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stock-investment-split

Introduction

Creating this project to solve personally encountered problem of how much to invest in each stock out of a basket to achieve a target % allocation for each stock.

Example

Let's say you have invested in 3 stocks (or any other instruments for that matter) viz. INFOSYS, TCS and WIPRO. Your initial investment in as follows:

Instrument Initial Investment Initial Investment % Target Investment %
INFOSYS ₹30 30% 33%
TCS ₹50 50% 33%
WIPRO ₹20 20% 34%

Now, you want to invest an additional sum of $₹30$ in such a way that your investment in each of these stocks reach closer to their respective target investment %. So, how much should you invest in each of these three stocks?

If we assume that we invest $₹10$ in INFOSYS, $₹5$ in TCS and $₹15$ in WIPRO, then the allocation % would become:

Instrument Allocation %
INFOSYS 30.7%
TCS 42.3%
WIPRO 26.9%

However, these might not be the most optimal allocation. Our objective here is to find the most optimal allocation.

Running the code gives that we should split the amount of $₹30$ equally across all instruments:

>> python -m src.views.file
Optimizing the MSE to compute optimal allocation. Sit tight!
Final allocation of investment of unit 30 is as follows:
Instrument Initial

Investment

%		 Target

Investment

%		 Suggested

Investment		 Final

%
INFOSYS 30 33 10 30.7692
TCS 50 33 10 46.1538
WIPRO 20 34 10 23.0769

Mathematics

You have a portfolio of $n$ financial instruments: $[F_1, F_2, ..., F_i, ..., F_n]$ and your current investments in each financial instrument is: $[I_1, I_2,..., I_i, ..., I_n]$.

This means that your current investment allocation ratio (between $0$ and $1$) is $[{I_1 \over SI}, {I_2 \over SI}, ..., {I_i \over SI}, ..., {I_n \over SI}]$ where $SI = \sum_{i=1}^nI_i$.

Now, suppose you want to invest an additional amount of $SN$ split between these $n$ financial instruments. You want to achieve a target allocation ratio of $[T_1, T_2, ..., T_i, ..., T_n]$ for each of these instruments.

This implies that:

${(I_1 + N_1) \over (SI + SN)} = T_1,\ {(I_2 + N_2) \over (SI + SN)} = T_2,\ ...\ {(I_i + N_i) \over (SI + SN)} = T_i,\ ...\ {(I_n + N_n) \over (SI + SN)} = T_n$

where, $N_i$ is the new investment allocated to instrument $F_i$ and our objective is to find out these $N_i$. And, $SN = \sum_{i=1}^nN_i$ i.e. new investment that you want to make.

To solve this problem, we have converted it into an optimizing problem. If we assume some initial allocation for each instrument and calculate the Mean Squared Error ($MSE$) between the objective allocation ratio and actual allocation ratio. Then, we can simply use any (bounded and constrained, explained later) optimizing tool to solve the problem.

So, $MSE = {1 \over n} \sum_{i=1}^n ({(I_i + N_i) \over (SI + SN)} - T_i)^2$

And, we can minimize this function to find all $N_i$.

Assumptions

  • No selling. The whole point of writing this code is that we don't want to sell any existing instruments to adjust to the target allocation.
  • We assume that we would want to invest whole amount of new_investment i.e. if you input $₹30$ as new investment to be allocated, the model would try to allocate the full amount between the instruments.
  • We don't solve for the problem in a rigorous way. The correct way would be create $n$ equations for $n$ variables and solve them using some equation solver. However if that were easy, we wouldn't have invented Machine Learning. So, we instead solve the problem by minimizing the MSE between target and actual instrument allocation using a minimizer function (similar to how Gradient Descent would minimize error function in Machine Learning).

How to use?

Right now there are two ways of using the code. But first setup a virtual environment and install the requirements using pip install poetry and then, poetry install command. If there's an interest and people find it useful, I can build a simple UI for usage.

Using file

If you wish to easily change values to play around, you can directly modify the file src/views/file.py. It already contains example values from the README file. To run the code, run command python -m src.views.file from project directory.

Using Terminal

If you do not wish to temper with any file, simply run code python -m src.views.terminal and follow the terminal instructions. Example usage given below:

>> python -m src.views.terminal
Please add identifier/names of financial instruments separated by comma(,)
INFOSYS,TCS,WIPRO
Please add initial investment (all in same currency) of financial instruments separated by comma(,)
30,50,20
How much money do you want to invest?
30
Please add target investment ratio (between 0 and 1) of financial instruments separated by comma(,)
.33,.33,.34

Implementation Details

It's a simple program with scary looking but simplistic mathematics behind it as explained above. We have used scipy.optimizers.minimize function (with SLSQP method) to minimize the Mean Squared Error function. There are two more methods defined in the models viz. TRUST_CONSTR and COBYLA but they are not supported atm to keep things simple and avoid over engineering for a plain use case.

The repository contains three parts:

  • controller: It contains the core logic of the application.
  • models: It contains standard pydantic/enum models used across the code.
  • views: It provides interface to end users to interact with the code. Currently there are two interfaces viz. a terminal based src/views/terminal.py and a file based src/views/file.py.

Changelog

v.0.1.0

  • first working release.