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Calculating Future Returns Using Delta

08/12/2014 8:00 am EST

Focus: OPTIONS

Alan Ellman

President, The Blue Collar Investor Corp.

Alan Ellman of TheBlueCollarInvestor.com maps out the how and why of different number calculations in order to aid the newbie options trader as well as the seasoned professional.

Understanding option calculations is an integral part of the process but knowing the how and why of these numbers will make us all better investors.

This article was inspired by Peter, one of our members. He was concerned about the potential drop in share price of a covered call trade he was in and wanted to calculate future returns based on the current delta of the option. Before I set up the trade for you let’s define delta:

The amount an option value will change for every \$1 change in share price. Delta values run from 0 to 1 and the greater the chance that the strike will end up in-the-money, the higher the delta (the closer it is to 1).

Here is Peter’s trade from several months ago so I will use our generic BCI as the stock and 1 contract for simpler math:

• Buy 100 x BCI @ \$62.46
• Sell 1 x \$55 call @ \$9.75
• Current share price is \$60.06
• Current “ask” for the \$55 call is \$9.85
• Delta for the \$55 call = 0.68 (moves \$0.68 for every \$1 move in share price)

Peter’s initial returns using the multiple tab of The Ellman Calculator:

Click to Enlarge

We see an impressive 1-month return of 4.2% (time value only) and protection of that profit of an also impressive 11.9%

Calculating future returns using delta:

Peter was wondering what his position would be if share price dropped by \$2 in the next week. Let’s calculate using delta with the understanding that there are other factors that will influence option premium like time value erosion (theta) and changes in implied volatility of the underlying security (vega). So all other factors remaining about the same, the delta of 0.68 will cause option value to decrease by \$1.36 (2 x \$0.68) when share value drops to \$58.06. That means the cost to close (ask) will be \$8.49 (\$9.85-\$1.36). Okay everybody, take off your shoes and socks and let’s calculate this hypothetical circumstance:

• Share loss = \$4.40 (\$62.46 – \$58.06)
• Option credit = \$1.26 (\$9.75 – 8.49)
• Net debit = \$3.14 per share or \$314 per contract (\$4.40 – \$1.26)

The takeaway here is that if Peter closes his entire position given this hypothetical scenario, he would lose \$314 per contract. So where would he be if he didn’t close?

To close or not to close:

Unless some egregious news has come out about the company in question, Peter is still in great shape in this trade. The deep in-the-money strike sold (\$55) generated an 11.9% downside protection of the time value component of the original option sale (4.2%). This means that Peter was guaranteed a 4.2% 1-month return as long as share value did not decline below \$55. Even if the \$2 drop in share value does occur, there is still another \$3.06 in downside protection protecting that profit. At this point, the trade is still a classic take no action situation, again, as long as there was no unusual news reported by the company.

When do we start losing money:

Well, we always have our exit strategy arsenal in place to avoid or mitigate losses but our breakeven is always share price—total option premium. In this case:

\$62.46 – \$9.75 = \$52.71

With the stock currently trading at \$60.06, even a share drop of \$2 will leave us a galaxy away from the breakeven. Sometimes the best action to take is no action at all.

By Alan Ellman of TheBlueCollarInvestor.com