LONDON -- Investors could be forgiven for being confused about banks' profitability. One of the striking features of the recently published third-quarter results of Lloyds Banking (LSE: LLOY.L) (NYSE: LYG), Royal Bank of Scotland (LSE: RBS.L), and Barclays (LSE: BARC.L) (NYSE: BCS) is the vast difference between headline results and the unadorned statutory profit.

In the case of Lloyds and RBS, billion-pound profits on one measure become losses on a similar scale on the other:

Profit for 9 months to 30 Sept 2012, in millions of pounds

LLoyds

RBS

Barclays

Underlying basis 1,904 1,047 5,954
Statutory basis (583) (1,258) 712

Wary
The underlying profit is variously described as "underlying," "managed," or "adjusted." Investors are normally wary when companies present adjusted profits that show a different picture from the statutory result. It is far too easy to paint the picture management wishes shareholders to see, and sweep bad news under the carpet.

On the other hand, it can be perfectly legitimate and reasonable to separate out one-off and non-recurring items in order to show underlying performance. Which is it in this case?

Adjustments
To get a handle on this question, I have classified the adjustments between underlying and statutory profit into three categories: exceptional items, provision for litigation, and fair value adjustments.

Exceptional items include things such as restructuring costs, and gains or losses on disposal of businesses. They are one-off items, but their nature is such that they come along from time to time, and might properly be regarded as unavoidable consequences of the business.

Provision for litigation covers the massive liabilities that the banks have incurred through various forms of misconduct. The big numbers stem from the mis-selling of payment protection insurance (PPI) and LIBOR-fixing. It is a sad fact that provision for such misconduct penalties has become commonplace in the banking sector, and while it may hopefully not be a permanent feature of the industry, there is certainly still much to come.

Fair value adjustments are the marking-to-market of many financial items that modern-day accounting requires. This has a dramatic effect on banks' accounts. Far and away the biggest item is the fair value adjustments to banks' own debt. To most people not burdened with the mind-set of accountancy, this is counterintuitive and misleading.

When banks' creditworthiness improves, the marked-to-market value of their own liabilities increases, and this is charged as a cost in the P&L account. When banks become less creditworthy, their P&L is boosted!

Analysis
So let's look at those numbers again, with my judgmental analysis of the adjustments:

Profit for nine months to 30 Sept 2012, in millions of pounds

LLoyds

RBS

Barclays

Underlying basis 1,904 1,047 5,954
Exceptional items 249 (450) 227
Litigation (2,225) (400) (1,450)
Fair value adjustments (511) (1,455) (4,019)
Statutory basis (583) (1,258) 712

The impact of the (very real) cost of PPI mis-selling and LIBOR-fixing, and the (highly technical) fair value adjustments is clear. If, like me, you think the fair value adjustments are misleading, it makes sense to look at statutory profit before these adjustments.

Adding in last year's comparable figures, a clearer picture emerges:

Profit for nine months to 30 Sept., in millions of pounds

Lloyds 2011

Lloyds 2012

RBS 2011

RBS 2012

Barclays 2011

Barclays 2012

Underlying basis 1,904 768 1,047 2 5,954 5,062
Statutory basis before fair value adjustments (72) (4,025) 197 (618) 4,731 2,095

There is a consistent message here. On both measures, all three banks have improved dramatically. Operationally, these banks have performed well this year and may indeed have turned the corner.

Share price
This has been reflected in their share price performance. In the year to date, shares in Lloyds are up 69%, RBS up 38%, and Barclays up 36% against the FTSE 100 (UKX), up just 5%.

Does this mean these banks are good investments? It depends on your attitude to risk and what keeps you awake at night. I have written recently why I think banks' balance sheets can't be trusted. They still harbor potential bad debts and are especially vulnerable to economic dislocation such as renewed crisis in the eurozone.

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