Introduction to Financial Concepts using Python

Python provides us with a variety of tools as well as libraries that help us work with the foundations of probability. Probability has a wide scale use case from AI content detection to card games. The random module is often used for probability related problem statements. This combined with libraries like numpy and scipy (and matplotlib and seaborn for visualization) can be of great advantage when the data is large scale and mainly in the form of csv files. Probability problem statements can further be clubbed with statistics to gain more insights. It doesn’t matter if you are a beginner or a practitioner, there always be more to find out in the field of probability.

Python can be used in order to help with these financial concepts which would reduce the amount of human input required and make the process simple. Some financial key concepts that can be implemented using Python are as follows:

• TVM − Time Value of Money deals with the idea that the value of varies from time time due to factors like inflation and interest rates.

• Interest calculation − A variety of interests like simple interest, compound interest and continuous compounding and be computed with the help of python.

• Portfolio Optimization − It is the process of selecting a variety of investments and predicting ways to maximize returns while minimizing risk.

• Monte Carlo Simulation − This is a statistical technique that can be used in order to model and analyze behavior of financial systems over a period of time.

• Algorithmic Trading − Automated trading algorithms which can be used to make buy or sell decisions based on market conditions and various related factors.

TVM

TVM stands for Time Value Money, is a financial concept according to which a sum of money worth right now will be worth less in the future due to its earning potential in the interim. It is as good as saying that Rs 100 in 1958 had the same value as Rs 8411 has today. TVM is influenced by factors such as inflation, risk, market conditions and many more.

The formula for TVM is −

$$\mathrm{FV = PV * (1 + r)^{n}} $$

Where,

• FV stands for Future Value,

• PV stands for Present Value,

• r stands for rate of interest and

• n stands for Number of periods (example years) for which the investment will be held.

Here is a simple program to demonstrate TVM using Python.

Example

def tvm(pv, r, n):
   fv = pv * (1 + r) ** n
   return fv
pv = 10000
r = 0.05
n = 10
fv = tvm(pv, r, n)
print("Future Value of ₹",pv,"in",n,"years will be ₹", fv)

Output

Future Value of ₹ 10000 in 10 years will be ₹ 16288.94626777442

Interest Calculation

Interest is the additional price paid to borrow money or the cost you charge to lend your money. Interest are of different types:

Simple interest: The interest is paid only on the initial principal amount.

Example

def simple_interest(principal, rate, time):
   interest = principal * rate * time
   return interest

principal = 10000.0
rate = 0.05
time = 2
# simple interest is principal * time * rate / 100
interest = simple_interest(principal, rate, time)
print("Simple Interest on Rs",principal,"will amount to Rs", interest)

Output

Simple Interest on Rs 10000.0 will amount to Rs 1000.0

Compound interest: The interest is paid on the principal amount is expressed as the initial principal amount and the interest till date

Example

def compound_interest(principal, roi, time_period):
   interest_paid = principal_amt * (pow((1 + roi / 100), time_period))
   return interest_paid-principal_amt

principal = 10000
rate = 5
time = 2
interest = compound_interest(principal, rate, time)

print("Compound interest on Rs",principal,"will amount to Rs", round(interest,2))

Output

Compound interest on Rs 10000 will amount to Rs 1025.0

Portfolio Optimization

Here we select a combination of assets in such a way that we minimize the risk and maximize the returns or gains. This is known as optimization and is of great use in the financial sector. The Modern Portfolio Theory is a mathematical model that is of great use for this.

Example

import numpy as np
import cvxpy as cp

# Define the expected return and covariance matrix
returns = np.array([0.1, 0.2, 0.15])
covariance = np.array([[0.015, 0.01, 0.005], [0.01, 0.05, 0.03], [0.005, 0.03, 0.04]])

# Define the optimization problem
weights = cp.Variable(len(returns))
risk = cp.quad_form(weights, covariance)
returns = returns @ weights
obj = cp.Minimize(risk)
constraints = [sum(weights) == 1, weights >= 0]
prob = cp.Problem(obj, constraints)

# Solve the optimization problem
prob.solve()

# Print the optimized weights
print(weights.value)

Output

[7.77777778e-01 4.49548445e-23 2.22222222e-01]

In the example above the expected returns and covariance matrix for three assets are defined. A portfolio optimization problem is then defined and the cvxpy library of python iis used here which minimizes the portfolio risk subject to the constraints of sum of weights equal to 1 as well as non negative weights.

The solution of this optimization problem predicts the optimal weights for each asset in the portfolio.

Monte Carlo Simulation

Monte Carlo Simulation is a simulation method which is often used to model the behavior of a system by random sampling using probability distribution. It can be used to predict the outcome of a complicated system by iterating repeatedly and averaging the results.

Example

import numpy as np
import matplotlib.pyplot as plt

# Define the parameters
mean = 0.1
stddev = 0.2
num_simulations = 1000
num_steps = 20

# Generate the simulated returns
returns = np.random.normal(mean, stddev, (num_simulations, num_steps))

# Calculate the cumulative returns
cumulative_returns = (returns + 1).cumprod(axis=1)

# Plot the results
plt.plot(cumulative_returns.T)
plt.xlabel("Time Step")
plt.ylabel("Cumulative Return")
plt.title("Monte Carlo Simulation of Stock Returns")
plt.show()

Output

Algorithmic Trading

The use of automating the buying and selling of assets in financial markets by making use of mathematical and statistical analysis to identify and help execute trades in a systematic method. The main goal here is to execute trades based on certain fixed rules and data rather than subjective judgment which can lead to ambiguity.

The link for the dataset (stock_data.csv) used below is here.

Example

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

# Load the stock data
df = pd.read_csv("stock_data.csv")
df["Date"] = pd.to_datetime(df["Date"])
df.set_index("Date", inplace=True)

# Run algorithmic trading strategy
capital = 1000
shares = 0
for i in range(1, len(df)):
   if df.iloc[i]["Close"] > df.iloc[i-1]["Close"]:
      # Buy shares
      shares += capital // df.iloc[i]["Close"]
      capital -= shares * df.iloc[i]["Close"]
   elif df.iloc[i]["Close"] < df.iloc[i-1]["Close"]:
      # Sell shares
      capital += shares * df.iloc[i]["Close"]
      shares = 0

# Plot the results
df["Close"].plot()
plt.title("Stock Price")
plt.xlabel("Date")
plt.ylabel("Close Price")
plt.show()

# Output the final capital
print("Final capital: ${:.2f}".format(capital + shares * df.iloc[-1]["Close"]))

Output

Final capital: $34.25

Conclusion

With the use of python, a large number of financial concepts ranging from algorithmic trading to Time Value Money can be implemented. Libraries such numpy, pandas, matplotlib provide a variety of tools which help in data processing, analysis, and visualization for financial analysis. The ease of use and readability of Python makes it a highly useful tool not only for working professionals but also students. Although we aim to achieve maximum accuracy and indulge in best decisions, often errors can occur which can lead to massive losses and hence it is important to understand the risks before implementing it to real life uses.