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:



Sources and additional links for reference:



Ed Thorp interview post from Fundseeder



A Coin Flip

The result of the 2016 US Presidential Election was a win for Donald Trump. This result was indicated as less likely by some forecasting models – which saw Clinton as a c. 70 percent favorite to win the election. In such a situation, with essentially only a binary outcome, a heads-biased coin will still sometimes come up tails. Given the unpredictability inherent in forecasting the future, even with sophisticated modeling, how can we build an investment strategy around binary events?

  • Win/Loss Ratio = magnitude of the profit from winners divided by the loss from the losers (greater than 1.5 as a reference value)
  • Asymmetric outcomes – similarly, understanding the potential downside vs. upside of a position and looking for option-like payoffs
  • Margin of safety – from a value investing perspective, this will come looking at assets or cash flows that are undervalued by the market; there is also a probabilistic approach, where margin is achieved through high expected value.
  • Mispricings – following on from the last bullet, look for high probability events (based on your conviction, developed through fundamental analysis) priced assuming a low probability.
  • Loss aversion – Consider Jesse Livermore’s advice to “always sell what shows you a loss and keep what shows you a profit” or similarly the Wall Street adage to “cut your losses short and let your winners run.”

Sources and additional links for reference:






TED Spread

Today I read a case study on the events leading up to the Lehman Brothers bankruptcy. The case cited the record level of the TED Spread at that time as a measure of interbank credit risk. So what is it – and is it still relevant?

  • TED Spread = 3 month Libor (interbank lending) less 3 month T-bill rate (US Gov)
  • Indicative of credit risk and perceived health of the banking system
  • Values consistently above 50bps are relatively high (reached 4.5% after Lehman)
  • The spread has trended gradually higher throughout 2016 (now above 50bps)
  • WSJ article cites impact of new money market fund regulations as a factor
  • The spread still remains a relevant indicator of interbank liquidity and risk

Sources and links for reference:






Election night approaches in the United States. Gold has received attention as a refuge (http://www.bloomberg.com/news/articles/2016-11-06/hedge-funds-are-hiding-out-in-gold-as-election-fears-grip-market) although the price came off today (http://www.kitco.com/charts/livegold.html) along with other safe haven assets. So what are the key price drivers for this precious metal?

1 US currency – historically an inverse relationship (priced in USD)

2 US inflation rates and money supply – positively correlated (inflation hedge)

3 Risk, politics and monetary system – positively correlated (safe haven status)

4 Demand – c. 70% for jewelry, this is seasonal

5 Supply – from mines (c. 60%) and sales of existing gold (Central banks, c. 25%)

6 Other commodities, global growth – indicative of increased demand

Real interest rates – inverse relationship (non-interest bearing asset)

Sources and additional links for reference:



Six major fundamental factors