Lancashire, a FTSE 250 constituent, has agreed to pay £266m for the business.
Alchemy owned 63 per cent in the company after buying the then- holding company of the Lloyd’s underwriter in December 2006.
The Balance was largely owned by Cathedral management and staff including CEO Peter Scales.
Earlier this year it was reported that Alchemy was looking to sell the company for £250m.
Alchemy advises over £800m of assets held in the Alchemy Investment Plan and manages over £700m of assets in the Alchemy Special Opportunities funds. The firm is currently investing from its £500m Alchemy Special Opportunities Fund II, raised in March 2011.
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