How To Trade Stock Dispersion With Options

Moves in equity markets over the summer of 2024 might be described as either calm or full of big surprises, depending on which metrics you look at. On one hand, broader European stocks could be seen as trading sideways, with the benchmark Cboe Eurozone 50 Index slowly trading down less than 5% from about 18,200 on June 10^th to just under 17,400 on September 10^th. On the other hand, the same three month period saw relatively strong up moves in “old economy” sectors like Tobacco, where British American Tobacco and Imperial Brands rose 26% and 15% respectively, and in Telecommunications, where Telia rose 26% and Ericsson gained 16%, as well as in grocery stores Tesco and Ahold, which delivered returns of 20% and 12% respectively. At the other end of the market, some of Europe’s worst performing stocks over this period were car makers, with Volkswagen down 35% and BMW down 24%, followed by luxury, where Kering, Richemont and LVMH declined by 30%, 20%, and 18% respectively, and even in semiconductors, where Dutch giant ASML fell by 30%.

In this article, we introduce the concept and practical implementation of a “dispersion trade”, which generally involves trading a straddle on an index versus an opposite position in a basket of straddles on stocks in that index. These trades aim to profit not by taking a view on market direction, or even on the magnitude of market moves, but rather, on how widely dispersed the returns of the different stocks in the index end up being over the term of the trade.

The Simplest Straddle Dispersion: A 2-Stock Index

To introduce the concept of a straddle dispersion, it can help to use an unrealistically simple example where the index has only two stocks: stock A and stock B, in equal weight. We will say this index currently has a value of 100, and that this index is calculated as the simple sum of the prices of stock A and stock B, which just happen to both be exactly 50 at this time. We then consider a trade where we buy straddles on each stock A and stock B, offset by the sale of a straddle on the index. In total, this requires 6 option trades, though some brokers may be able to execute these as a package:

1.   Buy a 50 strike call on stock A

2.   Buy a 50 strike put on stock A

3.   Buy a 50 strike call on stock B

4.   Buy a 50 strike put on stock B

5.   Sell a 100 strike call on the index, and

6.   Sell a 100 strike put on the index.

In the absence of arbitrage, the straddles on stocks A and B will cost more than the straddle on the index, and only trade at the same price if A and B are perfectly correlated. For this example, let’s assume the straddle on the index costs 8, and the straddles on each of stocks A and B each cost 5, so that the net cost of this whole trade is that the trader pays two points (or €200) up-front to enter this trade. This makes sense when we consider the three possible outcomes of this trade:

1.   If both stocks A and B are above 50 at option expiry, then the payoff from the long calls on the stocks will exactly offset the payoff to the short call on the index, and all puts expire worthless, so the net option position expires worthless.

2.   If both stocks A and B are below 50 at option expiry, then the payoff from the long puts on the stocks will exactly offset the payoff to the short put on the index, and all calls expire worthless, so the net option position expires worthless.

3.   If one stock is up and the other is down, regardless of which is which, then the payoff from the stock options will exceed the amount paid out on the index options, resulting in a net positive payout, and a profit if this payout exceeds two points.

Re-stating these three outcomes using specific numerical examples, let’s say:

1.   If stock A finishes at 57 and stock B finishes at 53, then the index finishes at 110. The call on A pays out 7, the call on B pays out 3, but then the trader needs to pay all 10 of this out on the index call, resulting in zero net payout. The puts expire worthless.

2.   If stock A finishes at 43 and stock B finishes at 47, then the index finishes at 90. The put on A pays out 7, the put on B pays out 3, but then the trader needs to pay all 10 of this out on the index put, resulting in zero net payout. The calls expire worthless.

3.   If stock A finishes at 57 and stock B finishes at 47, then the index finishes at 104. The call on A pays out 7, the put on B pays out 3, and then the trader pays 4 of this out on the index call, resulting in a net payout of +6 points (or €600), tripling the premium put at risk in this trade.

In other words, this type of straddle dispersion trade makes sense for a trader who has an above-consensus view that stocks A and B will move in opposite directions, without requiring a view on which will go up vs down.

Of course, real stock indexes have many more than 2 components, and most of these indexes have weightings that are harder to replicate than the oversimplified price-weighting example above. In the next section, we explore how a trader may trade a straddle dispersion using a sample of stocks in an index.

A More Realistic Straddle Dispersion: Index vs 5 Stocks

Even when an index tracks 50 stocks, very often the 5 largest of these stocks, while representing over 10% of the components by number, can often represent 20-25% or more of the index by weight, and as a group, these top 5 stocks often explain 80% or more of the short-term moves of the overall index. For this example, we will assume an index with a starting value of 1,000, of which the top 5 components, stocks A, B, C, D, and E, are each trading at 50. Even with these round numbers, the trader needs to decide how to round the weights of the number of options of each of stocks A-E, since they are unlikely to match the weights of these stocks in the index. For this example, we use the following numbers of straddles:

1.   We sell 1x 1,000 strike straddle on the index,

2.   We buy 5x 50 strike straddles on stock A,

3.   We buy 5x 50 strike straddles on stock B,

4.   We buy 4x 50 strike straddles on stock C,

5.   We buy 3x 50 strike straddles on stock D, and

6.   We buy 3x 50 strike straddles on stock E.

We will assume that each of the stock straddles costs 5 points, or €500 each, versus the index straddle we assume to sell at 80 points or €8,000, for a net cost of 20 points or €2,000 for the whole position. In this case, the notional value of the stock straddles we are buying happen to add up exactly to the notional value of the index straddle we are selling, but in practice, this will almost never be exact. More importantly, the tracking error between our chosen 5 stock basket and the index adds an additional variable, which we can illustrate with the following three scenarios:

1.   Stocks A-E all finish up at 60, 58, 56, 54, and 52 respectively, as the index rises to 1,120. The stock calls pay out 5x(60-50) + 5x(58-50) + 4x(56-50) + 3x(54-50) + 3x(52-50) = 132 points or €13,200, versus the index call on which we need to pay out the 120 point increase, or €12,000. The puts expire worthless. While the net payout of all these options is positive, it is less than the €2,000 paid up front for the options, so the whole trade adds up to an €800 net loss.

2.   Stocks A-E all finish down at 40, 42, 44, 46, and 48 respectively, as the index falls to 860. The stock puts pay out 5x(50-40) + 5x(50-42) + 4x(50-44) + 3x(50-46) + 3x(50-48) = 132 points or €13,200, versus the index put on which we need to pay out the 140 point decline, or €14,000. The puts expire worthless. Here, the net payout of the options is a negative €800, which in addition to the €2,000 paid up front for the options, making the whole trade add up to a €2,800 net loss.

3.   Stocks A-E finish mixed, at 60, 40, 55, 45, and 50 respectively, while the index makes a modest rise to 1,050. The stock options pay out 5x(60-50) + 5x(50-40) + 4x(55-50) + 3x(50-45) + 3x(50-50) = 135 points or €13,500, versus the index call on which we need to pay out the 50 point rise, or €5,000. Here, the net payout of the options is a significantly positive 8,500, over 4x the €2,000 paid up front for the options.

This example should make clear that the best case scenario for a straddle dispersion trade involving buying stock straddles vs selling an index straddle is one where the stocks move a lot, but on average, the index moves relatively little, which generally means that some stocks in the index rise while being offset by other stocks in the index falling. This may suggest that in cases where the trader wants to be a bit more selective about which sample stocks to buy straddles on versus the index, that some care should be taken to chose stocks that are as unrelated to each other as possible, for example by choosing top stocks in different sectors rather than just the five largest stocks in the index.

Variants on Dispersion Trades

The two introductory examples in this article both assumed the trader wanted to go “long dispersion”, meaning the trader would buy stock straddles versus selling an index straddle with the expectation of profiting if some stocks rise and others fall, leading the stock straddles to pay out significantly more than needs to be paid back on the index straddle. As with any options trade though, the trader could just as easily take the opposite view, effectively going “short dispersion” by buying the index straddle versus selling straddles on component stocks. This trade would generally pay the trader an up-front premium, with the expectation of paying out less than this premium if most of the stocks in the index move in the same direction, but with the risk of losing much more than the premium received if dispersion ends up being more than expected.

Another variant on the dispersion trade is to put it on with only call options or only put options, rather than by combining both into straddles on both side. For example, going long a “put-put” dispersion means buying put options on component stocks vs selling a put option on the index. With a put-put dispersion, scenario 2 in the above examples would look very similar, but for the other scenarios, the trader would need to work out the impact of not having the call side of the dispersion trade on.

Before closing, it is also worth highlighting the importance of one key variable to consider in dispersion trades: the choice of strike price. In the examples, we assumed all options in our dispersion trade would be at-the-money, but this need not be the case, especially when we consider that the eventual profit or loss of the dispersion trade depends highly on how far the stock prices disperse from their relative strike prices. A trader who expects dispersion to come in the form of the index rising +20%, but with some stocks rising +30% and others only +10%, then placing the strike price 20% higher might have better expected results that doing so at the money. 

Conclusions

While dispersion trades are an advanced strategy that generally involves trading a large number of options at a time, the concept and applications should hopefully be much clearer after these examples. Next time when faced with what seems to be a “stock picker’s market”, consider if a dispersion trade might be a way to profit from the uncertainty. 

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