7 ms·

If over time, your forecasts predictably change, then you can be arbitraged. If e.g. I know that you'll have a probability below 40% at some point in the futur

by ikeboy 8y ago

If over time, your forecasts predictably change, then you can be arbitraged. If e.g. I know that you'll have a probability below 40% at some point in the future, and I know you'll have a number above 41% at some point in the future, then it's trivial to create a strategy over time that is guaranteed to make money. Taleb's claim, as I understand it, is that Silver is incorporating random noise into his model and so will exhibit such predictably swings, which enables arbitrage.

andrewla 8y ago
So what you're saying, I guess, is that Silver, by dint of making point probability predictions, is offering a two-sided market with infinite liquidity trading at that value for a binary option, and you could make arbitrage gains by trading off of volatility? I'm having a fair bit of trouble picking up that from either Taleb's or Clayton's article, but let's say that it's a fair assessment. Is the complaint that the observed variance is high enough to enable these arbitrages? So in order to make his model arbitrage-free, Silver would have to provide a spread rather than a point price, with his forecast as the midpoint of the spread, and the width of the spread wide enough that .5 is always inside the spread, thus making the forecast economically useless? Or is it that Silver does not provide error bars that would estimate that uncertainty? Or is it that because of intrinsic uncertainty in the election?
- ikeboy 8y ago
  Well obviously Silver isn't actually offering to bet at those odds. But complaining that a model is incorrect because it enables arbitrage is a standard complaint, it's how you can prove all non-Bayesian models are irrational. That doesn't mean all Bayesian ones automatically pass the test though. Error bars and spreads are already outside the Bayesian paradigm, which demands a single number.
  - et2o 8y ago
    Curious about this. > It's how you can prove all non-Bayesian models are irrational Can you expand or link? > Error bars and spreads are already outside the Bayesian paradigm, which demands a single number Not following at all. What do you mean?
    - ikeboy 8y ago
      https://plato.stanford.edu/entries/epistemology-bayesian/supplement2.html https://plato.stanford.edu/entries/epistemology-bayesian/sup... >Not following at all. What do you mean? One assumption is that given a bet, you must choose to take a side of it. If you won't bet for something at X%, you must bet against it at 1-X%.
      - et2o 8y ago
        Ah, interesting link. I think I ran into some confusion since 'rational' and 'Bayesian' are somewhat overloaded terms. When I think of Bayesian analysis, I always think of Bayesian models which attempt to model uncertainty and always have a posterior distribution (spread) of outcomes. For example, in the Dutch Book page, instead of having a point-prior (P=0.51 (delta on P=0.51?)), each degree of belief could have some (different) distribution which could yield a posterior with a distribution and change the math here.
        ikeboy 8y ago
        Yeah well there's a difference if you're estimating a parameter or predicting true/false on an event.
        et2o 8y ago
        Not sure about that, think about the case of (Bayesian) logistic regression.
  - galby 8y ago
    Can you expand on this? Bayesian data analysis looks at the full posterior, and reducing that to a single number is frowned upon by most.
    - ikeboy 8y ago
      If you're looking at a single proposition then the probability of it being true is a single number. To say that the probability of it being true is a range is incoherent.
      - galby 8y ago
        I think most bayesians would disagree with you on this point :) It's not incoherent to analyze the posterior distribution by reporting a credibility interval instead of a single number (for example the posterior median).
        ikeboy 8y ago
        An interval to estimate a parameter is different from an interval to represent a probability. You can't have a range for a probability, you can have a range for a parameter you're trying to estimate.
        comex 8y ago
        Well, in theory you can divide the uncertainty into two parts, by supposing that the outcome is driven by a fundamentally stochastic process and you also have imperfect information about the parameters of that process. For example, the outcome could be determined by a coin flip but you’re not sure whether the coin is fair. In that case, there is a “true” probability of heads based on the nature of the coin, and separately, a Bayesian observer can have a probability distribution for (i.e. representing their beliefs about) the value of the true probability. The observer could then come up with a single number representing their belief in heads by taking the expected value of that probability distribution, and if they just want to gamble on the outcome, that number would be all they need. But in order to correctly update their beliefs given future information about the parameters, they have to remember the original probability distribution; they also might just be curious about the nature of the underlying stochastic process, in addition to the final outcome. How well that models an actual election is debatable, of course, but I think it does model it to some degree. In reality, there are not two stages but multiple, and none of those stages are necessarily fundamentally stochastic; rather, you just need exponentially more information to predict one stage than to predict the previous one, and without that information you may as well treat it as stochastic. For example, if I’m about to flip a coin, a god with exact knowledge of the state of my body and brain, the air currents in the room, etc. might be able to predict how I’ll throw it and how it will fall, but mere mortals have to treat a coin flip as random. Similarly, a god with exact knowledge about the state of the universe might be able to predict an election result eons in advance… though quantum randomness might trip them up. Getting more down to earth, if you just could poll every American about their political beliefs, you could make much better predictions than you can with real polls, which have to take random samples and thus accept some level of stochastic polling error. On the other hand, polls can also suffer from methodological error, which is fundamentally different in nature; it can be highly pernicious, but does require a smaller quantity of information to correct for. And so on.
mannykannot 8y ago
If over time, your forecasts predictably change, then they are not the best forecasts you could make with the information on hand (I take it that by "predictably change", you mean that they will change in a predictable way, not just that it is predictable that they will change somehow.) If I am not mistaken, an opportunity for arbitrage is not created merely by a certainty that they will change somehow; it would require that they change in a specific way, and deterministically so. Absent this, a bet would just be speculation, not arbitrage.
- ikeboy 8y ago
  >If over time, your forecasts predictably change, then they are not the best forecasts you could make with the information on hand. And this is precisely the complaint Taleb is making. An arbitrage is just a strategy that's guaranteed to make money. If you know for sure that something will go up and down at different points you could make money risk free. Simply buy at any point below the current price and sell at any point above.
  - Permit 8y ago
    > An arbitrage is just a strategy that's guaranteed to make money. If you know for sure that something will go up and down at different points you could make money risk free. Simply buy at any point below the current price and sell at any point above. This is not arbitrage. Also this is precisely the kind of strategy Taleb would have argued against in his book about black swan events.
    - ikeboy 8y ago
      Time arbitrage is arbitrage. If someone was flipping a coin and raising their price when it landed heads and lowering it when tails, arbitraging using reversion to the means would be a perfectly legitimate arb strategy. Taleb's argument is that Silver's estimates are based on random noise, and are thus vulnerable to this form of arbitrage.
      - lolc 8y ago
ummonk 8y ago
That isn’t arbitrage. Arbitrage entails making a guaranteed profit, not relying on predictable fluctuations.
- ikeboy 8y ago
  Arbitrage over time is properly called arbitrage. If the fluctuations are known in advance, then you make a guaranteed profit by trading over time.
  - ummonk 8y ago
    Yes, but you don't "know" the fluctuations in advance. You just have educated guesses about how they will mean-revert.
davidmanescu 8y ago
Silver's forecasts do predictably change, more precisely in that they swing deterministically in favour of one candidate whenever the most recent poll to come in favours that candidate heavily. Each time the probability drops below 40% (in your example) it is likely because the fair odds swung in the latest polls. To attempt to take advantage of this is to ignore the recent evidence (conditional upon that evidence being quite different to the current concensus). It's not at all unreasonable to do so, but isn't arbitrage. What if all polls started being increasingly conclusive leading up to election? 40, 39, ..., 0. No surprises and no arbitrage. Perhaps another way to express this critique of Silver's methodology is that it lends too much weight on recent outlier observations? Sure if you knew this you could profit off these swings, but making the arbitrage argument doesn't add much to the discussion to my mind.

by ikeboy 8y ago

andrewla 8y ago

So what you're saying, I guess, is that Silver, by dint of making point probability predictions, is offering a two-sided market with infinite liquidity trading at that value for a binary option, and you could make arbitrage gains by trading off of volatility? I'm having a fair bit of trouble picking up that from either Taleb's or Clayton's article, but let's say that it's a fair assessment. Is the complaint that the observed variance is high enough to enable these arbitrages? So in order to make his model arbitrage-free, Silver would have to provide a spread rather than a point price, with his forecast as the midpoint of the spread, and the width of the spread wide enough that .5 is always inside the spread, thus making the forecast economically useless? Or is it that Silver does not provide error bars that would estimate that uncertainty? Or is it that because of intrinsic uncertainty in the election?

ikeboy 8y ago
Well obviously Silver isn't actually offering to bet at those odds. But complaining that a model is incorrect because it enables arbitrage is a standard complaint, it's how you can prove all non-Bayesian models are irrational. That doesn't mean all Bayesian ones automatically pass the test though. Error bars and spreads are already outside the Bayesian paradigm, which demands a single number.
- et2o 8y ago
  Curious about this. > It's how you can prove all non-Bayesian models are irrational Can you expand or link? > Error bars and spreads are already outside the Bayesian paradigm, which demands a single number Not following at all. What do you mean?
  - ikeboy 8y ago
    https://plato.stanford.edu/entries/epistemology-bayesian/supplement2.html https://plato.stanford.edu/entries/epistemology-bayesian/sup... >Not following at all. What do you mean? One assumption is that given a bet, you must choose to take a side of it. If you won't bet for something at X%, you must bet against it at 1-X%.
    - et2o 8y ago
      Ah, interesting link. I think I ran into some confusion since 'rational' and 'Bayesian' are somewhat overloaded terms. When I think of Bayesian analysis, I always think of Bayesian models which attempt to model uncertainty and always have a posterior distribution (spread) of outcomes. For example, in the Dutch Book page, instead of having a point-prior (P=0.51 (delta on P=0.51?)), each degree of belief could have some (different) distribution which could yield a posterior with a distribution and change the math here.
      - ikeboy 8y ago
        Yeah well there's a difference if you're estimating a parameter or predicting true/false on an event.
        et2o 8y ago
        Not sure about that, think about the case of (Bayesian) logistic regression.
- galby 8y ago
  Can you expand on this? Bayesian data analysis looks at the full posterior, and reducing that to a single number is frowned upon by most.
  - ikeboy 8y ago
    If you're looking at a single proposition then the probability of it being true is a single number. To say that the probability of it being true is a range is incoherent.
    - galby 8y ago
      I think most bayesians would disagree with you on this point :) It's not incoherent to analyze the posterior distribution by reporting a credibility interval instead of a single number (for example the posterior median).
      - ikeboy 8y ago
        An interval to estimate a parameter is different from an interval to represent a probability. You can't have a range for a probability, you can have a range for a parameter you're trying to estimate.
        comex 8y ago
        Well, in theory you can divide the uncertainty into two parts, by supposing that the outcome is driven by a fundamentally stochastic process and you also have imperfect information about the parameters of that process. For example, the outcome could be determined by a coin flip but you’re not sure whether the coin is fair. In that case, there is a “true” probability of heads based on the nature of the coin, and separately, a Bayesian observer can have a probability distribution for (i.e. representing their beliefs about) the value of the true probability. The observer could then come up with a single number representing their belief in heads by taking the expected value of that probability distribution, and if they just want to gamble on the outcome, that number would be all they need. But in order to correctly update their beliefs given future information about the parameters, they have to remember the original probability distribution; they also might just be curious about the nature of the underlying stochastic process, in addition to the final outcome. How well that models an actual election is debatable, of course, but I think it does model it to some degree. In reality, there are not two stages but multiple, and none of those stages are necessarily fundamentally stochastic; rather, you just need exponentially more information to predict one stage than to predict the previous one, and without that information you may as well treat it as stochastic. For example, if I’m about to flip a coin, a god with exact knowledge of the state of my body and brain, the air currents in the room, etc. might be able to predict how I’ll throw it and how it will fall, but mere mortals have to treat a coin flip as random. Similarly, a god with exact knowledge about the state of the universe might be able to predict an election result eons in advance… though quantum randomness might trip them up. Getting more down to earth, if you just could poll every American about their political beliefs, you could make much better predictions than you can with real polls, which have to take random samples and thus accept some level of stochastic polling error. On the other hand, polls can also suffer from methodological error, which is fundamentally different in nature; it can be highly pernicious, but does require a smaller quantity of information to correct for. And so on.

mannykannot 8y ago

If over time, your forecasts predictably change, then they are not the best forecasts you could make with the information on hand (I take it that by "predictably change", you mean that they will change in a predictable way, not just that it is predictable that they will change somehow.) If I am not mistaken, an opportunity for arbitrage is not created merely by a certainty that they will change somehow; it would require that they change in a specific way, and deterministically so. Absent this, a bet would just be speculation, not arbitrage.

ikeboy 8y ago
>If over time, your forecasts predictably change, then they are not the best forecasts you could make with the information on hand. And this is precisely the complaint Taleb is making. An arbitrage is just a strategy that's guaranteed to make money. If you know for sure that something will go up and down at different points you could make money risk free. Simply buy at any point below the current price and sell at any point above.
- Permit 8y ago
  > An arbitrage is just a strategy that's guaranteed to make money. If you know for sure that something will go up and down at different points you could make money risk free. Simply buy at any point below the current price and sell at any point above. This is not arbitrage. Also this is precisely the kind of strategy Taleb would have argued against in his book about black swan events.
  - ikeboy 8y ago
    Time arbitrage is arbitrage. If someone was flipping a coin and raising their price when it landed heads and lowering it when tails, arbitraging using reversion to the means would be a perfectly legitimate arb strategy. Taleb's argument is that Silver's estimates are based on random noise, and are thus vulnerable to this form of arbitrage.
    - lolc 8y ago

ummonk 8y ago

That isn’t arbitrage. Arbitrage entails making a guaranteed profit, not relying on predictable fluctuations.

ikeboy 8y ago
Arbitrage over time is properly called arbitrage. If the fluctuations are known in advance, then you make a guaranteed profit by trading over time.
- ummonk 8y ago
  Yes, but you don't "know" the fluctuations in advance. You just have educated guesses about how they will mean-revert.

davidmanescu 8y ago

Silver's forecasts do predictably change, more precisely in that they swing deterministically in favour of one candidate whenever the most recent poll to come in favours that candidate heavily. Each time the probability drops below 40% (in your example) it is likely because the fair odds swung in the latest polls. To attempt to take advantage of this is to ignore the recent evidence (conditional upon that evidence being quite different to the current concensus). It's not at all unreasonable to do so, but isn't arbitrage. What if all polls started being increasingly conclusive leading up to election? 40, 39, ..., 0. No surprises and no arbitrage. Perhaps another way to express this critique of Silver's methodology is that it lends too much weight on recent outlier observations? Sure if you knew this you could profit off these swings, but making the arbitrage argument doesn't add much to the discussion to my mind.