The Zurich SME risk index, which measures the perceived level of business risk faced by SMEs, fell to 39.92 points in the third quarter of the year from 42.17 in the second quarter.
The highest level of risk is 100, while one means no risk at all.
Despite the improvement, 21 per cent of SMEs say their business shrunk during the third quarter.
One third of SMEs said they face a medium to high risk of going out of business over the next 12 months from September.
Two thirds of SMEs had doubts that the economic situation will not improve within the next quarter.
“It’s great to report again that SMEs are continuing to feel better about the risks their businesses face, reflecting wider signs of growth in the UK economy,” said Richard Coleman of Zurich.
“However, it’s clear that the wider economic environment is a source of increasing concern for SMEs even as their concerns over some of the more specific risks reduce.”