As stock prices are plunging around the world, demand for U.S. Treasuries -- which are viewed as a safe haven for investors during times of economic uncertainty -- is skyrocketing.

This increase in demand is pushing the price of Treasuries higher and, thanks to the inverse relationship between bond prices and yields, is pushing Treasury yields lower. We are especially seeing this happening at the long-term end of the yield curve.

As longer-term yields drop, the Treasury yield curve is flattening. At the beginning of June, yields on 10-year and 30-year Treasuries were near 3.4% and 4.3%, respectively. Now, yields on 10-year Treasuries have dropped below 3% -- their lowest level since April 2009 -- and yields on 30-year Treasuries are flirting with 4%.

This is a potential problem for two reasons.

Bond yields around the globe are painting a grim picture for anyone who is still bullish on the stock market.

Yields on the U.S. Treasury's 10-Year note dropped to a 52-week low of 3.09% on Wednesday, at the same time the yield on Japan's 10-year bond is hitting seven-year lows of 1.145%.

Investors also pushed yields on Germany's 10-year Bund to 21-year lows of 2.5%.

Sinking bond yields indicate demand for bonds is increasing, and we typically only see demand for bonds rise to these levels when investors are jumping out of the stock market.

To look at it optimistically, it's a period of risk aversion.

Economists, business executives, analysts, and certainly employees are hoping it doesn't become an 'era of risk aversion' - - a longer period where businesses shun expansions and new projects, and investors avoid stocks.

Further, the risk-aversion theme is prompting investors large and small to flock to the 10-year U.S. Treasuries bond, also called 10-year notes, the yield for which was 3.05% on Friday at mid-day. (Bond prices move in the opposite direction of yield. Hence, when demand is strong, such as now, a rise in bond prices pushes their yield lower.)

Moreover the 10-year yield is likely to fall further in the next two quarters, as more investors flock to safe investments amid the U.S. recession, so says economist Richard Felson.

"We're seeing the value of safety come to the forefront. In this climate, investors don't care about yield, their primary concern is capital preservation," Felson said. "And despite the increase in debt the United States is likely to record over the next two years, the lowest risk investment remains U.S. Treasury notes. It's quickly becoming a sort of electronic mattress, the way savers used to store money in mattresses decades ago. Investors are saying, 'Here, take my money and store it until conditions improve.' "