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Risk Analysis - Kelly Criterion

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:

    • You have in your pocket, available to spend $100

      • Consider that your “Stake”, or “Capital Available” or even your “Risk Tolerance”

  • Your choices are to take all, part or none of either game (but not more than all of either):

    • Game 1: Pay $70 to get $80

    • Game 2: Pay $70 to get an 80% chance of $100.

  • Always start by quantifying:

  • Your cost 

    • or how much you have to pay to play

  • Your gain

    • or how much you will get if you win

  • Your chance

    • or the probability you will win

  • Your capital available

    • Or how much you are willing to invest in risky ventures

  • 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 total of all your future gains converted to today equivalent dollars

      • It must be positive to consider it a possible investment

  • The Expected Value (EV)

    • The average value considering both winning and losing

      • If the EV is positive it is  potential investment

      • If the EV is negative it is a gamble and should be avoided

  • Your initial calculations:

  • The Present Value (PV)                                 PV=G-C

    • Game 1:  $80-$70=$10

    • Game 2:  $100-$70=$30

      The Expected Value (EV)                              EV=Ps * G -C

        • (the * means multiply in excel)

    • 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

      • John Kelly published this method while at Bell Labs in 1956 as a technique to evaluate the impact of noise during the transmission of information.  The example in the paper was betting on a horse at the race track.

    • Game 1: K= 10/10=100%  Game 2: K= 10/30 =33%

  • The Kelly Criterion suggest how much of your capital available you should consider spending on projects like these

    • Game 1: 100%*$100=$100 

    • Game 2: 33% * $100=$33

      The total unfortunately exceeds the capital available and $100 invested in game 1 exceeds the total cost.

  • Next calculate the Kelly Working Interest (KWI)

    • KWI=(EV/PV)*(Cap/C)

    • Game 1: KWI= (10/10)*(100/70)=143%

      • Unfortunately game 1 is limited to 100%

    • 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.

    • Excel Example

  • All of this can be built into a simple excel spreadsheet.

  •  

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James Mackay,
Jul 1, 2015, 12:39 PM
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James Mackay,
Jun 30, 2015, 12:36 PM
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