Thanks, really like this point (which I’ve kind of applied many times but not had such a clean articulation of).
I think it’s important to remember that the log returns model is essentially an ignorance prior[1]. If you understand things about the structure of the problem at hand you can certainly depart from it. e.g. when COVID emerged, nobody had spent any time trying to find and distribute a COVID vaccine. But it will be obvious that going from $1 million to $2 million spent won’t give you an appreciable chance of solving the problem (since there’s no way that could cover distributing things to billions of people), whereas going from $100 billion to $200 billion spent would do. Often early work can be valuable because it can spur future spending (so you might recover something like log returns in expectation), but in this case it was obvious that there would be much more than $2 million future spending whatever the early work did.
Well … also some problems which are solved via lots of little contributions actually have ex post log returns, rather than log returns just being an ex ante thing. But that’s a significantly smaller class of problems.
Thanks, really like this point (which I’ve kind of applied many times but not had such a clean articulation of).
I think it’s important to remember that the log returns model is essentially an ignorance prior[1]. If you understand things about the structure of the problem at hand you can certainly depart from it. e.g. when COVID emerged, nobody had spent any time trying to find and distribute a COVID vaccine. But it will be obvious that going from $1 million to $2 million spent won’t give you an appreciable chance of solving the problem (since there’s no way that could cover distributing things to billions of people), whereas going from $100 billion to $200 billion spent would do. Often early work can be valuable because it can spur future spending (so you might recover something like log returns in expectation), but in this case it was obvious that there would be much more than $2 million future spending whatever the early work did.
Well … also some problems which are solved via lots of little contributions actually have ex post log returns, rather than log returns just being an ex ante thing. But that’s a significantly smaller class of problems.