Successful hedge fund managers should do something unusual if they want to stay that way: Say no to new investors.

The bigger a hedge fund gets, the worst it tends to perform, according to a new academic study.

Holding other features constant, a 10 percent increase in fund size results­­­ in a decrease of 13 basis points per month (or 1.53 percent per year) in raw returns on average and a decrease of 10 basis points per month (or 1.21 percent per year) in style-adjusted returns, according to the paper from Purdue University.

"A key implication of our findings for investors is that performance persistence is achievable when funds maintain a small size," researchers Chao Gao, Tim Haight and Chengdong Yin wrote. "Fund performance declines with fund age and that declining performance is not significantly related to a variety of fund and family-level characteristics, nor is it significantly related to young funds assuming higher downside risk."

The paper clarifies prior literature that found that hedge fund performance peaks during the first few years of a fund's life, but declines thereafter at an average rate of 42 basis points per year.

The decline in performance, according to the Purdue researchers, appears to be due to managers taking their eye of the ball and focusing more on asset gathering (and the steady fees that come with them) rather than investing.

Other studies hold that historical compensation contracts in the hedge fund industry, such as 2 percent management and 20 percent performance fees, is not effective at aligning managers' incentives with investors' interests.

Yin's 2016 study, for example, demonstrates that the management fee comprises a larger portion of total compensation when funds grow large and thus a fund's optimal size, from a compensation perspective, exceeds the size that is optimal for performance.

The research comes amid an ongoing move by funds to offer more competitive fee structures amid lackluster performance, declining revenues and rapidly evaporating investor patience.

"When funds grow large, fund managers may have less incentive to improve fund performance because most of their compensation comes from the asset-based management fee," the researchers concluded. "Thus, investing in small funds, regardless of age, may provide for superior and sustainable returns."