"If things do deteriorate in Europe interest rates will deteriorate further."
However, if issues around Greece were resolved there could also be some relief and yields could go higher.
"It's a difficult time in terms of picking where things are going. We are relying on political decisions on the other side of the world."
The low yields are bad news for investors looking to maintain an income. Potter said the yields in the US were so low that once inflation was taken into account the real rate of return was negative. In New Zealand and Australia the return is still positive, although Potter said it was getting closer to a zero point.
The low yields signal that concerns are mounting of a global recession, but Potter said it might not eventuate as the concerns were also often a trigger for lower interest rates which provided stimulation through lower mortgage rates. New Zealand's 2023 bond, which is used as a proxy for 10 years, fell 11 basis points on Monday night and yesterday hit a yield of 3.635 per cent - much lower than the 4.2 per cent it hit during the global financial crisis.
Australia's 10-year government bond rate was also down, hitting 3.22 per cent, while US 10-year government bond yields also came close to an all-time low of 1.76 per cent.
Stock markets across the world have dropped sharply after Greece's political parties failed to form a coalition government at the weekend.
If a government cannot be formed, Greece will need to hold fresh elections next month, adding to fears it will exit the eurozone and default on its debt.
Japan's Nikkei 225 index fell 0.8 per cent to 8905.38. Earlier, the index briefly hit 8838.78, its lowest intraday level since February 3.
South Korea's Kospi index slipped 0.6 per cent to 1901.49.
Australia's S&P/ASX 200 lost 0.6 per cent to 4269.40.
Benchmarks in Indonesia and mainland China also fell.
But Hong Kong's Hang Seng, which some analysts said was oversold after more than a week of losses, rebounded 0.4 per cent to 19,816.55.
Oil prices fell to near US$94 a barrel on Tuesday in Asia, extending a two-week sell-off that has brought crude to a five-month low amid the concern.
"Greece's struggle to form a new government has moved to centre stage," energy trader and consultant Ritterbusch and Associates said in a report.
"The possibility of a significant economic slowdown in European economic activity is prompting contagion fears."
Oil investors are also taking their cues from global stock markets, which have slumped so far this month.