- Some are not computable. Bank runs can be set off by sunspots.
- The probability can only be estimated (underestimated!) from historical data.
- Pascal's mugging
- You need exponentially more evidence to get probabilities closer to 1 or 0.
- Probabilities cannot be zero or one, because then you cannot change your mind, as per Bayes' Theorem
Monday, 25 February 2019
Very low probabilities
Humans are bad at dealing with very high and very low probabilities.
Taleb on investment strategies and time horizons
Taleb points out that investment strategies can appear to work for a long time, but eventually fail. He also says that whatever works cannot be stupid.
There is no time horizon after which we can say that a strategy has worked. However, we can say for certain if a strategy has failed, and you lose all your money. A species can survive for a million years -- it appears to be successful -- then it goes extinct.
There is no time horizon after which we can say that a strategy has worked. However, we can say for certain if a strategy has failed, and you lose all your money. A species can survive for a million years -- it appears to be successful -- then it goes extinct.
Unambiguous forecasting
FiveThirtyEight.com is a website which aggregates political polls. It has a reputation as being more successful in its political predictions than other pollsters. How deserved is this reputation?
In the 2016 United States presidential election, the markets thought Trump had about a 20% chance of winning. FTE thought he had a 29% chance of winning, which is better than the market (Trump did win). Other pollsters were giving him a 15% chance. So if we trusted FTE, we would have bet on Trump and would make money over the long run, making similar bets.
But FTE does not make bets! Your performance at prediction depends not only on whether your odds are better calibrated than your opponents, but also on how much of your wealth you allocate to each bet. Bets function as a second-order expression of the error bars you assign to your odds. For example, if the market probability is 20%, and your odds are 29% plus or minus 10 percentage points, you might not make the bet.
We cannot judge the performance of FTE because they are not allocating bets, so we don't know how their confidence varies across their predictions.
If you make a bet, it forces you to make the question sufficiently unambiguous, enough so that it can be judged by a third party. Most predictions are not sufficiently unambiguous, and people claim undeserved victory afterwards.
That is not to say that predictions are worthless if criteria for success are too ambiguous to bet on. But one shouldn't crow about them.
In the 2016 United States presidential election, the markets thought Trump had about a 20% chance of winning. FTE thought he had a 29% chance of winning, which is better than the market (Trump did win). Other pollsters were giving him a 15% chance. So if we trusted FTE, we would have bet on Trump and would make money over the long run, making similar bets.
But FTE does not make bets! Your performance at prediction depends not only on whether your odds are better calibrated than your opponents, but also on how much of your wealth you allocate to each bet. Bets function as a second-order expression of the error bars you assign to your odds. For example, if the market probability is 20%, and your odds are 29% plus or minus 10 percentage points, you might not make the bet.
We cannot judge the performance of FTE because they are not allocating bets, so we don't know how their confidence varies across their predictions.
If you make a bet, it forces you to make the question sufficiently unambiguous, enough so that it can be judged by a third party. Most predictions are not sufficiently unambiguous, and people claim undeserved victory afterwards.
That is not to say that predictions are worthless if criteria for success are too ambiguous to bet on. But one shouldn't crow about them.
Competing monies
What is the probability of the price of gold falling to less than $100/oz before the year 2100? (Currently over $1000.) Approximately 0%?
It could be replaced by bitcoin, though it hasn't been replaced by any other currency yet.
What is the probability of the price of bitcoin falling to less than $100 before the year 2100? (Currently over $3000.) More than 1%?
It could be replaced by another cryptocurrency.
Demand for stores of value is distributed over various commodities. If demand remains constant, one currency's gain is another's loss.
It could be replaced by bitcoin, though it hasn't been replaced by any other currency yet.
What is the probability of the price of bitcoin falling to less than $100 before the year 2100? (Currently over $3000.) More than 1%?
It could be replaced by another cryptocurrency.
Demand for stores of value is distributed over various commodities. If demand remains constant, one currency's gain is another's loss.
Bubble dynamics
In a bubble, prices rise gradually, but they can crash suddenly. The stock market can fall 30% in one day, but it will never rise 30% in one day, though it might in one week. The reason people were so terrified about the 2010 Flash Crash was because it could have turned into a real crash, kicking off a depression.
Land and bubbleicity
Land exhibits bubbleicity. If the interest rate is 5%, the (risk-adjusted) return on a piece of land is unlikely to rise much above that, because entrepreneurs will bid up the price of the land, lowering the return. However, it is possible for the return on land to fall below the interest rate, far below it, as people bid up the price of land even further. Some property in London has a return of 5%, other property only 1%. People are over-paying for land. Why? Because they expect to be able to sell it to someone else for at least the same price. It exhibits bubbleicity, a permanent bubble. It is being used as a store of value.
The price of money
There is no fundamental way to value money. Money is in a permanent state of bubble, and there is no fundamental way to value something in a bubble.
Therefore, there is no fundamental way to value an exchange rate. All you have are historical prices. The only reason the health of a country's economy affects the price of its national currency is because people expect it to, but it doesn't have to.
Imagine a government issues a new currency: one million blank pieces of green paper. These will find a market value. If the same government issues another currency, one million blank pieces of blue paper, these will also find a market price. They are effectively different currencies. Just because they are issued by the same government, and the same quantity, there is no reason why they should reach the same price. People might start using one for small change, and one for higher-value transactions.
Imagine instead that the government issues green and blue paper as above, but prints the number "10" on the greens and "1" on the blues. Now we might expect them to trade at a ratio of precisely 10 to 1, and they are effectively one currency.
Therefore, there is no fundamental way to value an exchange rate. All you have are historical prices. The only reason the health of a country's economy affects the price of its national currency is because people expect it to, but it doesn't have to.
Imagine a government issues a new currency: one million blank pieces of green paper. These will find a market value. If the same government issues another currency, one million blank pieces of blue paper, these will also find a market price. They are effectively different currencies. Just because they are issued by the same government, and the same quantity, there is no reason why they should reach the same price. People might start using one for small change, and one for higher-value transactions.
Imagine instead that the government issues green and blue paper as above, but prints the number "10" on the greens and "1" on the blues. Now we might expect them to trade at a ratio of precisely 10 to 1, and they are effectively one currency.
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