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Successful options trading largely depends on precise understanding of stock's historical return distribution.

This page presents multiple quantitative analytical tools in order to depict historical return distribution metrics for a certain stock. Many valuable stylized facts can be revealed through careful observation of numeric metrics or visualization tools provided on this page, such as volatility cone, volatility mean reversion, earning cycles, expiry cycles, etc.

Each tool is briefly described below.

- Basic Market Data

This section provides a quick glance for the most important stock trading parameters, such as previous close price, trading volume, 50-day and 200-day moving averages, etc.

- Stock Return Profile

This table provides basic stock return metrics for various trading periods.

Autocorrelation coefficient is calculated for each trading period, this can be an important metric to observe in trading certain option strategies.

- Historical Volatility

Historical volatilities measured over 10-day, 20-day, 30-day, 60-day and 90-day periods are calculated, and ready to compare to readings from one week ago, and historical high/low range over the last trading year.

- Volatility Cone

Options trading depends on volatility forecast, and volatility forecast is based on understanding of historical realized volatility. In order achieve a confident volatility forecast, one needs to assess market conditions for the underlying stock, and evaluate market implied volatilities in the context of historical realized volatilities over past one year.

Volatility Cone provides a very useful visualization tool - it depicts high, low, mean, first and third quantiles for rolling realized volatilities for various measurement periods over the past one year. For example, 10-day realized volatilities were observed 252 times over past trading year, min/max/mean/1st quantile/3rd quantile values can be calculated; 20-day realized volatility metrics can be calculated the same way, so is 30-day, 60-day, 90-day and 1-year; lines connecting the same quantile data points for all measurement periods will show a cone style pattern - meaning volatilities are tend to be more volatility over short measurement period as oppose to long measure period, or volatility tends to mean-revert over time.

Plotting current observations of realized volatilities and market implied volatilities overlaying the cone will show current readings in historical context, and market views of volatility forecast can thus be deduced.

- Actual excessive returns in comparison to Normal Distribution

Stock returns are generally assumed to be normally distributed, option pricing models are usually based on this assumption.

In reality, stock returns hardly follow normal distribution. Excessive returns in the long tails of distribution curve can not be described by normal distribution. Capturing the excessive return patterns thus provides an edge in understanding return distribution and making more accurate volatility forecasts.

- Stock Price Chart vs. Historical Volatilities

This is a simple chart that overlays historical realized volatilities on price performance.

User may spot on negative correlations between realized volatilities and stock returns. More insights, such as cyclical spikes and troughs for realized volatilities, can be gained from careful study of the chart. Market views and trade ideas can be generated from such insights.

- Daily Returns Described in Terms of Historical Volatilities

The usual percentage form of stock returns is not useful in analyzing option strategies, as it ignores the impact of volatility regimes. A 2% stock return in a volatility regime of 15-20% is very different from the same 2% return in a volatility regime of 40-50%, in structuring and analyzing option strategies.

To make returns directly comparable across different historical periods, or across different underlyings, daily returns are re-engineered to take the factor of realized volatilities.

On a rolling basis, historical realized volatilities for various measurement periods can be calculated for each trading day. If we divide stock daily returns (in percentage form) by the realized volatility reading for the same trading day, we will obtain the stock daily return in terms of historical volatility, and this result can be directly compared to returns from other trading days or other underlyings.

Enter a stock ticker symbol below to see details.