Can you trust this buy signal?

Reliable signals that the stockmarket is under- or overvalued are few and far between. However, as Aswath Damodaran of the Stern School of Business at New York University highlights on his blog, the equity risk premium (ERP) has been one of the more reliable. Two Federal Reserve economists, Fernando Duarte and Carlo Rosa, note that today the ERP is high, suggesting we'll see "good stock returns in the future". But beware while this may have worked in the past, relying on it now looks risky.

The ERP can be calculated in various ways, but the principle is simple. The ERP is the gap between the return investors can get from investing in stocks compared with something low risk, such as a ten-year US or UK government bond. So if a government IOU yields 2% and equities return 8%, the ERP is 6%: so 6% is the extra (the premium') you are demanding for taking the risk of buying stocks. So a rising ERP may reflect that investors are nervous, while a shrinking one suggests confidence is growing.

Between 1961 and 2012, the ERP on the S&P 500 averaged 4.02%, says Damodaran. Today, it's more like 5.45%. So if the ERP reverts to the mean' (goes back to the long-run average), that would suggest stocks could go up by more than 20%. But Damodaran also looked at the two elements that comprise the ERP the return from stocks, and the return from a risk-free' asset. Here's the twist: the expected return from equities has been "surprisingly stable" at about 8%-9%. Yet the ERP has swung round. So most of the variation in the ERP is down to changes in the risk-free rate, rather than expectations for stocks.

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That creates two problems for the bulls. Firstly, developed-world government bonds are at historic, and artificial, lows, thanks to central-bank money-printing, which has pushed bond prices up and yields down. Secondly, due to this effort to keep rates down, "the relationship between the [US government] bond rate and the ERP has weakened", to the point where a 1% rise in interest rates has added around 0.26% to the ERP rather than reducing it. If this holds, it suggests the risk-free' rate has plenty of scope to return to a more normal range once central banks reverse course and far from compressing the ERP, it may well take the ERP up with it. In that case, stocks are certainly not undervalued now. We may, says Damodaran, be in the midst of a "Fed-induced market bubble and that script never has a good ending".