This is homework for me for '15.  I need to review this one over and over as it does not sink in so well.

The Kelly Criterion.

The half Kelly compared to the Full Kelly.

Some links of info are too complex and some too focused on poker.

I like the background story here

http://home.williampoundstone.net/Kelly.htm


Kelly died tragically young, of a brain hemorrhage at the age of 41. He was by then the head of Bell Labs' information coding and programming department and the author of several patents. Kelly has one further claim to fame. In 1961 Kelly and colleague Carol Lochbaum demonstrated a new voice synthesis system by making a recording of their machine singing the song "Daisy Bell," better known as "Bicycle Built for Two."


It has to do with allocation and that as the odds change( subjective probabilities that get substituted for a frequency table) so should the bet. Here is the part that I need to review..
Full Kelly
the simple formula 2x the probability-1= the bet ( allocation)

the half Kelly

The half Kelly bet has some interesting mathematical properties. For risk management purposes, the nice property is that it cuts your risk of temporary loss (i.e., volatility) by a large amount while reducing your return expectation only a little. The other important property of the half Kelly bet is that it gives a large margin of safety in the risk estimate. If you are off by a factor of two on your risk of loss estimate, a full Kelly bet will reduce your return expectation to zero. But a half Kelly bet will leave you with 2/3 of the return expectation. Not surprisingly, underbetting is far, far safer than overbetting.

With the full Kelly bet, your probability of temporary loss is a linear function of the amount of loss. For example, you stand a 90% chance of losing 10%, an 80% chance of losing 20%, a 50% chance of losing 50%, etc. Not many investors are comfortable with the prospect of a 50% probability of losing 50% of their money. With the half Kelly bet, your probability of temporary loss is a quadratic function of the amount of loss. For example, you stand a 81% chance of losing 10%, a 64% chance of losing 20%, a 25% chance of losing 50%, etc.

Your expected gain with the half Kelly bet is reduced by 25%. For example, if your expected gain is 40% with the full Kelly, it is 30% with the half Kelly, if your expected gain is 30% with the full Kelly, it is 22.5% with the half Kelly, and if your expected gain is 10% with the full Kelly, it is 7.5% with the half Kelly.

Commentary;  Don't beat yourself up if your allocation to a bet was NOT set for the maximal gain ( Full Kelly) as a half Kelly is pretty darn good.:-)

It's been a good yr. since I thought I had need of this info, so thats a good feeling also.