833      2.1094     -0.13361
    09-Jul-2009     -0.12264      -1.0469      0.53019      1.3641      1.6656     0.15018      2.2481      -1.1163

% group returns by year and month
mm = month(t.Time);
yy = year(t.Time);
g = findgroups(yy,mm);

% apply a function on each group (i.e., each month+year)
% the function get_max_return() here calculates the maximum
% value amongst all the returns of that group
tC = splitapply(@(varargin)get_max_return(varargin{:}),t,g)

tC = 172×1

1.9732 2.3662 2.3034 2.7011 3.2285 3.0647 2.9996 3.3741 2.8999 2.8206

function out = get_max_return(varargin)
out = max([varargin{:}],[],'all');
end