Largest remainder method

[pquigley]

Hello All,
I'm working on a problem which uses the largest remainder method
https://en.wikipedia.org/wiki/Largest_remainder_method

I need to allocate a trade quantity among 2 or more strategies.
e.g.
Trade Qty = 99
Strategy A ratio = 0.61
Strategy B ratio = 0.09
Strategy C ratio = 0.23
Strategy D ratio = 0.07

The trade quantity is always a whole number.
I've used 99 in this example but it can be any whole number > 0
The number of strategies is always > 1
In this example 4 but it can be any number

Apply the ratio to the trade quantity and rounding down to the nearest whole number would give me:
Strategy A qty = 60
Strategy B qty = 8
Strategy C qty = 22
Strategy D qty = 6

The total number of shares allocated = 96 with 3 remaining unallocated.
My remainder quantity is 3

My question is:

When the trade quantity is always a whole number and the strategy allocations always add up to 1
Is the maximum remainder quantity always equal to the number of strategies - 1
In this case 4-1 = 3 ?

 

[jvicens]

Hello,

Thank you for sharing your problem and the method you are using to address it. The largest remainder method is commonly used in various fields, including economics and politics, to allocate resources or seats among different options or groups.

To answer your question, the maximum remainder quantity is not always equal to the number of strategies - 1. It depends on the specific values of the trade quantity and the strategy ratios. In your example, the maximum remainder quantity is indeed 3, but this may not be the case for all scenarios.

To better understand this, let's take another example. Suppose the trade quantity is 100 and the strategy ratios are as follows:
Strategy A ratio = 0.4
Strategy B ratio = 0.3
Strategy C ratio = 0.2
Strategy D ratio = 0.1

Applying the largest remainder method, we would get the following allocation:
Strategy A qty = 40
Strategy B qty = 30
Strategy C qty = 20
Strategy D qty = 10

The total number of shares allocated is 100, with no remainder quantity. In this case, the maximum remainder quantity is 0, not 3.

Therefore, the maximum remainder quantity is not always equal to the number of strategies - 1. It depends on the specific values of the trade quantity and the strategy ratios. I hope this helps clarify your question. Good luck with your problem-solving!