**Finding Markets For Ratio Writing**

Using OptionVue 5 options analysis software, which allows you to survey all options according to specified criteria such as implied volatility and statistical volatility levels, makes it is easy to identify markets that might be tradeable using a ratio writing strategy. Figure 1 below displays a list of markets surveyed on Oct 14, 2002, for the highest percentile ranking of implied volatility. Wheat, cocoa and coffee came up at the top of a list. As you can see in Figure 1, wheat options, with implied volatility at 31.6%, had an average implied volatility ranking in the 99th percentile.

High implied volatility means options are expensive in terms of historical average levels. Because option implied volatility eventually returns to its historical mean (reversion to the mean), it would make sense to get short this high volatility when it is at these extreme levels (i.e., 99th percentile). This percentile ranking is based on six years of implied-volatility data, so 31.6% is, therefore, at a level that is 99% of the highest high reached during the past six years. Figure 2 shows wheat futures statistical (solid line) and implied volatility (broken line) from September 1999 to the present.

As you can see, the 30% level is an extreme point, reached just one other time during the period (Apr/May 2000). Although not shown here, the average implied-volatility level over the previous six years is 22.2%, and statistical historical volatility level for the same period is 20.3%. Therefore, with average implied volatility of 31.6%, we have potential profit from a reversion to the six-year average level of 22.2%.

Figure 1: Survey of futures options with the highest implied volatility. Created using OptionVue 5 Options Analysis Software. |

The first requirement then is to find overall option markets with high implied volatility, which we have here with the March wheat futures options. Next, we need individual option strikes to have an implied volatility skew. Agricultural commodities, such as wheat options, typically develop what is called a "forward implied volatility skew".

By forward skew, we mean that the implied volatility of options increases as you move higher up the strike-price chain. This type of skew works well with ratio writing strategies because we are selling the higher strike price call options in greater number than the long futures (or long calls if ratio spreading), which are the ones with the higher implied volatility due to the forward skew.

Higher implied volatility means we can collect larger amounts of option premium; furthermore, this skew works well when you are buying a just out-of-the-money call and selling a larger number of deep out-of-the-money calls (ratio spread). The forward skew works well because it gives you a pricing advantage: you are buying the relatively cheaper options and selling the relatively more expensive ones. (Remember, with a forward skew, the implied volatility rises as you move higher up the strike price chain.)

Figure 2 – March wheat futures implied and statistical volatility chart. Created using OptionVue 5 Options Analysis Software. |

By looking at the March wheat options in Figure 3, we can see that they have a pronounced volatility skew, with implied volatility rising from 24.6% to 36% as the strikes get higher (going from 310 to 480). For example, the call option strike price of 460 (the one we will be selling) has implied volatility of 34.6%, which is significantly higher than lower strike implied volatility. The 460 strike price also has higher implied volatility than average volatility for all the strikes, which, as we indicated above, is 31.6%.

Figure 3: March Wheat Futures Options Chain and Implied Volatilities. Data derived using OptionVue 5 Options Analysis Software. |

Searching for markets to apply a ratio writing strategy requires two steps: (1) screening for markets with implied volatility (less than 90th percentile is best), and (2) examining individual strike price implied volatilities to determine if there is a forward skew.

**Constructing Our March Wheat Ratio Write**

Given that we have high overall implied volatility and a forward implied-volatility skew, we can construct a ratio write using the March wheat futures and futures options. With March wheat futures price at 369, we could go long 1 future and sell 5 Mar 460 calls, which are trading at 6 cents ($300 each, or $1,800 in premium collected). Now let's take a look at the profit/loss profile for this trade to determine at which points we will have a breakeven.

Take a look at Figure 4: should futures rally while we were in this trade, the breakeven upside point would be 490.5 (where the solid profit/loss plot seen above the futures price passes below the dashed breakeven horizontal line). This gives us plenty of breathing room should we have a higher breakout. By looking back at figure 2, we can see that the underlying March wheat futures (the shaded bar chart) can be seen behind the volatility plots, which show a September high (Sept 9, 2002) of 440. In order to provide some buffer, place breakeven points well above significant highs reached by the underlying futures contract. In this example, we have the breakeven at 50.5 points above 440, the most recent major highs. A major breakout on large volume, however, should be a signal to make an adjustment or even to close the trade altogether, especially if we move too fast too far.

At the same time, the breakeven is at 338.5 (where the solid profit/loss plot seen below the futures price passes below the dashed breakeven horizontal line), the point at which the short calls in the trade stop covering losses on the long futures contract. Should we continue to move lower, it is possible to buy back our calls and write additional ones lower for more premium, which allows for moving the downside breakeven point lower. And we could purchase a shorter-term put for protection.

Figure 4 - Created using OptionVue 5 Options Analysis Software. This example excludes commissions and fees, which can vary from broker to broker. |

Finally, this trade, based on prices taken Oct 14, 2002, expires on Feb 22, 2003. The maximum possibility of profit is $6,078 (minus any commissions or fees). As shown in Figure 4, the maximum profit would be at the strike price of 460, where the profit/loss plot pivots lower. If the market were to fall at expiration, every cent below your breakeven of $430 would result in a $50 loss. Initial margin for this trade would be approximately $600, but it can change with movements of the underlying futures.

Since we are selling high implied volatility with ratio writes (and are therefore short vega and long theta), we can have a profit even if the underlying futures is stationary, which, in fact, is often the best scenario. For a call ratio write, however, a moderately bullish move is generally going to give you the best profit. With the underlying futures remaining stationary and a reversion of implied volatility to the historic average along with time-value decay, we have the potential to profit even before the expiration date arrives. It is therefore possible to close the trade early and to take a partial profit, which can free up capital for another trade.

**The Bottom Line**

This article outlines the basic requirements that a market must meet to offer you a profit potential if you are using a ratio-writing strategy. The best conditions are high implied volatility (well above the historical average) and option prices with a forward volatility skew. We sold the higher strike call options in greater number than that of underlying futures contracts that we purchased (5 x 1 ratio). This generated a credit (premium collected), which we will retain as profit should the underlying futures remain inside our breakeven points. The underlying futures should have a neutral to bullish bias, but too much bullishness may require adjustments or closure of the trade to minimize potential losses.