Last month I wrote about how bond-market valuations are supported by the shape of the yield curve. This month (inspired by a presentation by BNP Paribas’ Kokou Agbo-Bloua I saw recently) we will turn to equities.

Just as with bonds, the consensus is that US equities are overvalued, backed-up by comparing the standard trailing P/E ratio (just under 18-times, 15% higher than its long-term average) with the cyclically-adjusted version (CAPE, which at 25-times is more than 50% higher than average). I will use the Gordon growth and capital asset pricing models to ask if current valuations imply crazy earnings-growth expectations.

The Gordon growth model holds that the value of a company should be equal to the proportion of earnings paid out to shareholders divided by the cost of equity (COE) minus the earnings-growth rate. Given the S&P 500’s mar- ket cap of $17trn (€12trn) and last year’s earn- ings of $1.1trn, to calculate the implied growth rate we simply need an appropriate discount rate in the form of US companies’ COE.

To get my discount rate, I subtracted the rolling 12-month arithmetic average of the 20-year US Treasury yield from the rolling 12-month arithmetic average S&P 500 total return, for the past 20 years, and then took the average of those readings to represent the equity risk premium (ERP): 3.6%. Following the CAPM, I added that to the past year’s average 20-year yield to get the current COE: 6.9%.

The implied sustainable growth rate would equal that COE, minus the proportion of earnings paid out divided by the value of the S&P 500 (that is, the earnings yield). With about 30% of earnings being paid out in dividends during 2013, that translates to just under 2%, and an implied growth rate of 4.9%.

Earnings growth of 4.9% seems fairly optimistic given current US GDP growth of 2.5%. We might look to today’s 5Y5Y US forward rate for a longer-term view on GDP growth: 3.8%. That still makes 4.9% look optimistic. What do we have to do to our assumptions to imply earnings growth closer to the magic 3% to which the 10-year yield is anchored? We could see the S&P 500 lose 40%: that seems unlikely. We could see earnings halve: again, overly gloomy. Might the two meet in the middle? It’s possible. That would match up with what the CAPE tells us, more or less.

But I think it’s more likely that the adjustment should come in the discount rate. To get implied growth down to 3%, we have to move from 6.9% to 5%, suggesting an ERP of less than 2%. If we are generous and allow our earnings growth rate to go up to the current 5Y5Y rate, we get a COE of 5.8% and an equity risk premium of 2.6%.

That doesn’t seem unreasonable. There are many imponderables, but in terms of asset allocation my conclusion would probably be that bonds are far from over-valued and that equities are pretty close to fair value – but with a fairly nasty tail risk lurking should growth sentiment turn darker.