4 ms·
Yes, this is called the Kelly Criterion[1] which tells us we should optimize the expected value of the log of wealth, not the expected value of wealth directly
by olooney 3y ago
Yes, this is called the Kelly Criterion[1] which tells us we should optimize the expected value of the log of wealth, not the expected value of wealth directly. On a log scale, it's clear that doubling and halving have the same magnitude but opposite signs so are perfectly balanced.
[1]: https://en.m.wikipedia.org/wiki/Kelly_criterion https://en.m.wikipedia.org/wiki/Kelly_criterion
- cubefox 3y agoYes. Though the logarithms aren't essential here. It really is about maximizing the "geometric expectation", the expected value calculated by using the geometric mean instead of the usual arithmetic mean. Arithmetic mean: sum all values, then divide by the number of values. Geometric mean: multiply all values, then take the nth root, where n is the number of values.