Every major stock index — The S&P 500, Dow Jones Industrial Average, Nasdaq 100 and the Russell 2000 — has futures contracts that reflect market pricing of the underlying stocks. There are two basic groups of securities that are described by two pairs of indexes. The S&P 500 and DJIA describe the price movements of a more stable set of companies — on average larger and more traditional in their operations. The Nasdaq 100 and Russell 2000 indexes combined cover a wider range of stocks and include some that are relatively new to the market and prone to wider swings in price.

As shown by the two charts in “Stock index ETFs” (below), the four index ETFs have similar price movements — primarily trending in the same direction with almost identical dips and peaks, but at the same time maintaining their individual characteristics. For example, in both charts the S&P 500’s SPY and DJIA’s DIA are close together — sharing the price movements of larger, well developed, traditional enterprises. Meanwhile the Nasdaq 100’s QQQ and Russell 2000’s IWM exhibit greater volatility, especially after August 2016.

During the two periods, 2013 and 2014-2016, the Nasdaq 100 ETF, QQQ, gained the most from its greater volatility. Russell 2000 IWM did well during 2013 but fell to negative cumulative percentages of price changes after January 2014. QQQ and IWM remain the most volatile of the four index ETFs — one gaining while the other was sinking — showing that volatility works both ways.

### Option volatility

How does volatility affect the options on stock index mini futures compared to other non-index futures? “Crude, corn and index e-minis” (below) shows that the crude oil and corn September 2016 calls have higher values when implied volatility is the only factor separating the six series. The two pairs of index options — Nasdaq and Russell are higher, S&P 500 and DJIA are lower — have call price curves low enough to intersect the horizontal axis where the futures price-to-strike price is 0.86 to 0.90 while crude oil and corn intersect the horizontal below the ratio of 0.75.

Delta values (slopes of the price curves) are relatively low and flat for the stock index minis. “Stock index calls: September 2016” (below) illustrates the flat nature of the index call price curves. Russell IWM and Nasdaq QQQ are higher, reflecting their greater volatilities. S&P SPY and DJIA DIA are lower and paired more closely, matching the way their cumulative percentage price movements are paired in the two periods covering the three and a half years shown earlier. From the ratio of futures price/strike price equal to 0.94 to 1.00, all four call price curves are virtually on a straight line with a delta value not varying greatly from 0.500.

There are two types of volatilities in terms of timing: Short-term and long-term. Short-term price changes for the stock index ETFs are illustrated by day-to-day percentage price changes. For example, over the 594 days from Jan. 6, 2014, to May 2, 2016, there were a number of days during which the price increased by 2% or more; 23 for IWM, 22 for QQQ, 12 for SPY and nine for DIA. The number of days on which the price decreased by 2% or more was 19 for IWM, 16 for QQQ, eight for SPY and eight for DIA. The daily percentage changes during this period reflect the same relative volatilities as shown on the call price charts and historical charts of cumulative percentage price changes. The greatest volatility — short-term or long-term — belongs to the Russell 2000 ETF (IWM) followed by QQQ, SPY and DIA.

There are also two types of volatilities in terms of the defining source. For example, in estimating the options market’s implied volatility, one method is to use the Black-Scholes pricing model, finding the standard deviation of price movements for the underlying asset that makes computed call and put prices equal to the related market prices. This method assumes that all of the pricing data other than implied volatility are known, and that the only variable that needs to be found is volatility.

The alternative measurement of volatility is the calculation of an underlying asset’s standard deviation of price movements independent of the market’s implied volatility. By calculating the volatility based on actual price changes, the alternative source is computing past volatility and assuming this will continue into the future — at least through the period to an option’s expiration date.

Volatility-based past price movements — the second, non-implied source — is used by options exchanges and other providers of options price chains to show the thousands of put and call prices for contracts that have no trading volume but still need to be included to make the options price chain complete.

The LLP pricing model is based on options price chains data provided online by Barchart.com and Yahoo finance. Price chains online include the data computed based on past underlying price movements — theoretically accurate pricing based on Black-Scholes or similar options pricing models — and also contain the prices from actual trades during the day. Actual trade prices may be close to the accurate model, or may show significant variations.

Most variations from the theoretically accurate call price curve occur when the underlying-to-strike price is between 0.90 and 1.00. This is the area of most active trading because at lower than 0.90 the options are increasingly out-of-the-money and when higher than 1.00 the call prices are moving toward equality with intrinsic value, limiting the potential spreads between call market prices and their predicted values along the options price curve.

### Effect of trades

When trades take place at some distance from the predicted price curve computed by regression analysis, it is possible that options having larger variances are distorting the computed price curve, slanting it in their direction, either higher or lower.

By computing the options price chain along the accurate (non-implied) curve, the differences due to larger variances should be more visible and may assist in forming spread trades between strikes having positive versus negative price variances.

“Effect of inaccurate pricing” (below) shows the differences between the variations between call market prices and predicted values using combined accurate and implied pricing vs. prices that are all theoretically correct. The first column of predicted option prices, column A, is the regression curve based on listed call option prices for Russell 2000 Mini index September 2016 futures. Larger variations from the predicted price curve as the strike price approaches the current futures price show the effect of the options market mispricing calls, with several negative variances.

By using the highest five strike prices that have corresponding call prices that are probably computed as theoretically correct, a revised computed price curve is shown in column B. The variances remain low for the high strike prices, but become dramatically more negative as the strike prices approach the current futures price. The original negative variations are not as negative as they should be, and this is due to the original curve being pulled in their direction. Revised price curves based on theoretically correct prices rather than implied market prices should improve decisions on spreads between strike prices—shorting overvalued strikes and hedging with those that are undervalued.

### Matching pairs

The four stock index ETFs and the four mini-sized stock indexes may be classified in two pairs: (QQQ-IWM) and (DIA-SPY) in the ETF group; (Nasdaq 100-Russell 2000) and (DJIA-S&P 500) in the mini-index group. As shown earlier, QQQ-IWM form the most volatile pair of stock index ETFs, and for that reason may offer profitable trades based on the concept of collective behavior.

Charts showing price movements over time illustrate the idea of a flock, swarm, or school of stock indexes—separate individuals but all representing a species. Collective behavior of this type follows a typical pattern in which the group grows close together, is repulsed and separates, then regroups to repeat the sequence. The indexes tend to become closer as prices descend to a trough, then widen with the different individuals separating as prices rise to a more gradual top.

With DJIA, S&P 500 and their ETFs (DIA and SPY) continuing in the middle with a relatively constant difference in price movements between their price movements, the choice for trades based on collective behavior is the volatile pair, QQQ and IWM. “QQQ–IWM” (above) shows the difference between cumulative percentage price changes for the pair for the period from Sept. 1, 2015, to May 2, 2016. During this period there are two sets of widening and narrowing differences in cumulative percentage price movements. “Trading collective behavior” (below) summarizes the potential trades suggested by the widening and successive growing closer as prices decline.

The collective behavior trades are credit spreads because the more expensive ETF is sold, and risk is minimized because the indexes and their ETFs reflect price movements of a large and diverse number of stock issues moving in the same direction on average. The result is small to moderate returns on a low required short-term investment.