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2014issue C0820-25

Expected value and bet size are separate controls

A 25-year sample of 250 S&P 500 constituents put median expected value below a roulette house-side comparison. Approximate growth tracks expected value times down-move size, and an approximate Sharpe ratio tracks expected value rather than bet size.

  • A 25-year sample of 250 S&P 500 constituents produced a median expected value of 0.035, versus 0.0526 for the house side of a 38-pocket roulette comparison.
  • Median buy-and-hold annualized return in that equity sample was 12.4 percent, below the 29.2 percent house-side roulette figure computed at N=252.
  • Approximate buy-and-hold equity growth is proportional to the product of expected value and down-move size, so a respectable edge still produces modest returns when exposure per period stays small.
  • An approximate Sharpe ratio expression is proportional to expected value, so raising bet size does not by itself improve reward per unit of volatility.
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Current trackSharpe ratio14 readingsExpected value18 readings

Sample comparison

A 25-year sample of 250 S&P 500 constituents produced a median expected value of 0.035 versus 0.0526 for the house side of a 38-pocket roulette comparison.

Median buy-and-hold annualized return in that equity sample was 12.4 percent, below the 29.2 percent house-side roulette figure computed at N=252.

Growth and exposure

The index-tracking fund in the same study had expected value of 0.048 but a down-move size of only 0.77 percent and daily standard deviation of 1.16 percent, consistent with its 9.76 percent annualized return.

Approximate buy-and-hold equity growth is proportional to the product of expected value and down-move size, so a respectable edge still produces modest returns when exposure per period stays small.

Win-size tilt

When the average up-move is smaller than the average down-move, the win-size ratio falls below 1.0 and the resulting tilt reduces expected value and compounded return.

A 0.1 shift in tilt around a balanced win-size ratio of 1.0 changes approximate annualized equity by about 12.6 percentage points when N is 252 and the up-day fraction is near one half.

Sharpe ratio and bet size

An approximate Sharpe ratio expression derived in the study is proportional to expected value, so raising bet size does not by itself improve reward per unit of volatility.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
10 of 12 in the Sharpe ratio track
201539-39 pp.Next on Sharpe ratioConstructing a Sharpe-style score from profit and loss variabilityThe Sharpe construction is a classic return-to-risk score that compares realized returns with the variability of those returns.
All readings on this track · 12 readings
  1. 1986Auditing stochastic crossovers with moving-average baselines
  2. 1994Evaluating system changes with chi-square, Sharpe, and leverage
  3. 1995Evaluating mechanical switch rules with a stop-loss order and Sharpe ratio
  4. 1995Intermediate-term allocation with drawdown filters
  5. 1996Evaluating a multi-market book without picking winners
  6. 1996Regime-aware allocation beyond a single equity trend
  7. 1997Evaluating managed futures as portfolio diversifiers
  8. 2008Audit an out-of-the-money covered-call overlay against a Sharpe control
  9. 2013Constructing the Sharpe ratio as return over variability
  10. 2014Expected value and bet size are separate controls
  11. 2015Constructing a Sharpe-style score from profit and loss variability
  12. 2019Continuous futures series and long-horizon allocation evaluation
By fieldSizing and leverage42 readingsBy year201489 readings
All 14 readings tagged Sharpe ratio
Also on Sharpe ratio5 readings
1984Evaluating managed account portfolios on the risk-return frontier1986Auditing stochastic crossovers with moving-average baselines1994Evaluating system changes with chi-square, Sharpe, and leverage1995Evaluating mechanical switch rules with a stop-loss order and Sharpe ratio1995Intermediate-term allocation with drawdown filters