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Options Education: Delta 101

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Option traders talk a lot about delta. Delta is one of the risk variables that we use to describe a position - it's as important for describing an options position as hair color or height is for describing a person. The strict definition is that delta measures the rate of change in the price of an option per unit change in the underlying asset. Here are some other ways of thinking about delta:

1. Hedge ratio: delta is the a ratio of underlying contracts to options required to establish a neutral position, e.g. for every five 40-delta calls purchased, two underlying contracts (or 200 shares of stock) should be sold short;

2. Stock exposure: as an equivalent to the underlying, e.g. owning a 40-delta call is equivalent to owning 40 shares of stock;

3. Probability proxy: as the rough probability that an option will expire in the money.

When you're trading options, many times you want to isolate the volatility-related part of a trade and ignore other variables, like price. To get price biases out of the picture, you need to flatten your position delta. I've demonstrated some ways to do that in several volatility arbitrage trades here at OP, usually using shares of the underlying stock.

However, sometimes we do want to keep some delta exposure, and in those cases the next question is which strike prices to choose for the trade. For example, take the iShares MSCI South Korea Index Fund (EWY) position opened earlier this week: the trade was motivated by a historically flat volatility term structure, rather than by a price outlook for the ETF. But the bearish fundamentals and strong short-term price trend mean we don't want to be completely neutral, so instead of trading a simple at the money calendar spread, we bought a long-term call that was two strikes higher than the short-term call we sold. The May 56 call has a delta of 47; the January 2014 58 call has a delta of 45.

So by selling the May 56 strike and buying the January 58 strike, we are effectively short two shares of the underlying (-47 + 45). If you traded ten or fifteen lots of this spread, that's not a lot of directional exposure, but again, the primary purpose of the trade was to express a view about volatility. The modest negative delta exposure just means we don't have to fight the trend while we wait for our view to play out.

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