IF YOU think that financial assets are expensive at the moment, you are not alone. Deutsche Bank has looked at the prices of equities, bonds and residential property in 15 countries as far back as 1800. The average valuation of the three asset classes is above the level of 2007 and close to an all-time high (see chart).  

Of the three assets, bonds are the priciest. A combination of very low inflation and big purchases of government bonds by central banks means that nominal yields are close to record lows; real yields (ie, accounting for inflation, using a five-year average) have been lower only 17% of the time. For equities, because of the lack of long-term profit numbers, Deutsche compared share prices with nominal GDP. On this basis, equity-market values have been higher only 23% of the time (though shares looked dearer before August’s sell-off). For houses, Deutsche was only able to find data from 1970. It calculates that real house prices peaked in 2007 and are now at average levels.

The three asset classes have not always moved in tandem (which is why the average plotted in the chart does not reach one or 100): during the dotcom bubble in equities, for example, both housing and bonds looked quite cheap. The current high valuations owe much to the near-zero yield on safe, short-term investments in most developed countries: investors have been tempted by the higher returns available on less liquid (and riskier) assets, bidding up their prices.

The implication of high valuations is that future returns are likely to be subdued. This is most obvious in the case of bonds: a yield of 2% means the nominal return if you hold the bond to maturity will be 2%. The real return may even be negative if inflation rises.

When it comes to equities, returns can continue to grow only if profits rise rapidly, or if valuations get even higher. Since profits at American firms are already close to a record high relative to GDP, rapid growth is unlikely. And hoping for higher valuations is betting against the odds.

Worse still, there is always the chance that profits or valuations will return to their historical norms. If that happens, Deutsche reckons the average real return from equities over the next ten years will be negative. The same is true for Treasury bonds, European corporate bonds and American residential property.

This is sobering news for investors, who face a different kind of “money illusion” when valuations have been rising. The period of moving from a low valuation to a high one is pleasant; it is just not so nice when you get there. If equities move from trading on a dividend yield of 4% to a yield of 2%, then share prices will double (assuming dividends do not change). But to repeat the trick, the yield will have to fall to 1%. At some point, the lucrative revaluation must stop.

This makes for an especially grim outlook for those who have been counting on high returns, such as American pension funds, which tend to assume nominal gains of 7.5-8% a year when calculating how much money to put aside to meet their liabilities. They usually justify these assumptions on the basis that they have earned such returns in the past. But those past returns reflect two things: much lower initial valuations (or to put it another way, much higher initial yields) and the capital gains made as the valuations improved. For much of the mid-1980s, ten-year Treasury bonds yielded 8-10%. That was a very nice risk-free return to tuck away every year.

With such bonds now yielding only 2.2%, future nominal returns are likely to be much lower. Even if equities deliver a normal “risk premium” over bonds of four percentage points or so, that would still equate to returns of only 6-7%. The aggregate return on the portfolio would fall well short of the target. And that is without incorporating Deutsche’s pessimism about the likely level of real future returns into the forecast.

Public-sector pension funds seem especially unwilling to accept this inconvenient truth. If future returns are low, they will have two choices. Employers can contribute a lot more (in practice, this means asking taxpayers to cough up), or the funds can cut benefits, which will involve disputes with trade unions and, in some states, may not be legal.

What is true of American pension funds is true of anyone planning for their retirement: they will need to save more. But the average payment into a defined-contribution pension scheme (from employer and employee combined) is just 10% of salary. That is not going to pay for any world cruises.