How to Put Delta and Theta to Work
Aug 7, 2023
By determining your portfolio goals at the start and then using them as your guide, you can mitigate the subjectivity of your analysis and remain far more objective than you could otherwise.
Simply put, by having clearly defined targets for both portfolio delta and portfolio theta, you can always keep an eye on how much your portfolio is dependent upon direction and how much it is dependent upon decay. Doing this first will give you incredible guidance and clarity with your day-to-day decision making, as you’re able to structure your trades more easily to fit with those portfolio goals.
Our preferred method for measuring our portfolio theta is to put it in terms of a percentage of net liquidating value (net liq). By doing this once you have determined your specific percentage, it will scale accordingly, based on your account size. We generally like to maintain a daily portfolio theta of 0.1% to 0.5% of net liq.
So, for example, with a $10,000 account, 0.1% would be $10 in theta, 0.3% would be $30 in theta, and 0.5% would be $50 in theta. Using a $50,000 account, 0.1% would be $50, 0.3% would be $150, 0.5% would be $250 and so on.
So how do you choose within that range? There are obviously several factors to consider, but two are your level of experience and the market's overall volatility. If you are less experienced or market volatility is low, then landing somewhere on the lower end of the range is probably a better choice. If you are more experienced and market volatility is high, then positioning yourself at the higher end of the range should certainly be on your radar.
With portfolio delta, the choice isn’t as clearly defined as with portfolio theta. This is largely because with portfolio theta, we know we want to have some amount of positive theta working for us, but with portfolio delta, one could make a persuasive case for a portfolio delta that is positive, negative or even neutral. The choice among those different directional options is beyond the scope of this article, but here are some guidelines for either holding positive delta or negative delta.
If you’re positive delta, then a good starting point is to match the level of exposure in your portfolio with the level of exposure of S&P 500 (SPY). To do this you would start by looking at the current value of 100 shares of SPY, which at approximately $450/share, is $45,000. This means that if you have a $45,000 portfolio, then holding 100 portfolio delta (that are beta-weighted) gives you the same exposure as the SPY index. If, however, you had $90,000, then you have 2x the amount of 100 shares of SPY, so you would want to hold 200 portfolio delta to match the index exposure. And if you only had $15,000 in your portfolio, then you have ⅓ the value of 100 shares of SPY, so you would want to hold 33 portfolio delta.
If you’re negative delta, then you can use the delta/theta ratio to calculate how much portfolio delta to hold. The tastylive research has shown that a delta/theta ratio of approximately 0.5 is a great target for this ratio. Therefore, if you’ve already calculated your portfolio theta to be 20, then you know your negative portfolio delta should be 10. If your portfolio theta is 45, then your negative portfolio delta is 22-23 and so on.
Jim Schultz, a quantitative expert and finance Ph.D., has been trading the markets for nearly two decades. He hosts From Theory to Practice, Monday-Friday on tastylive, where he explains theoretical trading concepts and provides a practical application of those concepts to a trading portfolio. @jschultzf3
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