Stock picker Julian Robertson and his protégés have ruled the Wall Street jungle for decades. But a reversal in 2016 is challenging their dominion.

For the year, hedge-fund losses at Tiger Global Management LLC were roughly $900 million, marking a 15.3% loss. Lee Ainslie’s $11 billion Maverick Capital Ltd. was down more than 10% in its flagship fund, while Viking Global Investors LP lost 4%, according to investors and people familiar with the firms. Other one-time employees of Mr. Robertson posted small gains or losses.

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