The June survey of fund managers conducted by Bank of America Merrill Lynch Global Research revealed that a net 44% of these investors feel equities are overvalued, the highest such reading on record and up from a net 37% the previous month.

That may be a new record, but fears about expensive stocks are hardly new and they have yet to end this long bull market. Part of the reason why elevated valuation multiples have not yielded to gravity may be that they are inadequate metrics for today’s environment.

Some of the earliest work on the value factor focused on ratios such as price to earnings and price to book that are still frequently cited. But book value is less useful for modern companies with fewer tangible assets, while using earnings as the denominator adds the problems associated with their calculation and reporting to say nothing of profitless businesses.

Past performance no guide

Even more sophisticated tools such as the cyclically adjusted price-to-earnings ratio invite questions: why should present valuations be adjusted for the very different experience of 10 years ago?

A new paper published earlier in June offers a novel approach to equity valuations with a fairly intuitive model.

 In the research, Jacques Saint-Pierre of Laval University in Canada considers the relationship between two ratios: a stock’s market value relative to its intrinsic value, and the company’s return on capital versus its cost of capital.

Profitability quadrant

That enables stocks to be placed into one of four categories: those with market values higher than their intrinsic values and higher returns on capital than costs of capital; those with market values lower than their intrinsic values and lower returns on capital than costs of capital; those with market values higher than their intrinsic values but lower returns on capital than costs of capital; and those with market values lower than their intrinsic values but higher returns on capital than costs of capital.

In the first two instances, a stock would be fairly valued: it’s justifiable to pay more than intrinsic value for a company with higher returns than costs, and to pay less than intrinsic value for one with higher costs than returns.

In the other two categories, a stock would be mispriced: low-return, high-cost firms should probably not trade above their intrinsic value, and those in the reverse situation should not be cheaper than their intrinsic value.

Crash test dummy

Saint-Pierre tested whether this hypothesis would have predicted past crashes, and it did. In 1987, for example, more than half of all US equities had higher market values than intrinsic values despite lower returns than their cost of capital.

 So where are we today? Saint-Pierre ran his analysis on the Dow Jones in late May, and found that only 20% of its constituents were overvalued by this definition.

Two-thirds were deemed to be fairly valued despite having higher market values than their intrinsic values because their returns on capital were also higher than their costs of capital.

Moreover, 17% were undervalued, with market values below their intrinsic values despite higher returns than their costs of capital.

Time to switch?

Saint-Pierre acknowledged that the Dow Jones index is a far smaller sample than other major indices, excluding the likes of Facebook and Amazon from its constituents. But for those who are concerned about valuations, that together with this study may be reason enough to switch from an S&P 500 to a Dow Jones tracker.