Discrete Allocation

Calculate how many whole shares to buy of each asset to hold weights with a portfolio value, at the latest traded (split-adjusted) closing price. Weights rarely come out in whole shares, so some cash is left over and the weights held differ a little from the targets; the smaller the portfolio value compared to the share prices, the larger the difference. With t_i = w_i V the target amount of asset i and p_i its price:

• method=”integer”: the number of shares n_i that minimizes the absolute deviation from the target amounts with the leftover cash c counted as a holding with a target of zero, min Σ |t_i - n_i p_i| + c with Σ n_i p_i + c = V and c ≥ 0, solved as an integer programme (Cornuejols, Peña and Tütüncü, 2018).
• method=”greedy”: every position is first rounded down to whole shares and the leftover cash then buys one more share at a time of the asset furthest below its target amount, while its price fits the cash. Quick and close to the integer programme, which can do better by leaving out a share of one asset to buy more of another.

A short weight becomes a negative number of shares, with the proceeds funding the long positions: weights that sum to one keep a net investment of the portfolio value. Short positions are rounded to a larger short, so the leftover cash is never negative.

For more information, see the following book:

• Cornuejols, G., Peña, J. and Tütüncü, R. (2018). “Optimization Methods in Finance.” 2nd edition, Cambridge University Press.

Also known as: share allocation, whole share rounding, lot sizing, order sizes.

Discrete Allocation in Python

Install the Finance Toolkit with:

pip install financetoolkit -U

Then call get_discrete_allocation as shown below.

from financetoolkit import Toolkit

toolkit = Toolkit(
    ["AAPL", "MSFT", "JNJ", "XOM"],
    api_key="FINANCIAL_MODELING_PREP_KEY",
    start_date="2021-01-01",
    end_date="2025-12-31",
)

weights = toolkit.portfolio.get_maximum_sharpe_weights()["Weight"]

toolkit.portfolio.get_discrete_allocation(
    weights=weights.drop("Portfolio").to_dict(), portfolio_value=25000
)

Which returns:

Parameters

get_discrete_allocation accepts the following parameters.

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