Real World Examples

Here are some examples:

Trading Context with Examples:

1. Stock Price Movements:

   • Scenario: Stock prices over time might not follow a normal distribution. You might have more days with tiny movements and a few days with large jumps or drops.
   • CLT in Play: If you take many samples of stock prices over, let's say, 30 days, the average of those samples will tend to have a normal distribution.
   • Visualization: On the x-axis, you have the average stock price from your samples. On the y-axis, you have the frequency of each average. The resulting graph should resemble a bell curve if you take enough samples.

2. Portfolio Returns:

   • Scenario: Let's assume you have a portfolio with a wide variety of assets, and the returns of these assets are distributed in various ways.
   • CLT in Play: If you look at the average return of the entire portfolio over many different periods (each period being a sample), those averages will tend to form a normal distribution, even if the returns of individual assets don't.
   • Visualization: On the x-axis, you have the average portfolio return for each period. On the y-axis, you have the frequency of each average return. Again, with enough samples, this should form a bell curve.

3. Trading Strategy:

   • Scenario: You have a new trading strategy, but the profit and loss on any given day doesn't seem to follow any pattern or particular distribution.
   • CLT in Play: If you were to analyze the average profit/loss of this strategy over many different periods (say, every 50 days), you'd find that these averages tend to form a normal distribution.
   • Visualization: On the x-axis, you have the average profit/loss from the strategy for each 50-day period. On the y-axis, you have the frequency of each average. Once again, with a sufficient number of samples, a bell curve should emerge.