Paul Tetlock’s latest paper on the subject of prediction markets “Does Liquidity Affect Securities Markets Efficiency?” follows the lines of the other authors whose model starts with the concept of first generation prediction markets, designed in such a way that their prices express probabilities.
First: We should not be surprised that those markets “underprice high probability events and overprice low probability events”. This is a consequence of continuous information arrival. Any binary option MUST show this behaviour, mathematically, depending on its In-the-money or Out-of-the money state.
In the framework of Price Information Theory, with continuous information arrival, you “lose” probability until the prediction horizon sigma sqrt T of the price differential. No “irrationality” there. (Remember: “Austrians” start on the premise that man is rational.)
Second: The immediate analogy from such binary contracts to behaviour of securities markets is not permissible. Securities markets price discounted future cash-flows in consideration of the two risks (ex-ante volatility and noise) affecting them. Applying the problematic binary framework to securities prices does not make binary options a security, they stay what they are. (Price predictions on rice in China does not make them edible.)
Third: Based on this, it is easy to explain why the conclusions of the paper appear overdrawn: The better the probability of a binary follows the information decay, the more mispricing the presented model would detect. Mr. Tetlock final thoughts appear to run in a similar vein by stating in the end that “…, liquidity may only appear to be a priced risk factor because it captures some systematic element of mispricing.”
So: On this one, let’s stay with the cited conventional models (Kyle) plus some empirical evidence from “real” securities markets: Mispricing is greater in illiquid markets.
Hubertus Hofkirchner
The commentary offered above is absurd on its face. And while I don’t normally let such absurdity bug me, I’m afraid that this time it got to me, partly because the author uses the language of science, but not its method.
Let me go through the three points noted.
First, Hubertus notes that Tetlock finds evidence of a favorite-longshot bias, but then claims that “Any binary option MUST show this behavior” (adding the that this is true “simply for mathematical reasons”). As an empirical fact, many binary option markets (try the Economic Derivatives markets) do not show such a bias. And second, such a bias implies the existence of a profitable trading opportunity: Buy high-probability securities which are underpriced (especially if transaction costs are small relative to the mispricing). How can the existence of excess returns ever be inevitable? Instead, I’m led to respond that Tetlock has unveiled an interesting fact requiring an explanation – based on market frictions, behavioral motivations, or perhaps other forces.
Second, he argues that “Applying the problematic binary framework to securities prices does not make binary options a security”. This is also a wierd statement. Many “standard” securities can be built up as a portfolio of small binary securities. For instance, one could replicate the returns to holding a stock with a series of binary securities each linked to potential firm earnings in each period. And it is a simple axiom of no-arbitrage pricing that we don’t expect two portfolios with the same payoffs in each date and state of nature to be sold at different prices – no matter whether they are constructed of binary or other securities.
And third, Tetlock’s paper is empirical: it presents facts. Assuming that he got his regressions right (and he’s a very skilled empiricist) there is simply no point arguing that facts aren’t true. There is nothing here to be refuted. The facts he presents are interesting, and arguably worth the rest of us spending time making sure that the models that we previously believed in are consistent with the facts.
Now Paul Tetlock may have considered disagreements with others (possibly including me) about the most likely causes of the empirical patterns he documents, but it is that conversation that moves knowledge forward, not the sort of attacks presented by Hubertus based on unstated “mathematical reasons”, an undefined “Price Information Theory”, a “premise that man is rational”, and a bizarre (presumably self-interested) claim about a “problematic binary framework”.
Justin,
while I wished that your response was less emotional, I will try not to let that bug me. Let me go through your three points.
Point One: “As an empirical fact, many binary option markets (try the Economic Derivatives markets) do not show such a bias”. Please put a specific reference and I will review. I recall empirical work about Economic Derivatives when it had a one-off auction – this one specific time point means for me that no information decay will be expressed like in a continuous market. And I did refer loud and clear to a market continuous information arrival. Your second sub-point is not correct: Arbitrage is not a choice because of the timing of information arrival, e.g. in a running soccer match, a goal could still be scored as long as the match goes on, but the winning probability goes to 0 or 1 every moment. And THAT is the problem. No arbitrage there.
Point two: “For instance, one could replicate the returns to holding a stock with a series of binary securities each linked to potential firm earnings in each period.” This is theory, but the hedging problem of digital and barrier options have been recognized by market traders as well as academics. The practical implementation of a replication strategy with an underlying position (even if it exists with stocks or FCY) is next to impossible due to the large negative delta and gamma values near the barrier or strike price. A trader would have to swing large positions and make large adjustments which comes (in the real world) at a huge cost. Also that is just a practical comment because it was not my point. Refer to my soccer example for what it was. Put in a CDA quote for a probability, wait some time, have a second person make a deal, and think through what mispricing you’d expect. Mathematically.
Point three: “Tetlock’s paper is empirical: it presents facts.” So he does and I never argued this if you read my post carefully. But on the conclusion given point one and two I opined on a short path of Logic and – if you want to criticise this – without going through the method of Paul (no time). However, I do not apologise for this method.
As Ludwig Mises has not stopped to point out to “empirical” economists, we have to start with a Theory and then use Logic, particularly if empirical data are puzzling. I rather chose this way. Further, I have presented the Price Information Theory to the community at the Vienna summit and pointed out its usefulness by providing answers to some current questions (e.g. “5 questions on prediction markets”).
And from this sense and with the logic above, the induction “illiquidity = better price” is not one I support.
Hubertus, Regarding your first question, you can google for “reverse favorite-longshot bias” to find further examples. Justin didn’t refer to arbitrage regarding the favorite-longshot bias, but said that its existence implies a positive expectancy strategy — that means that its existence is not inevitable.
More generally, you have made some strong claims here and elsewhere and I look forward to seeing your theory fleshed out, not to mention empirical tests.
For example, a statement like “with continuous information arrival, you “lose” probability until the prediction horizon sigma sqrt T of the price differential” sounds very “quanty”, but I can’t make heads or tails of it on its own.
Where can one find a copy of “Eine mathematische Theorie der Preisinformation”? If the answer is that it is proprietary, you can understand how this might be exasperating.
Jason,
Longshot Bias is clear, it’s the specific one on EconomicDerivatives which needs to be cited to allow an answer, really.
I will make a short English note on some pertinent angels of the Theory and put it on SSRN in the next few days.
Sigma is somewhat similar to Black-Scholes’ volatility but denotes only such future information as is not yet available to any market participant. Information available to at least one but not all agents needs to be treated differently.
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