I am currently working on the application of the Kelly Criterion to Decision Analysis. The Kelly Criterion originally developed by John Kelly in 1956 will optimize the amount of money you should spent on any risky investment
Introduction
to Risk Aversion using the Kelly Criterion Jim
MacKay 6/30/2015 See
GCAGS Transactions 9/2015 The
basic issue Laying
the groundwork: Your
choices are to take all, part or none of either game (but not more than all of
either): Always
start by quantifying: Your
cost Your
gain Your
chance Your
capital available Your
cost (C ) Game 1: $70 Game 2:
$70 Your
gain (G) $80 $100 Your
chance (Ps) 100% 80% Your
capital available (Cap) $100 Your
initial calculations: The
Present Value (PV) The
Expected Value (EV) Your
initial calculations: The
Present Value (PV) PV=GC
Game
1: 100%*$80$70=$10 Game
2: 80%*$100$70=$10
So
far we know both the PV’s and EV’s are positive and the EV’s are the same for
both games Next
calculate the Kelly Criterion (K) K=EV/PV The
Kelly Criterion suggest how much of your capital available you should consider
spending on projects like these
Next
calculate the Kelly Working Interest (KWI) KWI=(EV/PV)*(Cap/C) Game
1: KWI= (10/10)*(100/70)=143% Game
1: KWI =MIN(1,((10/10)*(100/70))) = 100% Game
2: KWI =MIN(1,((10/30)*(100/70))) = 48%
Ideally
we should pay 100% of $70= $70 for game 1 and 48% of $70 = $33 for game 2. We
have $100 so we pay $70 to play 100% of game 1 and we pay $30 to play 43% of
game 2. All
of this can be built into a simple excel spreadsheet.
