In 1986, Gary Brinson, Randolph Hood and Gilbert Beebower published "Determinants of Portfolio Performance" in the Financial Analysts Journal. They took quarterly returns from 91 large US pension plans over 1974 to 1983 and compared each plan against a passive portfolio holding the same average asset mix.
A time-series regression gave an average R-squared of 93.6%. That is the number the industry has repeated ever since, usually rendered as "asset allocation explains 93.6% of returns".
That is not what the study measured. The 93.6% refers to the variation of a portfolio’s returns over time, quarter to quarter, not to the level of returns and not to why one fund beat another. As Vanguard and later commentators pointed out, a broadly diversified portfolio with limited timing will inevitably move with the markets it holds, which is what a high time-series R-squared captures.
Ibbotson and Kaplan revisited it in 2000 in a paper titled, pointedly, "Does Asset Allocation Policy Explain 40, 90 or 100 Percent of Performance?" Using 94 balanced mutual funds and 58 pension funds, they confirmed the roughly 90% figure for period-to-period variability, and then showed the high R-squared was driven mainly by shared exposure to the market itself. Different question, different answer.
The original study did report something concrete that gets quoted far less: over the ten years, market timing and security selection each cost the plans about 1.1% per year on average.
This is a good case for a classroom because the misuse is instructive. A real result, correctly computed, became a slogan by dropping the words "variation over time". Reading the sentence the authors actually wrote is a skill, and it is cheaper to learn it here than in a client meeting.
Educational material. Not investment advice.