The issue of ThinkOrSwim software when analyzing volatility's impact caused by Vega

I have been using the TOS analyzer to estimate the volatility's impact on portfolio or position's profit/loss for quite some time. I believe there are many other option traders & instructors analyzing it in the same way as I did. Recently I discovered there was a major issue in my past volatility analysis using the TOS platform.

After identification of some discrepancies in volatility used in TOS in my first post of the series and another discussion on how to estimate option implied volatility changes of each position in a Beta-weighted portfolio, I'd like to discuss the real issue here and figure out a way to work around it.

The above chart of ThinkOrSwim showes that Delta and Gamma are Beta-weighted while the Theta and Vega are not. For Theta, there is no issue since each instrument contribute time decay daily based on its corresponding Theta. But for Vega, the situation is different from Theta and somewhat similar to Delta. Like P&L caused by Delta of each instrument, the P&L caused by Vega of each instrument changes differently in each market day.

For example, if SPX moves 1%, the VIX may change 2 points. The IV of OTM options of the SPX position may change 0.6 percentage point. At the same day, RUT may move 1.2% (just an example number) point and its volatility RVX may change 2.5 points. The IV of OTM options of the RUT position may change 0.8 percentage point. So if we assume a 0.6 point change of IV of the SPX beta weighted portfolio, and use the straight sum of the aggregated Vega to calculate the IV induced P&L, our results are not accurate at all. This is particularly an issue for larger trading capitals. The estimated results will be close to the actual P&L if we use some kind of special weights for Vega of each different position.

Besides the lack of proper weighting in the Vega analysis, I had used the analyzer by adjusting the volatility field according to VIX. I had assumed if SPX changes 10 points, the VIX is likely to change 1 point (which is OK). Then, I would adjust the volatility field by 1 point and observe the new P&L in the live price slice section. It usually generates a substantial change in P&L. This is a total overestimation of the volatility impact on P&L. In reality, the portfolio's IV does not change 1 point as the VIX does. The portfolio or position IV actually changes much less than the VIX, could be 30% of the VIX only.

In another word, if the IV of the position is adjusted for 1 point in the TOS analyzer, it would mean the VIX changes over 3 points and market has a major sell-off or jump-up. If we adjust the IV field by +2 points, it may require VIX to increase 6 points, which may correspond to SPX to drop 60 points.

I did not realized this before. So, it is an major error that I had in my previous Vega related calculations, including the post on proper Greek  values of Delta neutral portfolios.

The TOS analyzer does not help either. If a user increases the volatility field by 1, the analyzer increases all option IV by 1 and VIX (or RVX) by 1 as well. It gives user an impression that option IV changes at the same rate as the VIX. In the future, I need to figure out how to calculate the equivalent position IV change based on SPX changes so that we can use TOS analyzer more accurately.