Sir James Crosby and his successor, Andy Hornby, revealed HBOS's deficiencies in written evidence to legislators published on Monday, hours before their appearance before the banking standards committee.
Referring to the freezing of funding markets in 2007, Crosby said: "With the benefit of hindsight, it brought about a much more significant deterioration in the performance of HBOS's corporate loans than anyone would have expected or indeed should have been the case. That can only be because HBOS was taking more risk than it understood was the case at the time."
Crosby was chief executive until June 2006 when Hornby, who had been running the retail bank, succeeded him.
Hornby, who described how the board of the bank was run in a "broadly consensual style", said: "Looking back at the problems encountered by HBOS and others in the financial crisis, it now seems apparent that much of the stress testing carried out, while valid, failed to highlight the largest risk which materialised in 2007 to 2008, namely the closure of wholesale funding markets and the ensuing impact on corporate banking credit conditions."
Hornby, who runs Coral, the private equity-owned bookmaker, said the "ultimate weakness" in the corporate division was the "concentration risk in commercial real estate and in certain large exposures".
He admitted that "with the benefit of hindsight" this concentration in the corporate division on "commercial property, concentration in lower-rated exposures, large, single-name borrower concentration, and exposure to highly leveraged transactions did mean that the division was vulnerable to a major downturn".
Hornby, who was chief executive until Lloyds completed its rescue takeover in early 2009, said HBOS should have tried harder to amass deposits from its corporate customers, rather than rely on wholesale markets for to fund its lending.
He said in the "last two years of HBOS's existence", when he was at the helm, the bank had tried to tried to address is funding and liquidity issues. Hornby brought back the former finance director, Mike Ellis, who had retired, but its problems "proved insoluble".
The Financial Services Authority is compiling a report into what went wrong at HBOS, which was created in 2001 by the merger of Halifax and Bank of Scotland.
Peter Cummings, the HBOS banker whose division lent billions of pounds to property developers, was given a lifetime ban and fined £500,000 by the watchdog for his role in the banking crisis. He is the only former HBOS banker to be penalised by the FSA as a result of the near collapse of the bank.
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