Capital Requirements for fund management companies

Yes. A fund management company can invest its base capital (and financial resources, as applicable). It need not maintain the respective amounts in cash.

Base capital for a licensed fund management company (“LFMC”, including a fund management company restricted to servicing qualified investors ("A/I LFMC")) or a registered fund management company (“RFMC”) is defined as the sum of

a) paid-up ordinary share capital,
b) paid-up irredeemable and non-cumulative preference share capital, and
c) any unappropriated profit or loss in the latest audited accounts less any interim loss in the latest accounts and any dividend that has been declared since the last audited accounts