The terms agreed by Lloyds / HBOS for its participation in the asset protection scheme appear to represent a good deal for the bank but the attraction for private shareholders is significantly reduced by their enforced dilution due to upfront payment to the Treasury in new B shares.

Combined lending of Lloyds and HBOS in the form of loans and advances to customers and holdings of trading and investment securities amounted to £935 billion at the end of 2008. The £250 billion of assets to be covered by the insurance scheme represents 27% of this sum.

Lloyds will suffer a first loss of 10% on the covered assets and a 10% share of additional losses, for which it will pay a fee equivalent to 6.25%. So the total cost of participation will be:

10 + 6.25 + 0.1 * (L – 10) %

where L = the ultimate percentage loss on the covered assets.

To justify participation, Lloyds must believe that this cost is less than L itself, i.e.:

L > 10 + 6.25 + 0.1 * (L – 10)

Rearranging terms and simplifying, participation is worthwhile if the ultimate loss L is greater than 16.9%.

Now assume that Lloyds has dumped all of its suspect assets into the scheme and that losses will be negligible on the remaining 73% of its lending. The 16.9% breakeven loss on the covered assets then translates into a 4.5% loss on its total lending.

As explained in a previous post, British banks in aggregate suffered five-year credit losses of 8.9% and 7.1% of assets at risk following the recessions of the early 1980s and early 1990s respectively. Assuming that 1) current losses are on the same scale or larger, 2) the combined loan book of Lloyds and HBOS is of no better than average quality and 3) Lloyds has succeeded in placing its lowest-quality assets in the scheme, the fee charged looks inexpensive.