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Optimal Portfolio Allocation

Problem Statement:

You work for a prestigious investment firm that manages a large number of clients$$ portfolios.

Your task is to develop a program that determines the optimal allocation of assets in a given

investment portfolio.

The portfolio consists of N different assets, each with an associated expected return and

risk level. Your program should take as input the expected return and risk of each asset, along

with the total investment amount available. The goal is to find the allocation of assets that

maximizes the portfolio$$s expected return while keeping the risk within a specified tolerance

level.

Your program should solve this problem using two different algorithm paradigms: Brute

Force and Dynamic Programming Design and implement a dynamic programming algorithm that efficiently computes the optimal

allocation of assets. Your algorithm should make use of the principle of optimality to break

down the problem into smaller sub$-$problems and avoid redundant computations. Your program

should output the optimal allocation of assets, along with the corresponding expected return

and risk. Additionally, you should compare the runtime and efficiency of the two implemented

algorithms for different portfolio sizes and investment amounts. Note: You are not allowed to

use existing optimization libraries or functions readily available online. The purpose of this

project is to develop a deep understanding of the algorithmic paradigms and their application

in solving real$-$world problems. in JAVA

Sample run:

Input will be in the form of a text file your program should read. The input has the following

format:

ID$-$of$-$asset : Expected$-$return : Risk$-$level : Quantity$($units$)$

Example.txt:

Example $1$:

AAPL : $0\mathrm{.}05$ : $0\mathrm{.}02$ : $1000$

GOOGL : $0\mathrm{.}08$ : $0\mathrm{.}03$ : $500$

MSFT : $0\mathrm{.}04$ : $0\mathrm{.}015$ : $800$

Total investment is $1000$ units

Risk tolerance level is $0\mathrm{.}024$

Example $2$:

AMZN : $0\mathrm{.}07$ : $0\mathrm{.}04$ : $600$

TSLA : $0\mathrm{.}1$ : $0\mathrm{.}05$ : $400$

FB : $0\mathrm{.}06$ : $0\mathrm{.}025$ : $700$

Total Investment is $900$ units

Risk Tolerance Level is $0\mathrm{.}038$

Output Sample:

Example $1$: Optimal Allocation:

AAPL: $200$ units

GOOGL: $300$ units

MSFT: $500$ units

Expected Portfolio Return: $0\mathrm{.}064$

Portfolio Risk Level: $0\mathrm{.}024$

Example $2$:

Optimal Allocation:

AMZN: $100$ units

TSLA: $300$ units

FB: $500$ units

Expected Portfolio Return: $0\mathrm{.}079$

Portfolio Risk Level: $0\mathrm{.}038$