Key Concepts 4. Portfolio Management

Delta

Delta: Directional Exposure

Delta is the greek that helps us get a better understanding of our directional exposure. It also can be used to determine share equivalency, and as a proxy for calculating prob. ITM. It tracks the theoretical rate of change of an option’s price, given a \$1.00 increase in the underlying’s price. Strategies that are bullish will have a positive delta. Strategies that are bearish will have a negative delta.

If a long call option has a 0.30 delta, and the underlying increases \$1.00, that option should see an increase in price of \$0.30, all else equal (some other factors impact an option’s price, but we assume those are frozen for this example). If we saw the underlying decrease by \$1.00 instead, we would see the call option lose \$0.30, all else equal.

If a long put option has a (0.40) delta, and the underlying increases \$1.00, that option should see a decrease in price of \$0.40, all else equal. If we saw the underlying decrease by \$1.00 instead, the put would actually gain \$0.40 in value, all else equal.

It’s important to remember that buying an option does not always mean you’re bullish. As you see above, buying a put is actually a bearish strategy. Selling a put is bullish. When it comes to directional assumption with options, buying and selling are not synonymous with bullish and bearish like it is for stock purchases.

Delta: Share Equivalency

Delta can also be used as a way to add, subtract or neutralize deltas from being long or short stock. Each share of stock is 1 delta, so 100 shares of stock would equal 100 positive deltas. Each \$1.00 the underlying moves up would result in a gain of \$100. Some investors may want to adjust this exposure at certain times during the share ownership, and we can use options to do just that!

Let’s take a covered call for example, which is selling 1 call against 100 shares of stock. A short call is a bearish strategy, and therefore has negative delta naturally. Selling an out of the money (OTM) call with a delta of (0.30) would hedge our directional exposure by 30%! We would now have a net delta of 0.70, and no additional risk. We do cap my upside potential, but we reduce my loss potential if the stock price drops.

If we wanted to completely neutralize my delta temporarily, we could sell two at the money (ATM) calls at a delta of (0.50). This would net the delta out to 0, but we would be taking on more risk as one of the short calls would be uncovered.

It’s important to remember that deltas change, so in both of these examples if the stock price dropped the call deltas would decrease, reducing the overall hedge. Options can be a great way to fine tune directional exposure at any time.

Delta: Probability ITM Proxy

Delta can also be used as a proxy for estimating probability of being ITM. The two numbers are very similar, especially if volatility skew is low in a particular market. For example, if we’re looking for a 1 standard deviation option, which would be the 16% probability of being ITM, we can just look for the 16 delta option. It will likely be very close to the actual strike that would represent the 16% prob ITM, if it’s not that exact strike already!

Delta Neutrality

If you’re familiar with the show, you’ll notice the show hosts refer to being delta neutral a lot. This just means that they have various positions on (some bullish and some bearish) but their overall portfolio is pretty delta neutral. It can be very difficult to trade directionally, so we often choose to keep our deltas neutral. This means that if there are big directional moves in the market, our portfolio will be at less risk than if we were fully directional and wrong. We rely on theta decay, and implied volatility overstatement as our main drivers of long term edge, not directional trading.