# Qiskit sample - Portfolio optimization

I've recently tried to run this sample from Qiskit (Portfolio Optimization)

I was able to change RandomDataProvider to YahooDataProvider and able to run it on real stock prices.

However, there is one peculiar challenge I'm facing - I'm not sure if it is my lack of understanding. At this particular code

budget = num_assets // 2  # set budget
penalty = num_assets      # set parameter to scale the budget penalty term
qubitOp, offset = portfolio.get_operator(mu, sigma, q, budget, penalty)


No matter what budget or penalty I set this to, I always receive portfolio with about half of the total number of assets. For example, if my total number of assets is 5, then my budget is 2 (from above code). The result always contains 2 assets [0 0 1 1 0]

If I change my budget to

budget = num_assets // 3


and my total assets are 5, then I expect to see only 1 asset in the resulting portfolio. However, I see 2

If I increase my num_assets to 10 and make

budget = num_assets


I still get a portfolio of 5 or 6 stocks (close to half of 10) and not a portfolio of 10.

Note - I'm running on qasm_simulator

Is there a gap in my understanding? What role do these variables - budget and penalty - play while building the portfolio?

• As @tsgeorgios pointed out, the constraint is added as a penalty term. If you change the data source, you may need to adjust the penalty factor and increase it. The penalty factor must be large enough to enforce the constraint. Sep 6, 2020 at 10:57

## 2 Answers

The budget constraint is only added as a penalty term (multiplied by ‘penalty’ coefficient) in the Hamiltonian and does not enforce equality. This means the objective function is $$\text{min}_{x\in\{0,1\}^n} \hspace{0.5em} q x^T \Sigma x - \mu^T x + \text{penalty} \cdot (B - 1^T x)^2$$

Well you can fix it also. Like if you want to take 3 assets. THEN TAKE BUDGET=3. [BUDGET IS THE NO OF ASSETS U WANT TO SELECT OUT OF TOTAL ASSETS(num_assets)]

Now your number of assets can be 5, 10, 20 , etc. It will take and give out optimal value : By SELECTING 3 ASSETS.