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Capiche? Portfolio Margin Part 2: Greeks, Unveiled

April 17, 2017
portfolio margin greeks
Fredrik Broden

More leverage using portfolio margin (PM) means you need to bump up your risk management a few notches. And that means it’s a good idea to be sensitive to price changes. Now is a good time for a refresher course on the greeks—theoretical metrics that describe how things like stock price, time, and volatility “vol” can impact option prices. Though there are five greeks in all, we’ll cover the four most critical here—delta, gamma, theta, and vega.

Delta for how much change. Delta can be positive or negative, and can be expressed as either the number of shares an option position “acts” like, or the profit or loss an options position might have when the stock price moves up or down $1. So, all things equal, a call with a value of $3 and a 0.40 delta, could theoretically be worth $3.40 if the stock goes up $1.

Gamma for speed of change. The rate of change in delta (per $1 move in the stock) is due to gamma. For example, if a put with a delta of -0.40 has a gamma of 0.07, and the stock dropped $1 while other things stayed the same, the new delta of that put would be -0.47.

Theta day by day. Theta only impacts the extrinsic value (“time premium”) of options and is expressed in dollars. If you are short a put that has a theoretical value of $2, a theta of $0.10, and other things stay the same, the put’s theoretical value would be $1.90 tomorrow.

Vega for volatility. A change in implied “vol” also only impacts the time value of options, and is expressed in dollars. When vol goes up or down, time premium goes up or down, respectively. If you have a long straddle that has a theoretical value of $6, a vega of 0.50, and implied vol increases by 2%, and all other things stay the same, the theoretical value of the straddle would then be $7.

What's It Got To Do With Portfolio Margin?

Portfolio margin uses the greeks—or rather the theoretical pricing model behind the greeks—to figure out the largest loss a position could theoretically have across a range of underlying stock or index prices and volatilities. This is important because that largest loss is the margin requirement for a position in a PM account.

Suppose a short 150 strike put on a stock trading at $160 has a theoretical value of $4.00, a delta of 0.30, a gamma of -0.02, and a vega of 0.10. PM tests the loss on that put with the stock down 15% and vol up 10%. If the stock goes down $24 to $136, the put would be worth at least its $14 intrinsic value, which means the put loses $1,000, and the rise in vol could add another $100 loss because of the put’s short vega. If PM finds the the loss to be $1,100, the portfolio margin requirement is $1,100.

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