129 questions · full solutions

Statistics

Estimators, regression intuition, time-series traps, and the standard-error scaling that decides whether a backtest means anything.

  1. 01Estimating the Fleet From Four Serial NumbersMedium
  2. 02Variance of a DieMedium · Private
  3. 03Sixty HeadsMedium · Private
  4. 04Carrying the Normal TableEasy
  5. 05Halving the ErrorEasy
  6. 06What the Slope Really IsMedium · Private
  7. 07Diversification ArithmeticMedium · Private
  8. 08π from DartsEasy
  9. 09MLE for an Arrival RateMedium · Private
  10. 10The Biased MaximumHard · Private
  11. 11n or n − 1?Medium · Private
  12. 12Method of Moments in One LineEasy
  13. 13Consistent, Unbiased, or Both?Hard · Private
  14. 14What a p-Value Is NotMedium · Private
  15. 15Ninety-Five Percent of What?Medium · Private
  16. 16How Many Orders for the A/B Test?Medium · Private
  17. 17One Hundred Junk SignalsMedium · Private
  18. 18t or z?Easy
  19. 19Pair Your ExperimentsMedium · Private
  20. 20Covariance by HandMedium · Private
  21. 21Long Two, Short ThreeEasy
  22. 22Flows Predict Returns. Or Do They?Easy
  23. 23The Mean Above the BarHard · Private
  24. 24Best of Two NormalsHard · Private
  25. 25Two Uniforms Past 1.5Medium · Private
  26. 26The R² Beauty ContestMedium · Private
  27. 27The Ghost RegressorHard · Private
  28. 28Unequal Noise, Unequal DamageMedium · Private
  29. 29Why Backtest t-Stats LieHard · Private
  30. 30Why Betas Get Pulled Toward OneMedium · Private
  31. 31Two Random Walks Walk Into a RegressionHard · Private
  32. 32AR(1) Vital SignsMedium · Private
  33. 33Permanent or Transitory?Hard · Private
  34. 34Quiet Days, Loud DaysMedium · Private
  35. 35Error Bars on a Track RecordHard · Private
  36. 36The Price of RobustnessMedium · Private
  37. 37Updating a Hit RateMedium · Private
  38. 38Sizing the Sample for a Target WidthEasy
  39. 39Power of a Fixed-Size ExperimentMedium · Private
  40. 40Covariance of Functions of a NormalHard · Private
  41. 41Correlation of X and X SquaredMedium · Private
  42. 42The Algo That Wins Everywhere but LosesMedium · Private
  43. 43The k-th Smallest of n UniformsMedium · Private
  44. 44The Sophomore Slump, QuantifiedMedium · Private
  45. 45Information Ratio and the Fundamental LawMedium · Private
  46. 46Correlation Doesn't Care About UnitsEasy
  47. 47Error Bars on a Fill RateEasy
  48. 48Three Sigma Without a DistributionEasy
  49. 49MLE Pinned to the BoundaryMedium · Private
  50. 50Who Makes It Into the Resample?Medium · Private
  51. 51The Smallest p-Value Money Can BuyMedium · Private
  52. 52The Posterior Splits the DifferenceMedium · Private
  53. 53Correlated by ConstructionMedium · Private
  54. 54Counting a Rival's OrdersMedium · Private
  55. 55The Slope That Noise AteMedium · Private
  56. 56What a 52% Hit Rate BuysMedium · Private
  57. 57One Number to KeepMedium · Private
  58. 58Two Sharpe-One Strategies, One BookMedium · Private
  59. 59Fitting the Tail Thickness by MomentsMedium · Private
  60. 60Everyone Can't Hedge EveryoneMedium · Private
  61. 61The Fills You Never SawHard · Private
  62. 62The Floor Under Every EstimatorHard · Private
  63. 63Conditioning Your Way to 13x Less VarianceHard · Private
  64. 64A Whole Interval of MLEsHard · Private
  65. 65Why L1 Loves the MedianHard · Private
  66. 66Peeking Once Costs YouHard · Private
  67. 67What Fraction of Your Discoveries Are Junk?Hard · Private
  68. 68Significant and Probably FalseHard · Private
  69. 69Same Data, Two p-ValuesHard · Private
  70. 70How Long to Certify a 0.05 CorrelationHard · Private
  71. 71Thirty-One Years to Prove ItHard · Private
  72. 72Error Bars for an Option SellerHard · Private
  73. 73Good Managers Lose OftenHard · Private
  74. 74Root-T Breaks When Returns TrendHard · Private
  75. 75The Beta That Grows With the ClockHard · Private
  76. 76The R-Squared You Get for FreeHard · Private
  77. 77Weight the Quiet DaysHard · Private
  78. 78Regress Out the Market FirstHard · Private
  79. 79The Correlation Regime That Wasn'tHard · Private
  80. 80Ticks Sharpen Vol, Never DriftHard · Private
  81. 81Correlations Come in TrianglesHard · Private
  82. 82Two Events That Can't Fully CorrelateHard · Private
  83. 83The Hedge That Shorts the HedgeHard · Private
  84. 84Hedged Within Regimes, Correlated Across ThemHard · Private
  85. 85One Factor to Rule the MatrixHard · Private
  86. 86Fat Tails From Nothing but Vol SwitchingHard · Private
  87. 87Error Bars on a Vol MarkHard · Private
  88. 88How Wobbly Is an Empirical VaR?Hard · Private
  89. 89Six Breaches and a VerdictHard · Private
  90. 90Correlated Until It MattersHard · Private
  91. 91Shrinking Ten Traders at OnceHard · Private
  92. 92Your Best Day Means NothingHard · Private
  93. 93Bootstrapping Away the AutocorrelationHard · Private
  94. 94The Free Lunch in Mirrored DrawsHard · Private
  95. 95Factors From Thin AirHard · Private
  96. 96Five Bad DaysEasy
  97. 97Most Months Are Below AverageMedium · Private
  98. 98Forty-Five Percent, Still Not ProvenMedium · Private
  99. 99Two Extra KnobsMedium · Private
  100. 100Is the Router Playing Favorites?Medium · Private
  101. 101The Next Two RFQsMedium · Private
  102. 102How Fast Does the Edge Rot?Medium · Private
  103. 103One Print to Call the RegimeHard · Private
  104. 104Twin Tripwires at 19 to 1Hard · Private
  105. 105The 1.96 That Wasn'tHard · Private
  106. 106Selected Into AnticorrelationHard · Private
  107. 107Don't Control for the MessengerHard · Private
  108. 108Loud Noise on the Big DaysHard · Private
  109. 109Twenty Days Out, Two Different WorldsHard · Private
  110. 110Whose Correlation Is It?Hard · Private
  111. 111How Hard to Lean on the Peer GroupHard · Private
  112. 112The Optimizer Grades Its Own HomeworkHard · Private
  113. 113Aim Where the Tail LivesHard · Private
  114. 114Subtract What You Already KnowHard · Private
  115. 115The Information in a Day's RangeHard · Private
  116. 116The Second-Worst Day Is Not Your VaRHard · Private
  117. 117When the Prior Stops MatteringHard · Private
  118. 118Diversification Raised My VaRHard · Private
  119. 119The Size That Maximizes the TakeHard · Private
  120. 120Skew Arrives With the RegimeHard · Private
  121. 121Patching the Error Bar, Lag by LagHard · Private
  122. 122Three New Signals, Worse Than NoiseHard · Private
  123. 123Vol That Ignores the Fat FingerHard · Private
  124. 124Proving the Hedge DecayedHard · Private
  125. 125The Correction That Flips the VerdictHard · Private
  126. 126The Overlap IllusionHard · Private
  127. 127Does the Second Bet Help?Medium · Private
  128. 128Add a Third EngineHard · Private
  129. 129The Best of Twenty BacktestsHard · Private