There does actually seem to be a simple and general rule of extrapolation that can be used when no other data is available: If a trend has so far held for some timespan t, it will continue to hold, in expectation, for another timespan t, and then break down.
In other words, if we ask ourselves how long an observed trend will continue to hold, it does seem, absent further data, a good indifference assumption to think that we are currently in the middle of the trend; that we have so far seen half of it.
Of course it is possible that we are currently near the beginning of the trend, in which case it would continue longer than it has held so far; or near the end, in which case it would continue less long than it has held so far. But on average we should expect that we are in the middle.
So if we know nothing about the investment scheme in the post, except that it has worked for two years so far, our expection should be that it breaks down after a further two years.
Trivially true to the extent that you are about equally likely to observe a thing throughout that timespan; and the Lindy Effect is at least regularly talked of.
But there are classes of observations for which this is systematically wrong: for example, most people who see a ship part-way through a voyage will do so while it’s either departing or arriving in port. Investment schemes are just such a class, because markets are usually up to the task of consuming alpha and tend to be better when the idea is widely known—even Buffett’s returns have oscillated around the index over the last few years!
Another reason investment schemes are an exception is because they grow exponentially. This probably means you are much more likely to see them at their peak than at a random time.
Yeah, one has to correct, when possible, for likelihood of observing a particular part of the lifetime of the trend. Though absent any further information our probability distribution should arguably be even. Which does suggest there is indeed a sort of “straight rule” of induction when extrapolating trends, as the scientist in the dialogue suspected. It is just that it serves as a weak prior that is easily changed by additional information.
There does actually seem to be a simple and general rule of extrapolation that can be used when no other data is available: If a trend has so far held for some timespan t, it will continue to hold, in expectation, for another timespan t, and then break down.
In other words, if we ask ourselves how long an observed trend will continue to hold, it does seem, absent further data, a good indifference assumption to think that we are currently in the middle of the trend; that we have so far seen half of it.
Of course it is possible that we are currently near the beginning of the trend, in which case it would continue longer than it has held so far; or near the end, in which case it would continue less long than it has held so far. But on average we should expect that we are in the middle.
So if we know nothing about the investment scheme in the post, except that it has worked for two years so far, our expection should be that it breaks down after a further two years.
Trivially true to the extent that you are about equally likely to observe a thing throughout that timespan; and the Lindy Effect is at least regularly talked of.
But there are classes of observations for which this is systematically wrong: for example, most people who see a ship part-way through a voyage will do so while it’s either departing or arriving in port. Investment schemes are just such a class, because markets are usually up to the task of consuming alpha and tend to be better when the idea is widely known—even Buffett’s returns have oscillated around the index over the last few years!
Another reason investment schemes are an exception is because they grow exponentially. This probably means you are much more likely to see them at their peak than at a random time.
Yeah, one has to correct, when possible, for likelihood of observing a particular part of the lifetime of the trend. Though absent any further information our probability distribution should arguably be even. Which does suggest there is indeed a sort of “straight rule” of induction when extrapolating trends, as the scientist in the dialogue suspected. It is just that it serves as a weak prior that is easily changed by additional information.