Curriculum·R410 Copy Trading, Vaults, and Agentic Execution·about 33 min
Leaderboard forensics
By the end of this lesson you can
- →Name the three biases that inflate any self-reported performance record
- →Compute what the best result out of a large field looks like under pure luck
- →Reconstruct a return series rather than reading a headline number
- →State what a leaderboard can and cannot establish about the leader at the top of it
Senior · enrolled learners
This lesson opens with Malkiel and Saha on hedge fund databases, published 2005.
- What happened
- Burton Malkiel and Atanu Saha published Hedge Funds: Risk and Return in the Financial Analysts Journal in 2005, examining the TASS hedge fund database, to which funds, unlike mutual funds, report only if they choose to. They found three effects. Backfill bias, where a fund begins reporting only after good early results and fills that past record into the database, made backfilled returns higher than contemporaneously reported ones by about 7.3 percentage points a year on mean returns and about 5.7 on medians, across 1994 to 2003. Survivorship bias, where an index is computed only from funds still reporting, added about 4.4 percentage points a year across 1996 to 2003. And the mean return of funds still alive exceeded that of funds that had stopped reporting by more than 8.3 percentage points a year over the same period. Their conclusion was that hedge funds are riskier and provide lower returns than is commonly supposed.
- The decision point
- None of these effects needs any fund to have misreported anything. Each can arise with every number in the database a true statement about a real fund, and on the study's measures they moved the reported figures by several percentage points a year purely through who chose to report and who remained to be counted. A copy-trading leaderboard is the same construction with a shorter history, a larger field and no requirement to report anything at all.
What you will be able to answer
- →What are the three biases?
- →How large were they?
- →What does pure luck produce at the top of a large field?
- →What does a leaderboard establish?
Orientation and Year One are open: anyone can read them without an account. From Year Two onward the lessons are for enrolled learners, because progress through the later years only means anything if it is tracked against a record.
It is free. We do not sell the list and there is nothing to buy at the end of it.
Sources and review
- https://www.tandfonline.com/doi/abs/10.2469/faj.v61.n6.2775
- https://web.archive.org/web/20240721221813/https://www.atlantafed.org/-/media/Documents/news/conferences/2006/06fmc/06fmcMalkiel.pdf
- https://www.aei.org/wp-content/uploads/2011/10/20060515_SahaNPSTFinal.pdf
- https://faculty.haas.berkeley.edu/odean/papers/day%20traders/The%20Cross-Section%20of%20Speculator%20Skill.pdf
Confidence high·Volatility low·Reviewed 2026-10-22·Owner unassigned
Contested
Malkiel and Saha's Table 2 gives two backfill figures for the same 1994 to 2003 window: an average difference of 7.31 percentage points between backfilled and contemporaneously reported mean returns, and 5.74 points between medians. Their survivorship figure, 4.42 points, compares live funds with live plus defunct funds over 1996 to 2003, and the live against defunct gap over the same years is described in the text as more than 830 basis points (8.35 in Table 3). The survivorship analysis excludes backfilled returns, so the two figures are measured on different samples, and the worked example's subtraction of both from one headline is this lesson's simplification. Malkiel and Saha themselves note their survivorship estimate is larger than earlier studies, which range from 60 to 360 basis points, and later research has produced both larger and smaller figures with different methods. The range is stated rather than a point estimate and the argument does not depend on which end is used. The study is a 2005 TASS sample and the full text is linked from an archived Federal Reserve Bank of Atlanta copy, since the original Atlanta Fed link no longer resolves.
The order statistic in part two uses the leading-order approximation, the square root of twice the natural log of n, which overstates the exact expected maximum of n independent standard normal draws at these field sizes: the exact values are about 3.85, 3.24 and 2.51 standard deviations at 10,000, 1,000 and 100, against the approximation's 4.29, 3.72 and 3.04. At 60 percent volatility that is about 231, 194 and 150 percent rather than 257, 223 and 182, so the worked figures are an upper estimate and the conclusion holds at the exact values. Both also assume independent normally distributed annual returns, which real leader returns are not, being correlated with each other and fat-tailed. Correlation reduces the effective field size and fat tails increase the expected extreme, so the two corrections work in opposite directions. The conclusion, that a large field produces a spectacular leader under pure luck, is robust to both.
S205-04 owns tracing a specific leader's method. R408-06 owns the Taiwan evidence that persistent skill exists. This lesson owns the statistics of the ranking itself. Keep the splits.