x̄ - > Stock valuation and parametric value at risk

 Stock valuation is the process of determining the intrinsic value of a stock or a company's shares. It involves analyzing various factors such as financial statements, market conditions, industry trends, and future prospects to estimate the fair value of the stock.

There are several methods for stock valuation, including:

1. Fundamental Analysis: This approach involves evaluating a company's financial statements, such as its balance sheet, income statement, and cash flow statement, to determine its intrinsic value. Fundamental analysts consider factors like earnings, revenue growth, profit margins, and debt levels to estimate the stock's value.

2. Relative Valuation: This method compares the valuation of a stock to similar companies in the same industry. Common metrics used in relative valuation include price-to-earnings (P/E) ratio, price-to-sales (P/S) ratio, and price-to-book (P/B) ratio. By comparing these ratios with industry peers, analysts can assess whether a stock is overvalued or undervalued.

3. Discounted Cash Flow (DCF) Analysis: DCF analysis calculates the present value of a company's projected future cash flows. It involves forecasting the cash flows a company is expected to generate and discounting them back to their present value using an appropriate discount rate. The resulting present value represents the intrinsic value of the stock.

Parametric Value at Risk (VaR) is a risk measurement technique used in finance to estimate the potential loss on an investment portfolio over a given time horizon, with a certain level of confidence. VaR provides a quantified estimate of the maximum loss a portfolio is likely to experience under normal market conditions.

Parametric VaR uses statistical and mathematical methods to estimate portfolio risk. It assumes that the returns of the assets in the portfolio follow a known probability distribution, typically a normal distribution. The VaR calculation takes into account the portfolio's asset weights, historical return data, and standard deviation to estimate the potential loss.

For example, if a portfolio has a 5% one-day VaR of $10,000, it means that there is a 5% chance that the portfolio will lose more than $10,000 in one day, assuming normal market conditions.

It's important to note that VaR is a measure of downside risk and provides an estimate based on historical data. It does not account for extreme events or tail risks that may deviate from the assumed distribution. Therefore, it's recommended to use VaR in conjunction with other risk management techniques and stress testing to have a comprehensive understanding of portfolio risk.

example of stock valuation and parametric value at risk calculations using both R and Python code.

# Stock Valuation

dividend <- 2.50 # Dividend per share

discount_rate <- 0.1 # Discount rate

growth_rate <- 0.05 # Growth rate

valuation <- dividend / (discount_rate - growth_rate)

valuation

# Parametric Value at Risk

portfolio_returns <- c(-0.05, 0.02, -0.03, 0.04, -0.01) # Portfolio returns

confidence_level <- 0.95 # Confidence level

portfolio_value <- 1000000 # Portfolio value

# Calculate portfolio mean return and standard deviation

mean_return <- mean(portfolio_returns)

std_deviation <- sd(portfolio_returns)

# Calculate parametric value at risk

z_score <- qnorm(1 - confidence_level)

VaR <- -(portfolio_value * (mean_return + z_score * std_deviation))

VaR

example of stock valuation and parametric value at risk calculations using both R and Python code.

import numpy as np

from scipy.stats import norm

# Stock Valuation

dividend = 2.50  # Dividend per share

discount_rate = 0.1  # Discount rate

growth_rate = 0.05  # Growth rate

valuation = dividend / (discount_rate - growth_rate)

valuation

# Parametric Value at Risk

portfolio_returns = np.array([-0.05, 0.02, -0.03, 0.04, -0.01])  # Portfolio returns

confidence_level = 0.95  # Confidence level

portfolio_value = 1000000  # Portfolio value

# Calculate portfolio mean return and standard deviation

mean_return = np.mean(portfolio_returns)

std_deviation = np.std(portfolio_returns)

# Calculate parametric value at risk

z_score = norm.ppf(1 - confidence_level)

VaR = -(portfolio_value * (mean_return + z_score * std_deviation))

VaR