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Options

The Yin and Yang of Options – Part 4

Russ Allen
Instructor

In the last few weeks’ articles, I’ve talked about the equal and offsetting effects of option price changes on the option buyer vs. the option writer (seller). More about that today.

We began three weeks ago with an example using the SPY October 173 call option. Rosie was on the long side and Thorne was on the short side. At the time we started this example, SPY was at \$173.05 and the call was trading at \$1.87. As of this writing (October 2), SPY was at about \$169, and the 173 call was at \$.37. Rosie has lost \$1.50, and Thorne has gained that same \$1.50.

Vertical lines are drawn at the \$173 strike price; and at \$5 and \$10 increments above and below that \$173 price. This is so that we can compare what Rosie’s P&L would be if SPY were at different prices. Here’s some terminology for you:

1. Stock Price – the price at which each vertical line is drawn, and at which the following measurements are taken.
2. Theo P&L – the profit or loss that Rosie would have today, if SPY were at the price shown in column 1 now. Note that for all the rest of the columns, “…” means “if SPY were at the price shown in column 1 .”
3. Value – The value of Rosie’s position today … (Rosie originally paid \$187).
4. Pos Delta – the Delta this call would have … (It was originally .54)
5. Pos Theta – the amount of money that would be lost per day by Rosie due to time decay, …
6. Pos Gamma – the rate at which Delta would change for each \$1 of SPY price change …
7. Pos Vega – the amount Rosie would gain if SPY’s implied volatility changed by one percentage point …

Delta – Rosie’s Delta started at 54 when SPY was at \$173.05. With SPY now around \$169, her Delta is smaller. If SPY continues to drop, each successive \$1 drop will hurt her less and less.

Theta, Gamma and Vega – note that each of these is highest in the middle of the 5 rows on the table, where SPY is at the \$173 strike price. Each of these effects only time value. Since the at-the-money option (which the \$173 originally was) always has the most time value, these three forces have the largest effect on that option. They have less effect (have smaller values) for options whose strikes are either  higher or lower than the ATM option.

Now let’s compare those figures with Thorne’s situation.

Thorne’s graph has negative slope (slopes down), where Rosie’s has positive slope (slopes up). Thorne’s graph looks exactly like Rosie’s would if we flipped it top to bottom, around a horizontal line drawn at the zero P&L level.

Every value in Thorne’s table is the same number as Rosie’s, but with the opposite sign.

This is a graphic illustration (literally) that what Rosie loses, Thorne makes, and vice versa. At a stock price of \$173, Rosie’s “Theo P&L” today would be \$199.60; Thorne’s would be minus \$199.60. The same applies at any other SPY price.

The “Value” columns are also equal and opposite – for Rosie, they show what she could sell the call for today, if SPY were at the indicated price. For Thorne, they show how much he would have to pay today to buy the call and get out of the trade, with SPY at the indicated price.

Also note that all the Greeks – the delta, gamma, and theta values – are equal and opposite, not just net profit. Every kind of change – in underlying price; in volatility; as well as every day of time passing, helps Rosie and hurts Thorne (or the other way around) in exactly the same way and the same amount.

Yin and Yang indeed.

I hope this illustration has demonstrated the point that every option contract has two sides, whose situations precisely mirror one another in every way. By selecting the appropriate strategy and strike prices, we can always choose which side of every kind of change we want to be on. That is the Tao of options.