By Mark J . Higgins

A reliable rule of thumb for investors is that they can only hope to achieve exceptional returns by daring to be different than the crowd . This is because opportunities to produce exceptional returns are rare and quickly evaporate once the herd becomes aware . Among the great ironies of investing in the 21st century is that the most daring strategy — investing entirely in index funds — also happens to offer investors the highest probability of achieving their objectives and at a considerably lower cost . Understanding the history of active management reveals why index funds usually offer the most attractive prospects for both individuals and institutions . contestants guessed the weight of an ox , and the person closest to the actual weight received a prize .

After the contest ended , Galton persuaded the organizer to hand him the tickets submitted by participants . Galton ’ s subsequent analysis revealed that the median guess of the ox ’ s weight ( 1,207 pounds ) was remarkably close to the actual weight ( 1,198 pounds ). Even more fascinating was that approximately 90 % of individual guesses were worse than the median because the errors above tended to offset the errors below .

Diagram from Vox Populi

The relative accuracy of the median guess — a phenomenon Galton dubbed vox populi ( voice of the people )— was later described in a probability theorem known as the law of large numbers . The theorem proved that results observed in an experiment that involves repeated and independent iterations will converge on the average . The law of large numbers has many practical applications . In situations in which independent estimates are made using a common set of information , the average estimate tends to be superior to most individual estimates . In other

The Peculiar Wisdom of Crowds

“ It appears then , in this particular instance , that the vox populi is correct to within 1 per cent of the real value … This result is , I think , more creditable to the trustworthiness of a democratic judgement than might have been expected .”

— Francis Galton ( 1907 )

In the fall of 1906 , an English statistician named Francis Galton strolled the grounds of a livestock fair in a rural town about 200 miles from London . Galton was studying the effects of various breeding techniques , but on this day , he was captivated by a popular contest . For six pence ,

Source : Galton , F . Vox Populi . Nature 75 , 450 – 451 ( 1907 ). https :// doi . org / 10.1038 / 075450a0

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