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A Prisoner's Dilemma For Weekly Options

 November 28, 2012 03:33 PM

Weekly options may be good for traders, but fragmenting the distribution of options order flow across time makes analysis more difficult. Making options contracts more granular allows investors and traders to take positions that match more precisely their own expectations, but the cost of this increase in precision is a decrease in the ease with which we can make sense of the market and, in some cases, a decrease in liquidity.

First, let's get clear on why these tradeoffs matter. Precise financial instruments allow investors to take exactly the risks they want to and to lay aside the ones they don't. An investor who wants to hold Google for the long term but would rather give up the possibility of short-term 10% upside in the stock in exchange for a premium can sell call options against her shares. Options permit that kind of detail, which is why one of my favorite metaphors for options is that they are a kind of language, like French or Mandarin, allowing you to say all sorts of interesting things, where stocks and futures require more guttural up-or-down yeses and nos.

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Second, analytical clarity allows us to make sense of what other investors are doing. Perfectly granular data would be indistinguishable from noise and so unanalyzable. Finally, liquidity is necessary for investors to take advantage of their market views. Perfectly granular financial products would never trade, since markets require buyers and sellers who have conflicting views about some discrete claim, and too much division among types of claims makes it harder for traders to pair up.

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Take an extreme example: imagine that the market was only open one day per year, and all stock activity had to take place in that one session. The analytical task would be dead simple and there would be ample liquidity. But trading activity would be incredibly imprecise: it would express investor expectations about a wide range of possibilities for the year ahead, but would tell us nothing about sentiment at a three- or six-month horizon, much less about short term events like earnings announcements or economic data releases.

There are also some intuitive examples of this tradeoff specific to options: just think about the way that exchanges list strike prices among stocks. For a $500-600 stock like Apple that regularly makes daily moves of five or ten points, listing option strikes at one point increments would be unhelpful – it would add more precision than market participants require and would fragment the order flow among those strikes, reducing the liquidity of each individual strike. Conversely, options listed at every one hundred points would not allow investors to allocate risk with enough precision: options would start to function more like straight up-or-down bets on the stock price. Instead, options on AAPL are struck at five-point intervals which allows a good balance between precision and liquidity/analytical clarity.

What, then, should we think about weekly options, especially now that options on some stocks have options expiring every week listed up to a month in advance? The existence of potentially market-fragmenting financial products presents an interesting choice for investors. Here's how I think the game theory works out. Let's focus on the choices for two sets of agents in the options marketplace: you, and a substantial group of other traders.

If neither group trades weekly options, then the analytical cost to everyone is zero, since all of the informative market activity remains at the level of monthly and quarterly options and status quo liquidity is preserved. If we assume that trading weekly options would bring some valuable precision to some traders (which I think really is the case), then in this first scenario there is a loss of potential alpha. The first scenario is represented in the lower right-hand quadrant of fig. 1.

fig. 1. Game theory for agents facing new financial products. Source: Condor Options

Next, what if you trade weekly options but the substantial group does not? Since the group keeps its liquidity and analysis-changing activity in the status quo products, the costs to both you and the group are unchanged. But since you are trading the new products, you have a gain in alpha. As shown in the top-right quadrant of the table, this is a win for you and a loss for the group.

Conversely, if the group trades the new products and you don't, the situation is reversed. You still bear the costs of market fragmentation, which I'm representing with the letter Xi, but you don't get the alpha benefit. The group also has to pay the costs, but that is just definitional, since they are by stipulation a "substantial" group.

Finally, if both you and the group trade, everyone still bears the costs of the new product but everyone also achieves the precision benefit.

The attached graph is similar to the familiar layout of a prisoner's dilemma, especially since the non-collaborative move (not trading) is the worst outcome overall on the grid just as both parties confessing yields the worst net outcome in the prisoner's dilemma. Similarly, the collaborative move, where everyone trades or both prisoners refuse to confess, yields a better net outcome. This thought experiment actually might explain the success or failure of any new financial product – not just weekly options.

There are two important differences, though. First, the size asymmetry between you and the substantial group of other traders means the choice that is rational for you is always dominated by what the group chooses. If investors in general don't trade the new product, there's no incentive for any one individual agent to do so, either, unless the potential for alpha is great enough to overcome the transaction costs (including cognitive effort, regulatory & institutional inertia, etc.). If the real alpha potential for some investors is great enough, then it will be rational for them to trade the new product, and before long the sum of those individuals will amount to a substantial group. Once there is a substantial group involved, everyone already has to bear the liquidity and analytical costs, so it becomes rational for every investor to join in. In other words, the bottom left quadrant is never a permanent state for any rational individual – once enough critical mass (a substantial group) has been reached, the market should shift toward the top left state.

Second, whether a collaborative outcome in which everyone trades is actually better depends on whether the potential alpha is larger than the analytical and liquidity costs. In the case of weekly options, I don't have a strong intuition about that question for the market as a whole. One worry is that more front-loaded gamma will exacerbate short term market swings, as is already the case in the last few days of the monthly options cycle.



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