A Coin Flip (II)

There is more to be learned from the coin flip analogy with investing. In particular, given that investing typically also involves a repeated process over multiple events with binary outcomes, a coin flip can be used to examine potential strategies. Having read the FT article below, I tried my hand at the linked exercise. Although I played according to the Kelly Criterion and consistently went for heads, when the clock finished my capital position was below that at the start. What lessons could be learned from this?

  • Is the amount suggested by Kelly appropriate?
    • The Kelly Criterion suggests the fraction of capital to bet (F) is given by the expression:     F = PW – (PL/W)   where
      • W = Bet return (win size over loss size)
      • PW = Win Probability
      • PL = Loss Probability
    • Volatility of capital in my example was relatively high – in particular, peak-to-trough was c. $70
    • Fractions of Kelly are often recommended (for example, half Kelly reduces the return expectation by about three-quarters with half the volatility)
    • Also, the capital base to which the Kelly Criterion is applied should be your maximum tolerable drawdown, and not your total bankroll)
  • How long to keep playing?
    • From my example, there were two distinct occasions when returns were approximately 200% of starting capital
    • These occurred after runs of approximately 10 coin flips, where the majority (80 – 90%) were favorable
    • The expected number of coin tosses to get a run of only 5 consecutive heads is 62, which points to the number of rounds required to get a positive return from this game
    • The advice “You’ve got to know… when to walk away” is worth heeding, although this may be easier said than done
    • Another option is to consider ways in which you can improve your odds of winning from any given round

My results:

 

kelly

Sources and additional links for reference:

http://coinflipbet.herokuapp.com

https://www.ft.com/content/7cd9b6c8-9cd7-11e6-8324-be63473ce146

Ed Thorp interview post from Fundseeder

https://en.wikipedia.org/wiki/The_Gambler_(song)

http://math.stackexchange.com/questions/364038/expected-number-of-coin-tosses-to-get-five-consecutive-heads

Leave a Reply

Your email address will not be published. Required fields are marked *