Measuring Risk with ESP

Richard Croft
November 5, 2012
5 minutes read

The options market is unique in the sense that it is all about risk modification. Traders can use options to leverage their risk profile or reduce variability within their portfolio. It all comes down to the quantity of options being employed and the strategy being implemented.

In my experience traders have little understanding as to the level of risk being assumed in a particular strategy. We know that a call option grants you the right to buy 100 shares of an underlying stock at a specific strike price, but does that mean your risk is the same as would be the case if you owned 100 shares of the stock?

Certainly changes in the value of the underlying stock will affect the options’ price. But the relationship between the underlying stock and the option is not linear. For one thing the option’s cost is the maximum risk which is a mitigating factor. Should the underlying stock decline by say $25 per share the options loss would be capped.

The relationship between the option and the underlying share value is notional in the sense that it will track the up and down movement but at a substantially reduced pace. If the underlying shares declined by $1.00 the call option might only lose 50 cents. That notional relationship is determined by the “delta”, which is a principal derivative in the option pricing formula.

Delta measures the amount an option is expected to move given a $1.00 move up or down in the underlying shares. Another way to look at delta is to ascribe an equivalent share position (ESP) to a particular option contract. The long call option with a delta of 0.50 is equivalent in terms of risk, to being long 50 shares of the underlying stock.

Taking this to the next level, ESP can be used to measure portfolio leverage and quantify the risk associated with complex option strategies.

Consider a $50,000 portfolio holding two stock positions; XYZ trading at $50 per share and ABC at $25 per share. The portfolio has exposure to these stocks through option strategies which includes 20 XYZ Oct 50 calls at a cost of $5.00 per share (total investment $10,000) and a covered call write on ABC.

To that end, the portfolio is long 1000 shares of ABC and short 10 six month 27.50 calls at $1.50 per share. Total ABC investment $23,500 (1000 shares x $25 less $1500 in option premium). The total capital committed for the two positions is $43,500.

At this stage, the portfolio is long XYZ calls, has a covered call write on ABC and holds $6,500 in cash. The objective is to determine how much risk and leverage is being assumed by the portfolio.

The XYZ Oct 50 calls have a delta of 0.55 which implies over short periods that XYZ Oct 50 calls should rise or fall approximately 55 cents for every $1.00 change in the price of XYZ. The ESP related to XYZ is 1100 shares at $50 (i.e. strike price) per share calculated as the underlying shares (2000) multiplied by the option’s delta (0.55).

The same methodology applies to the ABC covered call strategy. The portfolio is long 1000 shares of ABC which has a delta of 1 and translates into an ESP of 1000. Against the long ABC shares, the portfolio is short 10 ABC Oct 27.50 calls with a delta of -0.40.

Note that short calls give rise to a negative delta which translates into a negative ESP. In the ABC example, the short ABC covered call has a risk profile equivalent to being short 400 XYZ shares at $27.50 per share. The net ESP for the ABC covered call strategy is 600 shares at $25 per share.

To determine the portfolios’ risk or leverage simply multiply the ESP in each security by the underlying stocks’ current price. The 1100 XYZ shares (representing the ESP of the XYZ long call position) are multiplied by $50 per share which equals $55,000 total XYZ exposure.

To the XYZ exposure we add 600 ABC shares multiplied by $25 per share totaling $15,000. The total portfolio has risk exposure equivalent to $70,000 or stated another way, the portfolio is exposed to 40% leverage.

By understanding how to use ESP you should be able to 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.

Richard Croft
Richard Croft http://www.croftgroup.com/

President, CIO & Portfolio Manager

Croft Financial Group

Richard Croft has been in the securities business since 1975. Since February 1993, Mr. Croft has been licensed as an investment counselor/portfolio manager, operating under the corporate name R. N. Croft Financial Group Inc. Richard has written extensively on utilizing individual stocks, mutual funds and exchangetraded funds within a portfolio model. His work includes nine books and thousands of articles and commentaries for Canada’s largest media channels. In 1998, Richard co‐developed three FPX Indexes geared to average Canadian investors for the National Post. In 2004, he extended that concept to include three RealWorld portfolio indexes, which demonstrate the performance of the FPX portfolio indexes adjusted for real-world costs. He also developed two option writing indexes for the Montreal Exchange, and developed the FundLine methodology, which is a graphic interpretation of portfolio diversification. Richard has also developed a Manager Value Added Index for rating the performance of fund managers on a risk adjusted basis relative to a benchmark. And In 1999, he co-developed a portfolio management system for Charles Schwab Canada. As global portfolio manager who focuses on risk-adjusted performance. Richard believes that performance is not just about return, it is about how that return was achieved.

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