Equity market valuation is often assessed using Professor Robert Shiller's "cyclically-adjusted price-earnings ratio" (CAPE), which divides the real (i.e. inflation-adjusted) index level by a 10-year one-sided moving average of real earnings per share. The smoothing is an attempt to estimate trend earnings, with 10 years consistent with the typical 7-11 year length of the dominant economic cycle (the Juglar business investment cycle).

For the S&P 500, Shiller's CAPE stood at 21.0 in early October versus a median since 1881 of 15.7, a 34% premium, suggesting that equities are significantly overvalued relative to history – see first chart.

Because the moving average is one-sided, however, it can under- or overstate trend earnings when the growth rate is changing. S&P 500 trend earnings expansion may have accelerated in recent years, partly reflecting a stronger contribution from foreign profits related to US companies' exposure to emerging economies.

A further problem at present is that, unusually, the 10-year moving average incorporates two major earnings recessions, reflecting the proximity of the 2001 and 2008 economic downturns. These two factors suggest that Shiller's CAPE is overstating equity market valuation.

The first issue can be addressed by using a two-sided moving average, so that the trend measure incorporates future as well as past data. The average, of course, cannot be calculated for recent years (the last five years in the case of a 10-year window). Trend, however, can be estimated using consensus earnings forecasts and extrapolation – the estimates will be subject to revision but the procedure may produce superior results to one-sided smoothing.

This two-sided approach also solves the current problem of the moving average incorporating two earnings recessions, since the 2001 downturn is no longer within the time window of the calculation.

The second chart shows S&P real earnings per share, expressed at 2010 prices, together with an estimate of trend calculated on this basis. Earnings are back at trend following an unprecedented collapse in 2008-09.

The third chart shows a price-earnings ratio calculated using the trend earnings measure. The current level of 16.3 compares with a median since 1881 of 14.5 – still 12% higher but a much smaller deviation than for Shiller's CAPE.

Comparing current valuations with a median extending back to the late 1800s is questionable – the equity risk premium may have fallen, reflecting such factors as greater diversification possibilities, improved liquidity and lower trading costs. As the second chart shows, a trend line through the data has a mild upward slope. If this line, rather than the median, is used to gauge sustainability, equities are 8% undervalued, based on a current price-trend earnings ratio of 17.7.