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1991issue C051-2

Binomial counts for unrelated position construction

A complementary success rate and failure rate can be expanded across a fixed number of unrelated positions to list every discrete win-loss count. An editorial reading treats name count as a construction variable that can be checked before any market forecast is attached.

  • A complementary pair of success and failure rates can be expanded across n unrelated positions to list every discrete win-loss count.
  • With a success rate of 2/3 and a failure rate of 1/3, a five-position model assigns 0.21 to majority-loss counts, 0.79 to a winning majority, and 0.0041 to all-failure.
  • Raising the position count to ten under the same rates lowers the majority-loss probability to 0.077 and the all-failure probability to 0.000017, with a complementary probability of 0.923 of winning or breaking even.
  • Editorial reading: diversification increases the number of unrelated positions so that majority-loss and all-failure become less probable, and the same counting procedure remains usable if the count or the rates change.
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Current trackBinomial probability model8 readingsDiversification29 readings

A discrete count of unrelated positions

A complementary pair of success and failure rates can be expanded across n unrelated positions to list every discrete win-loss count. The success rate is the assumed chance that one unrelated position finishes as a winning outcome. The failure rate is the assumed chance that one unrelated position finishes as a losing outcome.

When five unrelated positions are modeled, the expansion coefficients for zero through five successes are 1, 5, 10, 10, 5 and 1.

Five-position probabilities

With a success rate of 2/3 and a failure rate of 1/3, the five-position model assigns 0.21 to counts in which failures outnumber successes. Those counts are the majority-loss outcomes. Under those same five-position rates, the complementary probability of a winning majority is 0.79.

The five-position all-failure probability is 0.0041. All-failure is the single outcome in which every modeled position finishes as a loss.

Raising the position count

Raising the position count to ten under the same rates lowers the majority-loss probability to 0.077 and the all-failure probability to 0.000017. The ten-position complementary probability of winning or breaking even is 0.923.

Editorial reading: diversification is a construction choice that increases the number of unrelated positions so that majority-loss and all-failure counts become less probable under a stated success rate. The same discrete counting procedure remains usable after the position count or the success and failure rates are changed.

Majority-loss outcomes among five unrelated names

With five independent names and a two-thirds success rate, the chance that losers outnumber winners is 21 percent, and most of that mass sits in the three-loss cell rather than a five-name wipeout. The bars are the sidebar’s first three binomial terms, given as 1/243, 10/243 and 40/243.
With five independent names and a two-thirds success rate, the chance that losers outnumber winners is 21 percent, and most of that mass sits in the three-loss cell rather than a five-name wipeout. The bars are the sidebar’s first three binomial terms, given as 1/243, 10/243 and 40/243.

The source fixes failure at one-third and success at two-thirds, treats the names as unrelated, and calls a loss any case where failures exceed successes.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
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All readings on this track · 7 readings
  1. 1989Auditing price motifs against binomial chance
  2. 1991How equal independent stakes change the odds of a complete loss
  3. 1991Binomial counts for unrelated position construction
  4. 1996Log-change regression and binomial outlier clusters as an evaluation pipeline
  5. 1996Constructing a log-change stationarity screen with regression or binomial tests
  6. 1998Binomial baselines for discount-rate change timing
  7. 2002Trade-count horizon for equity-curve survival
By fieldPortfolio construction104 readingsBy year199198 readings
All 8 readings tagged Binomial probability model
Also on Binomial probability model5 readings
1991How equal independent stakes change the odds of a complete loss1989Auditing price motifs against binomial chance1994Constructing hourly index futures lattices from live volatility1996Constructing a log-change stationarity screen with regression or binomial tests1996Log-change regression and binomial outlier clusters as an evaluation pipeline