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Why Fancy Probability Charts are Useless

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Most software packages and brokerage platforms that focus on options will give users a way to gauge what the market expects a given options contract to do. Statistics falling in this category include: probability of expiring in the money, probability of profiting at expiration, and visual probability cones and histograms -- things like that. These sorts of tools actually are useful sometimes, despite my title, especially for traders who are learning to structure a new type of options spread or who want an intuitive handle on how a position is likely to act during its life, assuming market prices are correct.

However, taken at face value, none of these sorts of metrics could ever provide the justification for entering a position:

1. An investor who thinks an asset is efficiently priced should be unwilling to buy that asset except as part of a market portfolio. (If the price is right, then don't buy.)

2. Market-implied probability and volatility statistics for an option are accurate if and only if market prices for the option are efficient. (Probability stats are true iff the price is right.)

Logical biconditionals like (2) are commutative, so:

3. From 1 & 2, it follows that if market-implied probability statistics for an option are accurate, then the option is efficiently priced, which means an investor should be unwilling to buy that option.*

As I said above, making plain the ranges of movement implied by current market prices can be genuinely helpful in understanding what investors believe about the value of some asset. But for a trade to be reasonable, you had better either disagree with the market price, or be hand-crafting an artisanal replication of the broad market click by glorious click. If you do disagree, then taking market-implied probability figures at face value doesn't make sense: the whole premise of your trade is that the figures on the screen are wrong in some way.

* What about investors who use options not to speculate, but simply to reduce the risk in an otherwise very risky asset? I'll argue that they're basically just working to make their portfolio look more like the market portfolio in a cost-effective way, which is consistent with (1).

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