Learn Challenge: Compute Portfolio VaR | Risk Analysis and Portfolio Optimization

Before you begin working on portfolio risk, it is important to recap what Value at Risk (VaR) represents in finance. VaR is a widely used risk measure that estimates the maximum potential loss of a portfolio over a specific time frame, given a certain probability level. The historical method for calculating VaR uses actual past returns to determine the loss threshold that will not be exceeded with a given confidence level. For example, a 1-day 5% VaR of -2% means that on 95% of days, the portfolio's loss will not be greater than 2%, but on 5% of days, losses could be worse.


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import numpy as np
import pandas as pd

# Simulate 2 years of daily portfolio returns (about 504 trading days)
np.random.seed(42)
returns = np.random.normal(loc=0.0005, scale=0.012, size=504)
dates = pd.date_range(start="2022-01-01", periods=504, freq="B")
portfolio_returns = pd.DataFrame({"returns": returns}, index=dates)

print(portfolio_returns.head())

To calculate multiple VaR thresholds, such as the 1% and 5% daily VaR, you need to determine the appropriate quantiles from the historical returns distribution. Visualizing these VaR levels on a histogram helps you see where the most extreme losses fall relative to the rest of the data. By plotting the returns and marking the VaR thresholds, you can better communicate the risk profile of the portfolio.

Task

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You are given a DataFrame of daily portfolio returns. Your task is to calculate the 1-day 1% and 5% historical Value at Risk (VaR) for the portfolio, plot the returns distribution with both VaR thresholds, and print an interpretation of the results.

Compute the 1-day 1% historical VaR from the returns column of portfolio_returns.
Compute the 1-day 5% historical VaR from the returns column of portfolio_returns.
Plot a histogram of the daily returns and mark both VaR levels.
Print a statement interpreting the meaning of these VaR values for the portfolio's risk.

Solution

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Section 3. Chapter 3

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              12345678910
            
import numpy as np
import pandas as pd

# Simulate 2 years of daily portfolio returns (about 504 trading days)
np.random.seed(42)
returns = np.random.normal(loc=0.0005, scale=0.012, size=504)
dates = pd.date_range(start="2022-01-01", periods=504, freq="B")
portfolio_returns = pd.DataFrame({"returns": returns}, index=dates)

print(portfolio_returns.head())