Defining portfolio risk associated with complex option strategies

The option business is about risk assessment. Yet many option traders don’t understand portfolio risk when utilizing option strategies. The more complex the option strategies, the more complicated the risk assessment.

One way to approach risk assessment is a concept known as equivalent share position (ESP). ESP allows you to assess the total number of underlying shares associated with an option strategy and ultimately the leverage being employed within a portfolio.

To add some meat to this skeleton, consider a hypothetical example. A trader with a $50,000 portfolio takes a position in two stocks: ABC trading at $25 per share and XYZ trading at $50 per share. The options on both stocks are trading at implied volatilities of 40%.

The first trade involves the purchase of 20 XYZ Oct 50 calls at $5.00 per share (total investment $10,000). The second trade is a covered call write, where the trader buys
1,000 shares of ABC and writes 10 Oct 27.50 calls at $1.50 per share. Total ABC investment $23,500 (1,000 shares x $25 less $1,500 in option premium). The total capital committed is $43,500.

At this stage, we have a long call position on XYZ and a covered call write on ABC. The objective is to determine how much risk and leverage is being assumed by the portfolio.

The 20 XYZ calls grants the trader the right to buy 2,000 shares of the underlying stock, which you might argue is the ESP of the strategy. But that is not exactly correct. In reality, if XYZ were to decline to zero, the calls would expire worthless. But the most the trader would lose is $10,000 (2,000 shares X $5.00 per share = $10,000), the total cost of the calls.

If we are to examine the risk profile of an option strategy, limited risk plays a role as does time to expiration and the relationship between strike price and the price of the underlying security. ESP calculates this in real time.

ESP takes into account the option’s delta. This is a derivative of the option pricing formula that tells us how much an option is expected to rise or fall given a $1.00 move up or down in the underlying stock.

Any internet based option pricing calculator provides delta along with a number of other derivatives. You can use the option calculator at the following link from the Montréal exchange http://www.m-x.ca/outils/calculateur/calc_legal_en.html.

In the XYZ example, the XYZ Oct 50 calls have a delta of 0.55. That suggests over short periods, the XYZ Oct 50 calls should rise or fall approximately 55 cents for every $1.00 change in the price of XYZ.

The ESP is simply the underlying number of shares (2,000 shares in this case) multiplied by the option’s delta. The option trader has a position that is equivalent in terms of risk, to holding 1,100 shares of XYZ (20 contracts X 100 shares per contract X 0.55 = 1,100 shares) at $50 per share.

The same methodology applies to the ABC holding. In this case, the trader bought 1,000 shares of ABC. When you buy stock, you are buying a delta of 1.00, which represents an ESP of 1,000.

The delta on the ABC Oct 27.50 call is 0.40. But unlike the XYZ example where the trader was long the calls creating a positive delta, the short ABC calls correspond to a negative delta of
-0.40. That represents an ESP of -400 shares (10 contracts X 100 shares per contract X 0.40 = 400 shares). Effectively then, the risk in the ABC covered call write is equivalent to being long 600 shares of ABC at $25 per share.

At this stage, our investor’s portfolio is assuming the risk associated with 1.600 shares of two stocks trading at different prices. To determine portfolio risk, simply multiply the 1.100 shares by $50 plus 600 shares multiplied by $25 per share, which equals $70,000.

Essentially the investor is holding a $50,000 portfolio that, in terms of risk, will act like a portfolio worth $70,000. For the record, this portfolio is leveraged to the tune of 40%. The point is, investors would do well to understand position risk before committing to a trade.

ESP is simply a tool that can help break down the risk and leverage associated with complex option positions. Understanding how to use ESP, can help traders fine tune the risks associated with any position, and by extension, provide a clearer perspective as to leverage being employed at a point in time.