ANALYTICAL TOOLBOX: Platinum Backtest Tools, IV Model
April 19, 2007
Newly employed combination strategies can be backtested via the Platinum Greek Model discussed last week or via the Implied Volatility [IV] Model. This second model may provide insight that is less intuitive than greeks are to the experienced trader. As a result, the learning curve for the new strategy may be accelerated.
Strategy Set-Up & Scan
A call calendar spread that appropriately addresses risk is established by selling a shorter term call option and buying a longer term call option. Risk is appropriate because the short call is protected by the long call through its expiration. When the strategy uses different strike prices, the call calendar represents a diagonal spread.
An ideal calendar scenario exists when there is an IV skew for the calendar pair. That is, the short term IV is higher than the longer term IV. This may occur when the near month option is at-the-money [ATM] or near the money and the longer term option is in-the-money [ITM]. Such a combination can be evaluated with the Covered Call trade finder along with other Platinum tools.
On a monthly basis, a scan is completed on the Monday following expiration searching for IV skews that include near month call options for the short position and further out options for the long position. The top two positive skews with a minimum Probability of Profit value are traded, if these two criteria, along with others are met. This system is part of the OASIS Trading with Probability Curve topic and will be further outlined there. The calendar spread is closed on the last trading day before the short expiration by buying back the short position and selling the long position.
Backtest Using the Greek Model
The calendar scans described were backtested over two periods; a bearish period from Jul 2000 to Jun 2002 and a bullish period from Jan 2005 Dec 2006. The first trade from each period is used here to display the greeks over the course of the trade.
The first calendar established was an Amazon (AMZN) Aug-Jan 40-35 spread on the Monday following Jun 00 expiration. AMZN closed at $38.75, so the 40 strike short call with approximately 1 month to expiration was near the money while the 35 strike long call with approximately 6 months to expiration was ITM. The IV skew was +11.86 with IV levels higher for the short position that would experience quicker time decay ([selling the higher IV).
Figure 1 displays the backtest Greek Model from trade initiation to expiration of the short option. Since closing values are used, there is a significant change in greek values when the short leg expires worthless (highlighted, with a close for AMZN at 39.00). Net IV and the skew increases the first two days the trade was in place, then net IV oscillates between 169 and 194.
Figure 1: Platinum Greek Model for AMZN Calendar Trade Initiated Jul 24-2000
(Click here for larger view.)
Although the IV skew served as a basis for the trade, the trader new to such a position will gain more information from the Delta and Theta columns. Note the values from Jul 28th through Aug 1st for price, delta and theta. A $0.13 rise in price holds losses steady over the weekend [net change to position = 0], but the following day a $0.12 rise improves the position by $19.
IV Model Components and Review
The Platinum IV Model Backtest tool provides daily historical values for a user-defined period that includes position profits (actual and model), delta and breakevens, as well as ATM IV and other data. In addition, three more unique measures include:
- Odds to One,
- Kelly Bet Fraction [KBF] and
- Platinum Probability of Profit.
A quick review of the three components is provided here. For more detail, check the Aug and Sep 2006 Analytical Toolbox article series on these topics.
Odds to One: Odds incorporates trade profit expectations and payoffs. These expectations are derived from a large series of trials using actual outcomes and payoffs to calculate the expected probability of profit for future trades, then the odds. The calculations are similar to betting probability and odds.
A common betting example provides a good introduction. If an individual pays $1 for the opportunity to receive $2 each time a tail results when a fair coin was tossed 1000 times, the probability of profit and odds for the trial are calculated as follows:
Probability of Profit
= Tails Possible / Total # of Tosses
= (1 in 2 chance of Tails, 1000 times) / 1000 tosses
= ( * 1000) / 1000
= 500 / 1000
This represents a 0.50 Probability of Profit. The odds calculation incorporates the payout as follows.
Odds
= (1 chance in 2 for $2 gain (1000 times)) / (1 chance in 2 for $1 loss (1000 times))
= ( * 2 * 1000) / ( * 1 * 1000)
= 1000 / 500
= 2
Although there is a 50-50 chance to win each coin toss, the odds for the bet are favorable since the payout is twice the bet amount. The expected probability of profit is expressed as 1:2 and the odds are expressed as 2:1.
Platinum estimates these measures by running a very large number of simulated trades using statistical volatility [SV] for the underlying and certain assumptions about stock movement and volatility going forward. The Platinum Probability of Profit discussion covers this in slightly more detail and provides the actual Platinum Odds calculation.
Kelly Bet Fraction: The Kelly Bet Fraction is an aggressive betting approach that relies on certain assumptions about the wager. It was developed by John Kelly, a former Bell Labs scientist, and is based upon Claude Shannons work on information theory. It is aggressive because it uses a high percentage of the individuals account in attempts to build the account at the quickest rate. It also is based upon a smaller number of outcomes when compared to stock price movement.
KBF = 100 * {[(Probability of Profit * (Odds + 1)) 1] / Odds)
Using the example: KBF = = 100 * [(0.5 * 3) 1] / 2 = 100 * (0.5 / 2) = 25%.
This result suggests that given these probability and odds for a certain bet, 25% of the individuals funds should be wagered to optimize the account rate of growth. KBF is displayed in a variety of Platinum screens and is used as a ranking tool here. If you have more interest in this measure, you need to truly understand calculations underlying it and all implications of the results. Be sure to read the referenced articles and Platinum Help on the topic.
Platinum Probability of Profit (PoP)
Similar to Odds, the Platinum Probability of Profit runs a large number of simulated trades to determine expected probability of profits for a particular trade. Again, SV is used to create potential price movement paths, with the assumption that SV will remain the same throughout the trial and that the expected stock growth rate is 0. In other words, it assumes that ultimately price movement is sideways.
The tool generates simulated trades to determine expected PoP by dividing the number of winning trades by the total number of trials. The Odds to One measure takes this a step further by incorporating actual gain and loss values into the calculation and reducing the result to its equivalent value with 1 in the denominator (x:1).
Platinum PoP
= # of Winning Trades / Total # of Trade Simulations
Odds = $ Sum of Profits / $ Sum of Losses
These three measures are provided in the next backtest model. First, a review of the risk graph and probability curve for the AMZN trade is provided to display the information available to the trader on the day the position was established.
Backtest Using the IV Model
The risk graph and probability curve for the AMZN calendar spread are provided in Figures 2 & 3. The Probability Curve is generated by the Probability Calculator which is populated with trade information and accessible via the Probability of Profit value on the Risk Graph page. Since the default settings assume a stable volatility environment and sideways price movement, it is suitable for use without change on the AMZN calendar spreadat least initially while the short leg is intact. This price characteristic for the position is displayed as a profit peak on the risk graph that coincides with the trade entry value.
Figure 2: Platinum Risk Chart for AMZN Calendar Trade Initiated Jul 24-2000
(Click here for larger view of top half of chart.)
(Click here for larger view of bottom half of chart.)
The Probability of Profit using 90-day SV was 63 on July 24th. The Probability Curve shows this information graphically by first displaying two price cones for expected movement in AMZN using the historical 90-day movement along with standard deviation values, and second by delineating a trade profitability region using the grey breakeven lines. Using a period of 24 days into the future, 63% of the trials resulted in price movement that was profitable for the position.
Figure 3: Platinum Probability Curve for AMZN Calendar Trade Initiated Jul 24-2000
(Click here for larger view.)
When the IV Model backtest data is reviewed, we see the Probability of Profit (PoP) value along with trade Odds and the KBF. Since AMZN did not remain stable, but declined instead, we see these three statistics declining also. When PoP declines below 50%, KBF goes to 0.
On Aug 14th price returns to an area that, if stable should produce profits (34.88). At this level the short option would expire worthless while the long option would retain time value. As AMZN moves back towards the initial price where the trade was established, PoP, Odds and KBF all improve. On Aug 21st the short option is no longer a leg in the trade and PoP declines since it continues to calculate the likelihood for profitability given sideways price movement and AMZNs 90-day historical movement.
This backtest page is a great way to gain a better sense of PoP, Odds and KBF, providing you understand the model assumptions. On August 21st, the trader may decide instead to evaluate the PoP for a new trade using the existing long leg and a new short term, short leg.
Figure 4: Platinum IV Model for AMZN Calendar Trade Initiated Jul 24-2000
(Click here for larger view of top half of chart.)
(Click here for larger view of lower half of chart.)
Note the PoP, Odds and KBF movement as the price of WFMI fails to remain stable. A greater than 10% move upward right before expiration drops the PoP significantly. Also note the price-PoP relationship once the position consists of just a long leg.
Figure 5: Platinum IV Model for WFMI Calendar Trade Initiated Jan 24-2005
(Click here for larger view of upper half of chart.)
(Click here for larger view of lower half of chart.)
Summary
In addition to providing a trader with a sense of how the price of the underlying and position greeks impact the profit/loss values for a trade, the backtest function can also provide insight to other trade analysis tools. The IV Model allows a trader to gain a better sense of how a position may fare from a statistical standpoint. It doesn't mean certain PoP values guarantee profits, but it may provide a more realistic view of profit expectations for new strategies.
To see the other articles by this author, please click here.
Clare White, CMT
Contributing Writer and Options Strategist
Optionetics.com ~ Your Options Education Site
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