Private equity firm Silver Lake built its reputation on the back of investments in technology companies such as internet phone service provider Skype and chip maker Broadcom.

But in recent years, the firm, which manages more than $40bn in assets, has established itself as a major player in the sports and entertainment arena as well, investing billions of dollars in businesses that include cinema chain AMC Entertainment Holdings and the parent company of UK soccer team Manchester City. Now, some of these deals are coming under pressure.