Are Equity Markets Overvalued?

Many readers of The Index Investor hear and/or ask this question all the time. This month, we’ve done an analysis that highlights the difficult issues we face when we try to answer it. So get ready for a journey into the realm of financial theology!

Our starting point is the valuation model we will use to make sense of current equity market prices. While there are many valuation models that one could use, we have opted for a simple one whose key inputs are widely available. Variously called either the Gordon or the Dividend Growth model, this valuation approach says that the fair value of an asset (be it a share or a market index) can be determined by dividing (that is, discounting) its current dividend by the sum of the required rate of return on equity for the asset in question less the expected future growth rate of the dividend. This statement contains two (or possibly three) of the most contentious issues in finance.

First, there is the question of share repurchases, and whether or not they should be added to dividends to obtain the numerator of the valuation equation. Technically, the answer is yes, but practically it seems to be no. Technically, share repurchases are, like dividends, as means of returning cash to an asset’s owners. Practically, however, share repurchases take place much less frequently than dividends are paid, and data about them are not widely available to the public. Moreover, studies which have included them have reached conclusions that are very similar to those that have used dividends alone. So we have elected to just use dividends in our analysis.

The second contentious issue has to do with what constitutes an appropriate expected rate of return on equity for the asset in question. Theoretically, this is the rate of return that adequately, but not excessively, compensates an investor for taking on the level of risk inherent in the asset in question. Two elements are added together to determine the required rate of return on equity. First, there is the expected return on a risk free asset – usually a government bond. Second, there is an "equity risk premium" which reflects the return one expects for taking on incremental risk above and beyond that inherent in the risk free asset. The size of the equity risk premium is both one of the most important, and one of the most argued about numbers in finance.

Until recently, the most common approach used to estimate the equity risk premium was to look at historical rates of return on equity and government bonds, and use the average difference between them as the equity risk premium. The following table contains historical estimates of equity risk premia. The first set is the difference between the rate of return on the Morgan Stanley Capital International Equity Index for the country or region in question and the rate of return on government bonds with maturities of five years or more, between 1985 and 2000. The second set is from the book Triumph of the Optimists (by Elroy Dimson, et al), and is based on the period between 1900 and 2000.

However, in the past two years or so, the historical approach to estimating the equity risk premium (ERP) has been questioned by many respected academic researchers. They have concluded that there is often a big difference between the returns people reasonably expect to receive when they make an investment (the "ex ante" ERP), and the returns they actually end up receiving (the "ex post" ERP). In other words, historical, or realized rates of return on equities (and the difference between these returns and the returns on government bonds) may be very poor estimates of what people actually were thinking when they made these investments. These doubts have been reflected in a large number of academic papers. Broadly speaking, the general conclusion that has been reached is that the expected risk premium is probably lower than the realized risk premium. The following table presents the key conclusions from a number of these studies:

The third contentious issue is how fast dividends will grow in the future. In the aggregate, dividends cannot grow faster than the underlying economy for very long. Therefore, a good estimate of long term dividend growth (especially for broad market indexes) is the expected real growth rate for the economy. Actually, this is more of a maximum estimate, as some authors (notably Arnott and Bernstein) have pointed out that not all growth is investable; that is, a certain percentage of economic growth takes place in private (and often small) companies that are not included in market indexes. As a result, the maximum growth rate of dividends on publicly traded shares is probably somewhat below the overall real growth rate of the economy.

The overall economic growth rate is generated by two other factors: the rate at which the size of the labor force is growing, and the rate at which output per worker (productivity) is growing. Neither of these is easy to estimate. The rate of labor force growth results from at least three factors: the rate at which the native population is growing (that is, their fertility rate), the immigration rate, and what is called the participation rate, or the percentage of working age people who are working or looking for work. While future fertility rates are relatively easy to predict, immigration rates and participation rates are more difficult. In our analysis, we have used the International Monetary Fund’s estimates of future labor force growth.

Future productivity growth is also an issue about which reasonable people can and do disagree (often vehemently). At best, one can say that while recent productivity growth in the United States has been impressive, it is not yet clear how long it will continue, or whether other countries (some with very different regulatory environments) will be able to match it in the years ahead. In light of this, in our analysis we have used the IMF’s estimates of productivity growth over the 1994 – 2003 period. Our assumptions are shown in the following table:

The last assumptionwe need to make before moving on to our valuation analysis is the risk free rate to use. Historically, this presented a difficult issue, as nominal bond yields contain both a real risk free rate and a premium for expected inflation over the holding period. Fortunately, in recent years many countries have introduced inflation linked or "real return" bonds that provide a clear estimate of the real risk free rate of interest. We show these in the following table:

Having established our assumptions, let’s move on to our analysis. All of the following examples are based on the end of June, 2002 values and dividend yields for different FTSE Country and Region Indexes.

We began by taking the (very arguable) position that markets are efficient, and fairly value assets, so that their current prices are, in fact, equal to their true values. If this is the case, then the current dividend yield by definition equals the sum of the expected rate of return on equities less the expected growth rate of dividends. This is the same as saying that the dividend yield plus the expected dividend growth rate equals the expected rate of return on equities. And when you subtract the current real risk free rate from that, you derive the equity risk premium, as shown in the following table:

This table tells quite a story. Two of them, actually. First, if you assume the markets are fairly valuing equity markets today, then the implied equity risk premia are generally at or below the low end of current academic estimates of where they should actually lie. This would seem to be inconsistent with the notion of efficient markets, unless one believes that all the academic estimates of the true ex ante ERP have been too high.

Second, if the markets are accurately priced, then the only way we can achieve the same nominal rates of return on equity over the next five to ten years that we experienced in the recent past is to undergo fairly substantial and prolonged periods of global inflation. In the U.S.A., for example, to achieve the 10% to 15% nominal returns that some surveys suggest the investing public expects to earn, we would have to experience annual inflation of between 4% and 9%. Granted, the previous article on the dangers inherent in the current economic situation suggests that future increases in inflation are a distinct possibility. However, prolonged inflation in the 4% to 9% range would put us back in the 1970’s, which seems quite unlikely to occur (with the exception of the odd fashion mistake you see now and then). Assuming current inflation targets of around 2% per year are met by different central banks, then nominal rates of return on equities of 8% to 9% are what the markets are forecasting today.

Our next analysis assumes the markets are not efficient. We are therefore seeking to determine whether current indexes are over, under, or fairly valued. We ran a number of scenarios, but will present only the one which seemed most reasonable to us. In this scenario, we used an equity risk premium of 4 percent (for all countries), and further assumed that productivity growth in all countries would converge on a common rate of 3.5% per year (labor force growth rates, however, and real interest rates would still be different). This analysis generated the following results:

This analysis, though subject to the disagreements we have discussed over the correct assumptions to use, suggests that Canadian, Japanese and U.S.A. equity markets are still considerably overvalued, despite the price declines they have already seen. In contrast, the Australian, Eurozone, and U.K. markets do not seem to be overvalued.

As we have noted, there are certainly many points you can disagree with in this analysis, incorporating as it does many of the most contentious issues in modern finance. Nevertheless, the approach we have used has the important advantage of being easy to apply, because it uses data that are widely available (we got them all from the Financial Times). We hope you'll find it useful the next time someone begins to wax eloquent about whether or not the equity market is overvalued.

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