* Q3 net loss 83 mln euros vs 1.2 bln euro loss in Q3 2012
* Steadily cutting cost of funding
* Belgium, France main guarantors for Dexia's borrowing (Adds details of funding costs)
BRUSSELS, Nov 15 (Reuters) - Nationalised Franco-Belgian financial group Dexia lost 83 million euros ($111.7 million) in the third quarter, a relatively modest sum for the bailed out group, as it booked a gain for the sale of French public sector insurer Sofaxis.
Dexia, now largely a portfolio of loans and bonds in run-off, said it had cut its balance sheet to 238 billion euros, down by 119 billion since the end of 2012 and by 9 billion during the July-Sept period.
The group, once the world's largest municipal lender, is no more than a penny stock investment, but its results matter because France, Belgium and, to a lesser extent, Luxembourg are guaranteeing its borrowings by up to 85 billion euros.
The states, which have already pumped in billions of euros to prop up Dexia, are threatened with losses that could derail their efforts to rein in their budget deficits.
The bank, about 95 percent owned by the French and Belgian governments, made a net loss in the first nine months of 988 million euros. Last year, its loss in the third quarter was 1.2 billion euro and for the first nine months 2.4 billion euros.
Dexia said income slipped by 40 million euros compared with the second quarter, partly due to the sale of certain French entities, including Sofaxis, but also because of classifying some assets as non-performing.
Partially offsetting this, refinancing costs fell by 23 million euros by increasing funding under the 2013 state guarantee plan and cutting funding from central banks to 19 percent from 23 percent during the quarter.
The latter is more costly, although costs fell during the quarter as a result of the European Central Bank's reduction of interest rates in May. It cut rates again this month.
Dexia has also benefited from a sharp reduction in the fee it has had to pay for government guarantees to 5 basis points per year from an average 85 basis points in 2012.
So far this year, the guarantees have cost it 131 million euros, compared with 743 million for the whole of 2012.
Dexia has been stripped of all its activities, including public sector lending and retail banking, after it failed to recover from the 2007-2008 credit crunch, which deprived it of access to short-term money to fund largely long-term loans.
It is in the process of selling its last major commercial operation, Dexia Asset Management, to New York Life Investments. ($1 = 0.7430 euros) (Reporting By Philip Blenkinsop; editing by Robert-Jan Bartunek)