## The skew has it

March 16, 2015 12:00 PM

#1

Provable options trading systems are based on these three pillars: State-subsystem mapping (SSMap), the growth position (GroP) and continually following the current trend/state (CoFT). There are many implementations of options trading systems that are based on this general and conceptual design.

Here, we will describe the framework of these systems. This framework is designed to profit, primarily, from options skew. The goal here isn’t to detail the component trading strategies, but instead to show how they can be combined into a larger trading approach that should persevere, and profit, in all market states.

### OTM call, put price skew

There is a large difference between the prices of equally out-of-the-money (OTM) call and put options. For example, on April 18, 2012, when the price of the QQQ exchange traded fund was near 67, the price of the QQQ May 73 call was near 0.02 and the price of the QQQ May 61 put was near 0.20. Even though the strikes were equidistant from the current market, the options with those strikes were priced quite differently.

Indeed, even though both options are equally OTM and have the same time to expiry, the price of the put is about 10 times greater than the price of the corresponding call. We call this price difference the skew. We may quantify this skew as the ratio of equally OTM put/call prices with the same time to expiry. In the above example the skew is 0.2 / 0.02 = 10. For many actively traded options this difference exceeds 10.

We note that stock prices advance about 40% of the time and they decline about 30% of the time. And for a random stock the probability it will jump, say 20%, is almost the same as the probability it will slump 20%. So, the probabilities that both options will be profitable are about the same. Therefore, the prices of equally OTM call and put options also should be approximately the same. Given this, we can design a trading system that attempts to profit from this skew.

In general, profits from the skew can be had by trading mainly favorably skewed options. By trading “favorably skewed options,” we mean to buy/hold OTM calls and sell/write OTM puts. Some well-designed vertical put spreads and all at-the-money (ATM) and near-the-money options are considered favorably skewed.

Prices of ATM calls and puts usually are approximately equal, and the more OTM the options, the bigger their price skew. The OTM call is relatively cheap compared to an equally OTM put. Therefore, far OTM calls preferably should not be written (sold short), but they may be bought and held. The opposite is true for far OTM puts; it’s preferable to write them and minimize buying and holding them, but it’s fine to trade some well-designed vertical put spreads.

A strategy can profit from the skew by emphasizing buying and holding far OTM calls, and minimizing writing them; as well as maximizing writing and minimize buying/holding far OTM puts.
Let’s now look at how we can put these theoretical concepts into practice.

As mentioned, provable options trading systems are based on SSMap, GroP and CoFT. Let’s look at each in depth.

State-subsystem mapping: By its current volatility and trendiness we identify five states of the market, and we have a trading subsystem for each. We try to trade the subsystem that has the highest expected return with the lowest risk for each state. Almost everything we do depends on the current state. Before we trade, we try to identify the market state.

We can automate the SSMap even though we do not know the current state of the market, and we assume the market is a random walk. We are not sure about the current state and we know even less about the future. Nevertheless, as we’ll see later, most of the time we trade the subsystem that best fits the current state.

Growth position: There is a dream in options trading to find a strategy with a sure profit. We have good news and bad news about this. The good news is that we can approximate complex hedged positions that can only grow (GroPs). But the bad news is that such positions exist only temporarily. Therefore, for some states we must continually trade provable options trading systems to keep our portfolio to approximate a GroP.

“GroP” is a complex hedged position that has a positive expected return with a low risk for most states of the market. A key to success and a constraint here is that the GroP should be formed using mainly favorably skewed options.

Any single option or complex hedged positions—if held until expiry—has a negative expected return. So the only way we can get a positive expected return is to trade continually to follow the current state and in some states trade to keep our option portfolio to approximate a GroP.

There are many ways we may approximate a GroP. One way is to hold a far OTM call and a put vertical spread with the same deltas and time to expiry. Another example is to hold a straddle and write enough OTM iron condors to get a credit balance. This position will grow if there is a small uptrend, a small downtrend or no trend. But it has a relatively high risk. One way to minimize risk is to CoFT. So CoFT is our next pillar.

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