Melvin Capital Management, the hedge fund that has borne the brunt of losses from the soaring stock prices of heavily shorted stocks recently, lost 53% in January, according to people familiar with the firm. Melvin was founded by Gabe Plotkin, a former star portfolio manager for hedge-fund titan Steven A. Cohen. It started the year with about $12.5 billion and now runs more than $8 billion. The current figure includes $2.75 billion in emergency funds Citadel LLC, its partners and Mr. Cohen's Point72 Asset Management injected into the hedge fund last Monday.