Quant Analysis Course in Python - Probability Distribution of Stock Returns

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#python #algorithmictrading #tradingstrategy #quant #probability

This coding tutorial calculates the probability distribution of weekly stock returns to capture a stock's volatility and measure the probability of a stock increasing by a threshold percentage.

Calculating the stock return probability distribution is popular in statistics, quantitative analysis, and algorithmic trading to forecast future stock prices and assess risk management.

The probability distribution of stock returns represents the likelihood of different returns that a stock might generate over a certain period. Stock returns can be modeled using different probability distributions; this video explores the normal distribution.

Normal Distribution
Description: The normal (Gaussian) distribution is often used to model stock returns because of its symmetric, bell-shaped curve. It is characterized by its mean (average return) and standard deviation (volatility).
Pros: Easy to use in statistical modeling, and many financial theories (e.g., the Black-Scholes model) assume normally distributed returns.
Cons: Normal distribution may not accurately represent the tails (extreme gains or losses), often underestimating the probability of extreme events ("fat tails").

This coding video takes advantage of the yfinance python library to gather historic stock prices to derive weekly stock returns as a percentage.

This coding tutorial also uses the scipy library for the normal distribution functions like the survival function. The survival function (also known as the complementary cumulative distribution function, or CCDF) in the context of normal distributions describes the probability that a random variable x takes on a value greater than a certain threshold.

Hypothetical Scenario in this Video: We would like to start selling weekly Amazon $AMZN covered calls to make passive income through premiums. However, we want to manage risk since we do not want to have Amazon stock go pass our strike price, getting assigned, and being forced to sell our shares prematurely in Amazon. A probability distribution of Amazon weekly stock returns would provide us insight for our covered call strategy because we need to understand what the percent probability for Amazon is to increase by a threshold percentage in a week.

Other Use Cases for Probability Distribution:
Probability distributions of stock returns are valuable tools in finance, allowing analysts and investors to assess risks and make informed decisions. Here are some key use cases:

Risk Management:

Value at Risk (VaR): Using the distribution of returns, investors can calculate the potential loss in value of an asset or portfolio over a defined period for a given confidence level (e.g., 95% or 99%).
Tail Risk Assessment: Understanding the probability of extreme negative returns (tail events) helps in preparing for worst-case scenarios.

Portfolio Optimization:

Efficient Frontier: By modeling expected returns and their distributions, investors can optimize asset allocation to maximize returns for a given level of risk.
Diversification Strategies: Analyzing the correlation of returns from different assets can help in selecting a mix that reduces overall portfolio risk.

Options Pricing:

Black-Scholes Model: The probability distribution of returns is a key component in pricing options and derivatives, allowing traders to determine fair values for various financial instruments.
Implied Volatility Analysis: Comparing actual returns to the theoretical distribution helps traders identify mispriced options.

Sharpe Ratio: By analyzing the distribution of excess returns over a risk-free rate, investors can measure the risk-adjusted performance of investments.
Sortino Ratio: Similar to the Sharpe Ratio, but focuses on downside risk, providing a clearer picture of risk-adjusted returns.

Forecasting:

Monte Carlo Simulations: By simulating stock returns based on their probability distribution, analysts can forecast future price movements and assess the likelihood of achieving investment goals.
Time Series Analysis: Distributions can be used in modeling and forecasting stock prices, incorporating seasonality and trends.
Regulatory Compliance:

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*Intrendias is not financial advice.

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