In the mid-1990s Federal Express had a problem. Though the company’s safety record was exemplary, regulators had proposed new rules that would have posed an operational nightmare for the giant shipper.

The company flew Boeing 727 air freighters that each accommodated eight containers. Though they had never had a problem, the government’s concern was that if two heavier-than-average containers were loaded next to each other, it could cause the plane to become dangerously unbalanced.

To assess the risk, the company hired a statistician to estimate the probability of a “double-heavy” situation. According to his analysis, the risk was extremely low — about 3%. Then the company asked the statistician to analyze a sampling of actual container weights. What he found surprised everyone: While the probability was indeed 3% virtually everywhere, it turned out to be much higher in one place: In Austin, Texas, double-heavies occurred nearly every day. It was something of a mystery.

When the company took a closer look at what was going on in Austin, they quickly found their answer: A fast-growing local company was mailing an increasing number of heavy boxes each day. The company in question: Dell Computer, which is based in nearby Round Rock. This was in the days before lightweight laptops and flat-screen monitors. As a result, all those Dell shipments ended up pushing the frequency of double-heavies flying out of Austin far above 3%.

When I was in school, I was fortunate to hear this story from the expert who solved the puzzle. Though he was a professional statistician, he liked to share this story with students as a cautionary tale, to illustrate the limitations of statistics. His message: While textbook statistical methods do often approximate the real world, you need to be awfully carefully about those cases in which they do not. Statistics might tell you that package sizes will be evenly distributed in most places, and that might be a reasonable assumption most of the time, but the Dell case proves you always need to look beyond the numbers.

In my view, there is a popular corner of the investment world today which appears to fit that description — carrying more risk than the rosy numbers suggest: high yield or “junk” bonds. This concerns me because, in recent months, mutual fund industry data indicate that investors have been piling into junk bonds. But, while the numbers suggest that junk bonds are an attractive investment, I would urge caution.

Here’s what the numbers say: Over the past fifteen years, high yield bonds have delivered returns virtually on par with the S&P 500 Index of large-cap stocks, but with much lower volatility. And, better yet, the risk level appears low. In recent years, the default rate on high yield bonds has averaged just 2%, compared to a historical average closer to 4%. (In bond parlance, a “default” occurs when a bond issuer fails to make a scheduled payment.) In short, high yield bonds appear to offer attractive returns with modest risk.

In my opinion, though, we need to look beyond these rosy statistics. I see three issues:

It is true that in recent years high yield bond default rates have been around 2%, but it makes no sense to assume that the recent past will predict the future. Go back less than ten years, to 2008, and you’ll find that default rates quadrupled, inflicting double-digit losses on investors. Go back to 2001, and you’ll find that 11% of junk bond issues defaulted. And the 1980s were particularly bad for junk bonds. Nearly 50% of junk bonds issued between 1980 and 1985 eventually defaulted. So, the fact that default rates are currently low does not mean that they will always be so.

Since 1980, we’ve seen three major hiccups in the high yield market, but it could be even worse the next time. Prior to 1980, high yield bonds were virtually nonexistent, and yet the period since 1980 has been unusually favorable for bonds because of the nearly nonstop decrease in interest rates over that 30+ year period. So we’re in uncharted territory. No one knows how high yield bonds will react when rates increase for multiple years in a row.

Finally, the amount of junk bond debt out there is far larger than it has ever been before. According to the credit rating agency Moody’s, the proportion of companies now in junk status has increased by nearly 60% since 2009, to its highest level ever. In an ominous statement, in fact, Moody’s warned that, “a number of weak issuers are living on borrowed time while benign conditions last.”

For all of these reasons, I would be skeptical of the rosy statistics and steer clear of high yield bonds.