[kqr]

> Always think in absolute dollars and not in rates.

Technically, you should think in probability weighted log-dollars to maximise your economy over the long term. (The Kelly criterion.)

In some cases this is equivalent to thinking in terms of fractions of your total wealth -- this is how the Kelly criterion is popularly presented.

For small ("everyday", as Bernoulli put it) amounts, this is equivalent to absolute dollars. So you're right, but it's a special case of a more general principle.

[jenny91]

That assumes your utility of money is logarithmic in amount, which is not necessarily true.

[kqr]

Common misconception. It does not.

It makes only two assumptions:

- Growth compounds, and

- More is better.

Under those two assumptions, log-dollars is what you need to optimise.

By coincidence, logarithmic utility of money would also lead to the same conclusion, but that's mathematical happenstance, and not something going into the model.

----

Another way to put it: the Kelly criterion prescribes logarithmic utility. It says that to maximise growth (under above assumptions) you ought to adopt logarithmic utility. If you don't, you get worse results.

[jenny91]

That doesn't make sense, could you please elaborate? What do you mean by "growth compounds"? Do you mean that the value of 10% more is the same across all wealth levels, in which case you're implicitly assuming logarithmic utility?

[kqr]

By growth compounding I simply mean that the 2 % interest you earn today you earn not only on your starting capital, but also on the interest earnings of last year.

Another way to phrase it is that you reinvest your winnings.

[saeranv]

Looking at the wikipedia derivation of the Kelly criterion, taking the logarithm of the expected rate of return E[r] = (1 + fb)^p (1 - fa)^(1-p) is just to make finding the derivative easier (because logs are monotonic). Nothing else.