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Optimizing Equity Returns Using Derivatives...

SOMEWHERE BETWEEN A THREAT AND A PRAYER

During the height of the Cuban Missile Crisis, just hours before the United States was scheduled to invade the Soviet satellite nation, President Kennedy used a back channel communique to deliver a last-ditch offer for peace to Secretary Kruschev.  The Russian leader's first reaction was to call the letter 'somewhere between an threat and a prayer.' 

In this blog, I detail trades that use option overlays to manage the risk of the position.  However, as I have been analyzing these trades (and countless others that have preceded this dialog), I have admittedly found myself indecisive as to the most efficient way to apply the hedges.  While the ramifications aren't nearly as dire as those in the fall of 1962, I have felt like my judgements were somewhere between a wish and a prayer.  To remedy this, I have spent the last few days building an optimization model so I could replace the iterative process with one based in mathematical logic.

Here, I'll explain why I use option overlays for equity positions and the method I've just created to optimize the process.

WHY RISK MANAGEMENT IS NEBULOUS AND INEFFICIENT

There are seemingly thousands of tired cliches in finance.  I personally suspect that most of them were conjured up by sales and marketing "professionals" in efforts to convince prospective clients they knew what they were talking about... but I digress.

One trading chestnut is the 2:1 reward/risk notion.  The idea being that a trader (whether it be day trader, traditional asset manager or hedge fund manager) is looking for scenarios where the reward of a trade is - at minimum - twice the size of the risk.  This is what I was taught when I started trading and it seems to make sense.  If your winners are paying twice as much as your losers then you don't even need to be right half the time.  If you can do this, then it should only be a matter of time before you're on final approach to St. Thomas in your Gulfstream G650 where a 140ft yacht is waiting to whisk you away to a private bungalow on St. Barts where Giselle is waiting for you after she left that loser she was just with.  However, much like that last sentence, the 2:1 notion is a poorly-constructed, misconstrued fantasy.

Don't get me wrong, you definitely want your winning trades to make more than your losers lose.  The point I'm trying to make is that the 2:1 notion is flawed in the way traders attempt to pursue this payoff.

The first problem with the 2:1 notion is the management of the downside.  Back in May, YHOO was in a breakout pattern to the downside after it had moved out of a consolidation range around $45 to the low $40s.  On May 5th, the stock traded below $41 with an ATR of 81 cents... it looked like it was setup for a nice long move to the downside.  But just two days later, news broke regarding the sale of Alibaba and the stock gapped more than 5 ATRs back to $45.

Here's what it looked like:


This move took a lot of traders out of their short positions at a loss because they got stopped out or simply hit their risk limit.  Stops can be effective in protecting gains but they're mostly the trading equivalent of a prevent defense... the only thing they prevent is winning.  Look at what YHOO went on to do after the price jump... it resumed its breakdown and is now trading around $36 with - what looks to be - more downside to come.

If the downside management was the first problem with the 2:1 notion, then it's probably obvious that the upside is the second.  Traders commonly use price targets to determine exit points for trades but there are a couple of major drawbacks to this approach.

First off, price targets are nebulous.  Like I've previously written, it is impossible to predict equity prices and the means by which targets are set can be about as self-serving as the intelligence that lead up to the Iraq War or that followed the Gulf of Tonkin.  Practices for identifying price targets range from relatively sound fundamental valuation to the cartoonish like extending trend lines into the future.  Regardless of the legitimacy of the technique, they are often wrong - or more realistically, they are predetermined and self-justifying.

The second problem with price targets is that they fail to account for an important variable in the return equation... time.  It is far preferable to realize a 10% gain on investment in two weeks than in one year if you assume the risk is equal.  Due to the equivocal nature of price targets, there generally is no time frame associated with them and the longer it takes to realize the target, the lower the return on the capital devoted to the investment.


WHEN YOU'RE GOING THROUGH HELL, KEEP GOING

During the Battle of Britain, Churchill encouraged perseverance with the words, "When you're going though hell, keep going."  Hindsight clearly shows that this advice would have been beneficial to traders who were forced to exit their YHOO shorts after the price gapped back to $45... but at the time, there was no way of knowing what the stock would do in the aftermath of that dramatic move.

As I've noted before, I use option overlays on my equity positions.  This method addresses the failures of traditional risk management techniques like the 2:1 notion.

First off, in the event of a major move in the opposite of the intended direction, the option overlay will keep you in the trade as it can cover or - if well constructed - exceed the loss of the equity.  Going back to the YHOO example, a position with an overlay would have given the trader the option to 1) exit the trade at a small gain or 2) reset the option - taking the gains - and keep the short equity position.

Secondly, the issue of timing is also addressed when using overlays because the options are priced to an expiration date.   Take a look at the following chart which shows 25-day historical return paths of The Cheesecake Factory stock (CAKE):


The dispersion of the returns is generally widest at the end of the 25 day periods.  Options pricing reflects the relationship between time and price dispersion through the volatility component.  Therefore, it is inefficient to exit a trade before the expiration of the option... this also removes the necessity of having a target exit price as you simply exit the trade at the expiration of the option (or you can buy a new option and continue to hold).


ENGINEERING EFFICIENCY

The issue I had with using option overlays, however, was to know what the best combination of stocks and options was to use for each trade.  Options are available on any given stock in all shapes and sizes in terms of their risk characteristics and it's difficult to find the best one to use.

To solve this problem, I have spent the last few days building an optimization engine that accounts for multiple variables to produce the combination of assets that will maximize the expected value of a trade.

Here's a list of the input variables:
  • Volatility - historical, projected or implied
  • Expected Return (see the post 'Projecting Equity Prices...' on how return and vol expectations are calculated)
  • Three options with different strikes but the same expiration are made available to the optimization engine
  • Risk limits are set in the nominal form of maximum loss on the position at expiration of the options
The optimization model produces a projected range of equity values and then determines the most efficient combination of shares and options based on that projection.

Here's what it looks like:


This is an optimization on a potential long position on QIHU.
  •  The stock is trading at close to $65 and is in a bullish trend pattern.  
  • The model is given three September put options to chose from for the hedge: $65, $62.50 and $60.  
  • The maximum position loss at option expiration is set to ($10,000).
  • The model is also instructed to have a positive recovery in the case of a large down move in the stock.
The model returns a combination of:
  • Long 1,756 shares of the stock
  • Long 1 $65 put option
  • Long 20 $62.50 put options
  • Long 3 $60 put options
This combination of assets produces positive expected values in the range of one to three thousand dollars (there's a range because this is based on simulations).

This method will allow me to build efficient trades while continuing to reap the benefits of using derivative overlays.


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