SVB cut its estimate of 11 September gross losses by £7.1m ($11m) as it announced forecasts for its Lloyd's syndicates' performance.
But syndicates that would have made a profit are expected to be pushed into loss as a result of the terrorist outrage.
Syndicate 2147, forecast to turn in a profit of between 4% and 9% of its £40m capacity in 2001 excluding the 11 September losses is expected to lose up to 5% overall.
The worst results are forecast on Syndicates 1212 and 1241, which are both expected to make losses of between 7.5% and 12.5% of capacity.
SVB's participation accounts for 82.6% of Syndicate 1241's 2001 capacity and 67.6% of Syndicate 1212's 2001 capacity.
The best forecasts are for those syndicates on which SVB has 100% of the 2001 capacity. They are Syndicate 575 and Syndicate 2147. Both are forecast to lose up to 5% of capacity.
The company said low losses so far this year and further rate increases in its core lines of business added up to a favourable outlook.