The fund, still relatively small in size when compared to Gross's former Pimco vehicle, has attracted $66.4 million in inflows in September according to Morningstar, bringing it to $79.1 million.
Gross moved to Janus on 26 September after a year of patchy performance from his flagship Total Return Bond fund and ongoing tensions with management at Pimco, according to reports.
The Total Return Bond fund has haemorrhaged $42.8 billion from the start of the year to the end of September as a result of underperformance and seen outflows both before and after Gross announced his departure.
Pimco suffered a record $23.5 billion in withdrawals from the fund in September, with its largest daily outflow occurring on the day of Bill Gross's resignation from the firm. The fund is now around $201.5 billion in size, Morningstar figures show, down roughly $90 billion from its peak in April 2013.
Fixed income markets have witnessed renewed volatility in October, with the departure of Gross adding to market fears over global growth, according to analysts.
"The combination of fewer broker dealers and XXL-sized asset managers can put significant downward pressure on individual bonds or entire sectors that are being liquidated," global head of fixed income at Threadneedle Investments, Jim Cielinski, said in a recent note.
"Buying into a mega manager can hurt you on the way in, on an ongoing basis (due to greater difficulty fully exploiting security selection strategies) and on the way out," he said.
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