The Kelly Criterion in Modern Investing by acm63157


									 The Kelly Criterion in
  Modern Investing
 Undergraduate Honors Thesis
      By Bernard Gordon
Advisor: Ignacio Palacios-Huerta
• Impressive blow-ups by highly touted
  hedge funds
  – Long-Term Capital Management
  – Amaranth Advisors
• Very obvious that these funds failed at risk
  – How did managers trained and weeded by a
    more or less efficient market get so far without
    better risk management skills?
          Previous Answers
• Trader’s Option: Manager of hedge fund
  shares in the fund’s gains but not losses,
  so has an incentive to take on extra risk

• Media and other observers also cited
  “greed” of LTCM and Amaranth

• This contains an implicit assumption:
  Taking on risk will always be rewarded
• Is it always the case that an investor will
  be rewarded for taking on more risk?

• On a single bet, yes. The efficient market
  will compensate investors for taking risk.

• When a bet is compounded over time,
  though, this is not always the case.
• Consider a special casino with only 1 game:
  – Place a wager, and flip a fair coin
  – Lose your bet if tails
  – Win your bet plus 10% if heads
• This is great, a casino where gamblers can
  actually make money.
• How much will a gambler make over time?
  – Depends on the wager
  – If a gambler wagers his entire fortune every time, his
    expected wealth is:
  – E(WN) = 1.05*

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