It is no easy task to estimate just how much the stock market may be over- or undervalued. All indicators have their advantages and disadvantages and it is therefore advisable to take a wide range of measurements into account. An overall evaluation of a number of indicators can provide a more confident assessment of the market in question and among the many different measurements that can be used is the implied equity risk premium (IERP).

Before looking at the IERP it is useful to explain what we mean by the equity risk premium. This measurement is merely the recompense demanded by investors in terms of yield for investing in higher risk assets (stocks) instead of securities with a lower level of risk (public debt). An asset's level of risk is related to its dispersion or volatility or its historical yield. For instance, the standard deviation of the historical annual yields (from the end of the 19th century up to the beginning of the second decade of the present century) for shares listed on the US stock market is 20% while, in the case of 3-month US Treasury bills, this standard deviation is 4%. Naturally the reward for the higher risk entailed by the stock market is the much higher returns it provides compared with bonds. Historically the average annual real yield (inflation-adjusted) for the US stock market is 6.5% whereas, historically, the average yield for 10-year US bonds has been around 3% in real terms. The difference between both figures provides a historical equity premium of 3.5%. If we take into account the historical yield for US Treasury bills (1.6%), the equity premium rises to 4.9%, representing a considerable difference in yield demanded by investors to invest in stocks instead of public debt. In fact the difficulty encountered by economic theory in explaining such a large equity risk premium as the one observed in the data is still a conundrum today (known as the equity premium puzzle).

The IERP is merely the forward-looking version of this indicator. A comparison of its value with that of the historical equity risk premium can point to a market possibly being overvalued. This measurement is based on the estimated cashflows, fundamentally dividends, that will be generated by the equity portfolio in question (for example, members of the S&P 500). First we calculate the internal rate of return (IRR) implied in this path for dividends, taking into account the price at which the shares are sold, and then we deduct the risk-free interest rate (generally the yield on 10-year US bonds). A low IERP points to possible overvaluation.

So what can we say about the current IERP for the US stock market? Firstly, that it is close to 7%, above the historical risk premium observed. Consequently, in principle, this measurement does not appear to be at a level that suggests the market is severely overvalued, in clear contrast with what has been suggested by other indicators such as the CAPE (a ratio of the current price compared with the average earnings over the last 10 years).

Nevertheless we should remember that low risk-free interest rates justify a high IERP as it is logical for investors to expect these interest rates to normalise in the future. In fact, in the last few years the drop in interest rates has been almost offset by a rise in the IERP. On the other hand, and this is a fundamental problem for the indicator, a relatively high IERP is not necessarily incompatible with an overvalued stock market as the dividends used to estimate it may be too optimistic, something that occurs relatively frequently.

In summary, although the IERP does not currently suggest the US stock market is overvalued, it is important to remember its weaknesses as an indicator. In any case we should continue to keep a close eye on this indicator, together with many others.