ANALYTICAL TOOLBOX: Trade Odds
September 28, 2006
The September article series focused on a Probability of Profit value that
- Is derived using a statistically valid method to project prices, and from this
- Measures profitable outcomes versus the total number of outcomes.
The default mode for the Optionetics Platinum tool that calculates this measure favors sideways trading strategies, but can be adjusted by the user for other outlooks. In order to successfully apply the tool, the user must understand that the closing value for the underlying security on the day the analysis is performed is the expected future mean value for the calculation. In addition, this value and the selected volatility value remain constant over the price projection period.
Before leaving the topic behind, there remains one last concept that will help the user apply the tool. Since stock prices do not drop below zero, the application of the Probability of Profit calculation on the lognormal distribution results in a graphs with a slight upward bias. A more obvious view of this bias is displayed in Figure 1, which represents a sideways/neutral outlook with the default setting for the stock mean at a future date and a 100-day statistical volatility [SV].
Figure 1: Upward Bias is Inherent in the Calculations
Although the process uses price projections to determine the number of profitable outcomes relative to total outcomes, the data does not make use of expected profitability levels at expiration. That is, the Probability of Profits tool does not tally an expected profit or loss by using each price projection to determine individual profit and loss values. However, the Odds calculation—also available on the Platinum platform—does make use of projected prices to provide a measurement that incorporates profits or losses.
Odds & Expected Profits
When using the “Find a Trade” application in Platinum, the user has the ability to rank the trades by a variety of methods including the Probability of Profits and Kelly Bet Fraction (see Analytical Toolbox article “Kelly Bet Fraction” from 8/10/06). Once a table of trades is generated, the user can evaluate the data based on risk, greeks or volatility, each of which provide measures that allow for additional sorting. The default measure for volatility when needed in a particular calculation is the 100-day SV.
Using Find Trades III the trader can identify a direction and volatility outlook to search a specific security or list of securities. A variety of other search parameters can also be identified including:
- Volatility Settings
- Strike Price Variations
- Liquidity Filters
- Cost & Risk Filters
- Expiration & Time Filters
- Probability & Statistic Filters, and
- Implied Volatility Filters.
In this way the user can substantially limit the number of trades listed and use a volatility setting that reflects the time to expiration for one or all legs in the position.
Let’s assume the trader believes current volatility is low and has a bullish outlook for large cap stocks (S&P 100 is representative). Since it’s late September, a seasonally bearish period may be ahead, so the trader will include two types of calendar spreads in the search along with a debit call spread. The trader uses a 90-day SV setting and seeks stocks with at least 60 days to expiration. Although the there is a directional bias, the calendar strategies benefit most when the initial movement is sideways to moderately bullish. Because of this, the trader also sets the Probability of Profit filter to a minimum of 75% and elects a trade sort using Odds to rank the lost provided.
Figure 2 provides a look at the Find Trades III parameters while Figure 3 and 4 display headings for the different data tables available.
Figure 2: A Partial List of Find Trades III Parameters
Figure 3: Trade Analysis Data Using “Risk”
Figure 4: Trade Analysis Data Using “Ratios”
The highest ranked calendar spread for this analysis was a diagonal calendar spread for US Bancorp (USB) that goes long a Jan-07 30 call and short a Dec 32.50 call. The best case scenario for this strategy is for USB to remain below 32.50 through Dec expiration, then advance upward through Jan expiration.
A quick review of the trade profile follows: the cost of the trade is $2.30 per contract (1 long + 1 short) and the Dec call is covered by the January call. In the event the stock rises above 32.50 by Dec expiration and the short option assigned, the trader can exercise the long Jan call at 30 for a gain of 2.50 per share of stock. The maximum risk is realized if USB is trading below 30 at Jan expiration. The risk graph generated by Platinum follows, along with the Probability of Profit result.
Figure 5: Risk Graph for USB Diagonal Calendar
Figure 6: Probability of Profit for USB Diagonal Calendar
Although the Probability of Profit picture is very good (85.41%), we want to look at expected profits and odds for this trade. The calculations for these two similar measures are as follows:
Expected Profits = (Probability of win% * Size of win%) – (Probability of loss% * Size of loss%)
Odds = (Probability of win% * Size of win%) / (Probability of loss% * Size of loss%)
These two measurements use projected price values based on the current close and the 90-day SV to calculate the actual profit and loss outcomes based on the projections. In this way, the trader also makes use of statistical measures to rank by the level of profits for the strategy. Although the probability of profit is very high, the expected profit for the trade is $11.56 with odds of 2.5 to 1.
What are Odds?
Odds provide an unbiased method to determine the likelihood of an event given certain assumptions. Removing bias when trading absolutely helps, but we always need to consider how our assumptions impact the expected (statistical) result. Before we consider the impact, let’s breakdown Odds further.
A casino example is a useful start: the true Odds of rolling a 7 in dice are 6/36 = 1:6 while the true probability of rolling a 7 is Probability = [1/6 / (1+1/6)] = 14.3 %. In this case odds and probability reflect different ways of expressing similar information. The actual relationship between the two is as follows:
Odds = Probability of Profit / (1 - Probability of Profit) (Odds Equation)
In Optionetics Platinum, the Odds are affected by win or loss size, while the Probability of Profit is not.
One-to-one odds represent even odds. This actually means that 50% of the time we expect to win. If we bet a dollar and gain a dollar when we win, we expect to break even in the long run. Since traders seek to be profitable in the long run, they need to seek odds with payoffs that are advantageous.
Going back to the casino example, on a craps table the casino pays 5:1 for rolling a 7 rather than 6:1, so the casino is not paying true Odds. This is the house advantage and those that play with the house in craps are expected to have gains in the long run. In order for the individual to go against the house, the payoff would have to be better than 6:1 – for instance, 7:1.
Translating this to options analysis, the trader wants to consider market conditions and the risk-reward picture. When the payoff odds are better than the statistical odds, the position favors the trader. The statistical odds are those that result given the model assumptions (sideways trading with the designated volatility measure constant).
In Platinum, if true Odds using the equation with Probability of Profit values is less than computed Platinum payoff odds from trader quotes, then the option trade is favorable. In this instance the Kelly Bet Fraction [KBF] is a positive number. Otherwise KBF is 0.0 and the trade is not favorable.
Trade Review
So referring back to the trade selected, the USB diagonal calendar position, we note the following:
Buy 1 USB Jan 30 call @ $3.8 and simultaneously
Sell 1 USB Dec 32.50 call @ $1.50 for a net debit of $2.30
The max risk for the position is the net debit of $2.30 and the max profit at the near month expiration is $0.20 [(32.50 – 30.00) – 2.30 = 0.20]. In the event the near month option expires worthless, there is unlimited profit potential; however this is not part of the model and cannot be assumed in the analysis.
The probability of profit is 85.41%, the Odds for the trade are 2.5:1 and the KBF value is 80%. This means that the payoff odds (market conditions) are more favorable than the statistical odds and the position should be considered.
Of course the analysis cannot stop there. Consider that both options are in the money when the position is established and that the true position potential will only be realized if the stock undergoes a bearish move, followed by a bullish reversal. The trader still needs to ultimately determine whether or not their risk parameters are met and the extent to which the model assumptions fit the strategy.
Summary
As with anything else, the modeling tools in Platinum are best used when put into practice. In the world of trading and risk management, this means experimenting with the platform and creating paper trades that can be monitored during the term of the trade. This will allow the individual to determine which of their preferred strategies are well suited to the tools, the market conditions that impact strategy selection and will also provide a new way to evaluate potential positions.
Once a better intuitive understanding of the model and its assumptions is achieved, adjustments can be made to reflect the user’s reasonable outlook. The Probability of Profit calculator is best suited to sideways strategies. Always note the SV used for the probability calculations and be careful using those that may not be representative of the trading period.
The Odds calculation adds a profit-loss component to the calculations. When the payoff odds exceed the statistical odds, the KBF value will be positive. The trader can sort by any one of these three parameters to begin evaluating a list of trades obtained via the Find Trades tools.
Copyright© 2006 Optionsanalysis, Inc. and Optionetics, Inc. All Rights Reserved.
To access other articles written by Clare White, please click here.
Clare White, CMT
Contributing Writer and Options Strategist
John Broussard
Optionetics Platinum Developer
Optionetics.com ~ Your Options Education Site
Questions for Clare? Visit the Optionetics.com Discussion Board
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