Numpy - generate random array with restrictions on individual values in array - Portfolio Optimisation

Question

I'm developing a portfolio optimisation code with constraints using monte-carlo simulation. However, I have run into a problem. My problem is as follows:

I have a list of instruments ["Multi", "Equity 1", "Equity 2", "Equity 3", "FI", "Cash"]

And I would like to generate a list of random numbers for these instruments e.g.

weights (random numbers) = [xx, xx, xx, xx, xx, xx]

However, with multiple constraints such as :

All weights between 0.05 and 0.20.
Weight of say "Cash" must be between 0 and 0.10 (i.e. the 0<= weights[-1] <= 0.10)
Weight of "Equity 1" has to be 0.15 (i.e. weights[1] = 0.15)

Is there anyway that I can generate random numbers that satisfy all these criteria? and of course the sum of all weights must be equal to one.

Thank you all for your help!

What decimal precision do you need the weights to be ? e.g 0.15 , two decimal places or 0.15689754 8-decimal places , etc ? — Kenneth
– Kenneth, Commented Sep 24, 2020 at 11:37
I don't care about decimal precision in that sense, just a way to enforce these constraints in the weights (random numbers). — Dazz W
– Dazz W, Commented Sep 24, 2020 at 16:08

prody · Accepted Answer · 2020-09-24 11:28:36Z

You can generate the numbers one by one, computing at each step the total sum of the weights you already got. I will use random.randint function for my demonstration.

import random

weights_name = ["Multi", "Equity 1", "Equity 2", "Equity 3", "FI", "Cash"]
weights = [0] * 6

weights[1] = 0.15  # Equity 1 weight
remaining = 0.85 # the sum of the remaining weights

x = random.randint(0, 100)
weights[-1] = x/1000 # Cash weigth
remaining -= weights[-1]

So for the remaining weigths, you have to generate random values such that the last one wouldn't be larger than 0.2.

last_weight = remaining
while last_weight > 0.2:
    last_weight = remaining
    for i in [0, 2, 3]:
        weights[i] = 0.05 + random.randint(0, 150)/1000 # generating a random no between 0.05 and 0.20
        last_weight -= weights[i]
weights[4] = last_weight
for w in weights:
    print(w)

My output:

0.2
0.15
0.176
0.196
0.18200000000000005
0.096

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