With SPY closing at $136.47 last Friday, our hypothetical investor's option positions that were established last month (see Investing In A Paranormal Market: June Update) again expired worthless.

This was the desired outcome and results in the current "brokerage statement" shown in Table 1:

## Table 1

15-June-2012 | 20-July-2012 | |

Cash Balance | $ 12,360 | $ 12,360 |

SPY Jul 146 Call | $ 7 | $ 0 |

SPY Jul 142 Call | -$ 27 | $ 0 |

SPY Jul 123 Put | $ 76 | $ 0 |

SPY Jul 127 Put | -$ 123 | $ 0 |

Total | $ 12,293 | $ 12,360 |

Our investor now has a cash balance of $12,360 compared to an initial (January 6, 2012) balance of $12,200. The YTD gain of 1.31% lags significantly behind the gain in SPY over the same period (7.9% including a $0.688 quarterly dividend posted in June).

But the modest gain is a consequence of our conservative credit spread strategy for this investor, which included a cap on downside loss of -2.7%.

Given the continuing uncertainty about the global equity markets, a cap on downside loss seems prudent for our investor who is interested in *conservative* option strategies as a potential way to generate income on his largely cash position.

Looking forward into August, our investor decides to continue with this approach, again establishing put and call credit spreads on either side of the current price of SPY. To review the rationale behind this, you might want to go back to the first article in this series (January 9) and then glance at each subsequent monthly update.

To select the strike price boundaries for August expiration, our investor starts by making a rough assessment of the probabilities of a range of outcomes for the price of SPY on the August 17 options expiration date.

There are 20 trading days between market close on Friday, July 20, and market close on Friday, August 17. Looking at all of the 20-trading day price changes of SPY from January 29, 1993 (earliest available data for download from Yahoo! Finance), through the present, the mean 20-day price change has been 0.59% with a standard deviation (assuming a normal distribution of price changes) of 4.75%.

Repeating what I stated in last month's update, let's take a closer look at these mean and standard deviation values, especially since they may suggest a much higher degree of accuracy (and usefulness) than is actually the case.

First of all, I listed the mean and standard deviation numbers to two decimal places *only* as an aid to anyone who cares to try to duplicate these calculations using their own download of the Yahoo! Finance data. If you get 0.59% and 4.75% as well, then at least you know that your method of calculation is the same as mine.

... But getting the same numbers (or not) shouldn't be construed that either of us actually *knows* any more about what the market will do than we did prior to making the calculations.

*If* market prices follow a normal distribution (which they don't), and *if* past history is a predictor of future price movements (which it isn't), then one could say there is a 68.2% probability that the price change in SPY between last Friday and August 17 will be between -4.16% and +5.34%. You could also say that there is a 95.4% probability that the price change in SPY will be between -8.91% and +10.09%. These numbers represent +/- 1 and +/- 2 standard deviations, respectively, from the mean and are represented in Figure 1 below by the light green (+/- 1 standard deviation) and dark green (+/- 2 standard deviations) areas.

But if market prices don't follow a normal distribution and past history isn't a predictor of future price movements, what value is there in calculating and displaying mean and standard deviation numbers?

Well, another way of looking at these numbers is to say (again, if market prices follow a normal distribution) that * if* the change in SPY is outside the range of -4.16% and +5.34% on August 17, then this will be an event that happened only 31.8% of the time since March, 1993 (when the first 20-trading day period occurred after January 29,1993). And if the change in SPY is outside the range of -8.91% and +10.09% on August 17, this will be an event that happened only 4.6% of the time since March of 1993.

The subtle, but important, difference between *predicting* a probability and *observing* the number of times that potential changes were outside of an historic range helps our hypothetical investor in establishing risk/reward trade-offs.

More specifically, if our hypothetical investor wants to select strike prices on options with the goal of receiving a near-constant positive return across a broad range of outcomes that occurred over the past 19 years, then the following credit spreads may be suitable for this purpose:

- Purchase an August 145 Call contract for $0.09, and sell an August 141 Call contract for $0.38 (bear call spread).
- Purchase an August 127 Put contract for $0.40, and sell an August 131 Put contract for $0.74 (bull put spread).

*[Note: prices are based on the bid price for short options and the ask price for long options at market close on Friday, July 20, as reported on the Yahoo! Finance website. As such, the prices in this example may not be indicative of actual transaction prices that would have been realized intraday.]*

These strike prices were selected with the aid of an Excel spreadsheet that superimposes the proforma P/L (Profit/Loss) diagram at expiration with the mean and standard deviation values:

## Figure 1

The green circles illustrate how the value of the cash+options portfolio will change relative to the change in the price of SPY between the July 20 and August 17 option expiration dates. The gray circles show how the value of the portfolio will have changed between January 6 (when the portfolio was initiated) and August 17 based on the change in SPY between July 20 and August 17. This is useful to get a sense of whether we are making gains as the year progresses.

Figure 1 shows that the greatest return will be achieved if SPY closes on July 20 at a price between roughly -1 standard deviation to about +1/2 standard deviation from it's long term price change over 20 trading day periods.

The dashed line from the lower left to upper right of the graph illustrates how a portfolio consisting entirely of SPY would change compared to a change in SPY. The relevance of this line is that it illustrates the extent to which the portfolio will outperform SPY at expiration.

Thus, the cash+options portfolio will outperform SPY for those outcomes where the circles are above the dashed line. We see that for the coming month (green circles), the portfolio of cash and options will outperform SPY if the change in SPY is less than about 0.5%.

However, our investor will realize a modest 0.5% gain in his portfolio if the change in SPY is within the range of about +/-3%.

These potential outcomes are satisfactory for our hypothetical investor. In the best case, the investor will achieve a realized gain for the month of about 0.5%, or roughly 6% annualized. In the worst case, Figure 1 illustrates that he will realize a loss of about -2.7% for the month, or -1.5% YTD.

Summarizing for this month, then, Table 2 shows what our hypothetical investor's "brokerage statement" now looks like just prior to market open on July 23:

## Table 2

23-July-2012 | |

Cash Balance | $ 12,423 |

SPY Aug 145 Call | $ 9 |

SPY Aug 141 Call | -$ 38 |

SPY Aug 127 Put | $ 40 |

SPY Aug 131 Put | -$ 74 |

Total | $ 12,360 |

The next update to this series will be shortly after August 17 when these options expire. I hope you will continue to follow the progress of our "Paranormal" investor (to be alerted of the next update simply select the "Follow" button under my picture in the upper left of this page).

One last note. This simplified example does not include the impact of commissions or fees on the return of the hypothetical portfolio. Also, please be aware that investing in options carries certain risks and may not be suitable for all investors. You should consult with your financial adviser prior to initiating any options trades. Lastly, the example strategy illustrated in this article is for educational purposes only and may or may not be indicative of options strategies employed by Johnson Harper LLC on behalf of its clients.

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