How to Derive Volatility Drag

Roman Paolucci ยท Intermediate ยท๐Ÿ”ข Mathematical Foundations ยท1mo ago

About this lesson

*๐Ÿš€ Master Quantitative Skills with Quant Guild* https://quantguild.com *๐Ÿ“ˆ Interactive Brokers for Algorithmic Trading* https://www.interactivebrokers.com/mkt/?src=quantguildY&url=%2Fen%2Fwhyib%2Foverview.php *๐Ÿ‘พ Join the Quant Guild Discord server here* https://discord.com/invite/MJ4FU2c6c3 ___________________________________________ *๐Ÿช Free Jupyter Notebook Library ๐Ÿ‘‡* https://github.com/romanmichaelpaolucci/Quant-Guild-Library *๐Ÿ‘ค Video Setting Up Interactive Brokers ๐Ÿ‘‡* https://youtu.be/7hezNf49iKc *๐Ÿ”— How to Read Options Chains ๐Ÿ‘‡* https://youtu.be/RrRbz6oXwxE TL;DW Executive Summary: Volatility drag is a consequence of the geometric compounding of returns. If you bet with a proportion of your bank roll, you are implicitly using geometric compounding - you can't escape it - but you can structurally use it to your advantage in strategy and portfolio construction. More to follow! I hope you enjoyed, and I hope you learned something! - Roman ___________________________________________ *๐Ÿ“– Chapters:* 00:00 - What Volatility Drag Is & Why It Matters 00:48 - Portfolio Value, Compounding, and Period Returns 01:35 - Defining the Geometric Mean Return 02:35 - Rewriting Compounded Returns with a Single Growth Rate 03:27 - Using Logs to Simplify Products into Sums 05:07 - Averaging Log Returns Across Periods 05:59 - Taylor Series Approximation of ln(1 + x) 07:51 - Applying the Approximation to Geometric Returns 09:27 - Connecting the Expression to Mean Return 11:30 - Deriving Variance from Sum of Squares 14:59 - Simplifying Variance into a Usable Form 16:10 - Substituting Variance Back into the Growth Equation 17:10 - Isolating the Geometric Growth Rate 19:13 - Arriving at the Volatility Drag Formula 20:09 - Why Volatility Drag Matters for Leverage and Growth 21:12 - Sharpe Ratio vs. Geometric Growth Optimization 22:14 - Strategy Construction, Quant Guild, and Closing Remarks ___________________________________________ *๐Ÿ—ฃ๏ธ Shout Outs* A special thank you to m

Original Description

*๐Ÿš€ Master Quantitative Skills with Quant Guild* https://quantguild.com *๐Ÿ“ˆ Interactive Brokers for Algorithmic Trading* https://www.interactivebrokers.com/mkt/?src=quantguildY&url=%2Fen%2Fwhyib%2Foverview.php *๐Ÿ‘พ Join the Quant Guild Discord server here* https://discord.com/invite/MJ4FU2c6c3 ___________________________________________ *๐Ÿช Free Jupyter Notebook Library ๐Ÿ‘‡* https://github.com/romanmichaelpaolucci/Quant-Guild-Library *๐Ÿ‘ค Video Setting Up Interactive Brokers ๐Ÿ‘‡* https://youtu.be/7hezNf49iKc *๐Ÿ”— How to Read Options Chains ๐Ÿ‘‡* https://youtu.be/RrRbz6oXwxE TL;DW Executive Summary: Volatility drag is a consequence of the geometric compounding of returns. If you bet with a proportion of your bank roll, you are implicitly using geometric compounding - you can't escape it - but you can structurally use it to your advantage in strategy and portfolio construction. More to follow! I hope you enjoyed, and I hope you learned something! - Roman ___________________________________________ *๐Ÿ“– Chapters:* 00:00 - What Volatility Drag Is & Why It Matters 00:48 - Portfolio Value, Compounding, and Period Returns 01:35 - Defining the Geometric Mean Return 02:35 - Rewriting Compounded Returns with a Single Growth Rate 03:27 - Using Logs to Simplify Products into Sums 05:07 - Averaging Log Returns Across Periods 05:59 - Taylor Series Approximation of ln(1 + x) 07:51 - Applying the Approximation to Geometric Returns 09:27 - Connecting the Expression to Mean Return 11:30 - Deriving Variance from Sum of Squares 14:59 - Simplifying Variance into a Usable Form 16:10 - Substituting Variance Back into the Growth Equation 17:10 - Isolating the Geometric Growth Rate 19:13 - Arriving at the Volatility Drag Formula 20:09 - Why Volatility Drag Matters for Leverage and Growth 21:12 - Sharpe Ratio vs. Geometric Growth Optimization 22:14 - Strategy Construction, Quant Guild, and Closing Remarks ___________________________________________ *๐Ÿ—ฃ๏ธ Shout Outs* A special thank you to m
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Chapters (17)

What Volatility Drag Is & Why It Matters
0:48 Portfolio Value, Compounding, and Period Returns
1:35 Defining the Geometric Mean Return
2:35 Rewriting Compounded Returns with a Single Growth Rate
3:27 Using Logs to Simplify Products into Sums
5:07 Averaging Log Returns Across Periods
5:59 Taylor Series Approximation of ln(1 + x)
7:51 Applying the Approximation to Geometric Returns
9:27 Connecting the Expression to Mean Return
11:30 Deriving Variance from Sum of Squares
14:59 Simplifying Variance into a Usable Form
16:10 Substituting Variance Back into the Growth Equation
17:10 Isolating the Geometric Growth Rate
19:13 Arriving at the Volatility Drag Formula
20:09 Why Volatility Drag Matters for Leverage and Growth
21:12 Sharpe Ratio vs. Geometric Growth Optimization
22:14 Strategy Construction, Quant Guild, and Closing Remarks
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