NEGATIVE bond yields are a very modern phenomenon. The idea that rational investors would sign up to lose money in nominal terms would have seemed laughable 30 years ago. Now it looks as if European investors are embracing Islamic finance, which eschews interest altogether.

It is possible to explain negative yields in terms of deflationary fears or risk aversion. But Jérôme Teiletche of Unigestion, a Swiss fund-management group, says that such yields are fundamentally changing the risk-reward profile of government bonds and thus the role that bonds should play in investors’ portfolios.

Many natural phenomena, such as people’s heights, conform to what is known as the normal distribution or the “bell curve”. If the average male height is 178cm, say, the number of men who are shorter or taller will decline the further you get from that mark. The normal distribution is easy to model: 95% of the data will be within two standard deviations of the mean. It is thus common to use the normal distribution when analysing the financial markets—when calculating, for example, the “value at risk” of a portfolio.

But financial markets tend to have “fat tails”—more extreme outcomes, in the form of bubbles and crashes, than the normal distribution would suggest. The 23% fall in the Dow Jones Industrial Average on October 19th 1987 is an obvious example. Markets tend to rise more slowly than they fall. They may take months to advance by 15-20% but can drop that far in a week or even a day. In statistical jargon, this is known as “negative skew”.

Strategies with negative skew have been described as “picking up nickels in front of steamrollers”.

An investor may make a series of small gains, only to be wiped out by a sudden, large loss. An example would be offering insurance (selling put options) against a sharp plunge in the stockmarket.

Most of the time, the market will not fall, and the seller will pocket the premium. But at times like October 1987, the bill will come due.

Another asset class with negative skew is high-yield, or junk, bonds. At best, investors will be repaid at par on maturity; at worst, the company defaults and investors get back pennies on the dollar.

In contrast, government bonds have typically been used as “shock absorbers” within portfolios.

When equities or commodities are plunging, government bonds tend to do very well. Even when bonds do badly, the pain is not that great. Since 1925 the biggest annual loss in real terms (including the income from interest payments) in the Barclays US bond index was 15.5% in 2009. In contrast, the biggest real loss in equities was 38.9% in 1930; and there were seven other instances of a real annual loss of more than 20%.

When yields are zero or negative, government bonds clearly do not give investors an income.

The problem is that they may not function as shock absorbers either. It is hard to say precisely how far yields can fall: until recently, many people may have felt that zero was a firm limit.

Even if slightly negative yields are palatable, however, it seems inconceivable that investors would accept an annual loss of 5%, say.

Since prices move in the opposite direction to yields, it is thus difficult to imagine investors buying bonds at current yields making much of a capital gain. It is easy, though, to imagine them making a big loss. If inflation returns, nominal yields would rise sharply and prices would plummet. Government bond returns seem likely to have a negative skew.

As evidence, Mr Teiletche points to Japanese government bonds, which have had very low yields since the turn of the century. Japanese bonds have not been very volatile but they have had a negative skew. In this respect, they resemble equities and high-yield bonds (see chart).

If government bonds in the rest of the developed world start to behave like Japan’s, then some investors may doubt whether they are worth holding at all. They will simply offer reward-free risk.

Low yields may still last for a while, even so. Many investors—pension funds, insurance companies—are forced holders of government bonds for accounting or regulatory reasons.

Central banks also tend to hold other countries’ government bonds as a key component of their reserves. And of course, the European Central Bank and the Bank of Japan are committed to buying tens of billions of government bonds each month. But in doing so, Mr Teiletche implies, they are fundamentally altering the nature of the bond market—perhaps for ever.