The problem of the equity risk premium

Andrew Smithers

Jul 29 05:30



In some of my more gamesome moments I have challenged my students to produce an article about the equity risk premium, which made a useful contribution to our understanding of the way financial markets work. So far the challenge has not been met. This may reflect the modesty and good manners of those I teach but also, I hope and believe, the fact they are too sensible to wish to defend the way this often ill-defined and generally useless concept has been habitually discussed. In practice, comments on the ERP seem to me to have been a source of confusion and error rather than illumination.

The ERP can be defined in at least two ways. One is the historic difference between the returns on bonds and equities and another is the expected difference in these returns. Alternatively, the “risk-free rate” can be used in place of bonds.

Any of these concepts might be useful for something. For example, it might be useful for investors when making decisions about asset allocation. If the ERP were stable, it might also be useful for valuing equities. In fact it is useless for making asset allocation decisions; and the ERP is far from stable, whether it is defined as a historic relationship or an expected one.

Fundamentally the ERP is a hangover from the efficient market hypothesis. If markets priced assets efficiently, it would be reasonable to suspect that there would have been some stable relationship between historic returns on equities and risk-free returns. Alternatively, if government bonds or risk-free assets were priced efficiently, but not equities, it might be possible to value equities with reference to the return on bonds or risk-free assets.





Chart one shows the long-term real returns in the US on cash, bonds and equities. Two things are obvious. The first is that the long-term real returns on equities have been stable; the second is that this has not been true of cash or bonds.




Chart two shows the historic differences between equity returns and those on cash and bonds. It underlines the conclusion that there has been no stable historic relationship between the returns on these different asset classes.

It is nonetheless possible that there has been such a relationship between expected returns but that this has not applied to realised returns because investors have been bad at forecasting. If this is the case, then the poor ability to forecast must apply to real returns on bonds and cash rather than equities. As the latter is a title to ownership to real assets, and the value of cash and bonds is determined only in nominal terms, it is inherently likely that an inability to forecast inflation would be crucial.




Chart three shows that poor forecasting has clearly been a major factor in the variation in the realised returns from cash and bonds.

This does not prove that there has been a stable relationship between expected returns on cash/bonds and equities, but it does suggest that we need some measure of expected real returns in order to test it. The issue of Treasury inflation protected bonds (“Tips”) has provided us with this and, although these only started in October 1997, we now have enough data for a preliminary judgment.

As chart one shows, the long-term real returns on equities have been stable; it follows that, when the stock market rises in real terms, the rationally expected returns must fall and vice versa. It also follows that, if the expected returns on bonds and equities had a stable relationship, then a rising stock market, measured at constant prices, would be accompanied by a falling yield on Tips.




Chart four compares the yield on Tips with the S&P 500 measured at constant prices. It is clear from this chart that there is no stable relationship between expected bond returns and a rationally expected return from equities. Far from the yields on Tips rising when the stock market fell from 1999 to 2009, they fell.

It is therefore clear that the evidence is overwhelmingly against the ERP being stable, either when bond yields are measured by their historic out-turns or in terms of rationally expected returns.

The absence of a stable relationship between real bond and equity yields does not mean that there is no relationship at all. But, if there is one, its exponents are yet, as far as I am aware, to set out what it is in a way that can be tested and be shown to be robust when tested.

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