# The Risk Premium Puzzle, or Dividend Investing for Math Nerds

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by: IndexUniverse

By Elli Malki

The crisis in the global stock markets brought valuation ratios to levels that were not seen in many years. Dividend yields, in many stock markets, have reached skyrocketing levels that have attracted the attention of several market observers.

What should investors conclude from such high levels of dividend yields?

One approach, which is based on the Dividend Growth Model (DGM), is to look at the risk premium that is implied by the level of the dividend yield.

According to DGM, the price of a stock is the infinite discounted sum of its future dividends. This can be presented as follows:

(1) P = D / (r - g)

P - The price of the stock

D - The current dividend

r - The rate of return which will compensate investors for the risk of investing in equities

g - The expected long-term growth rate of dividends

Based on equation (1), we can present the rate of return that investors expect to receive in the stock market as the sum of the dividend yield and the expected growth rate of dividends:

(2) r = D/P + g

The rate of return that investors expect to receive when they buy equities is also the sum of two components: the risk-free rate of return and the risk premium.

(3) r = Rf + RP

Rf - The risk-free rate of return

Thus, we can present the risk premium as a function of the dividend yield, the anticipated growth rate of dividends and the risk-free rate of return:

(4) RP = D/P + g - Rf

Using equation (4), it is possible to calculate the risk premium that investors attribute to equities in different stock markets. Such calculation requires an estimate of the expected long-term growth rate of dividends. A plausible assumption is that the expected long-term growth of dividends is equal to the expected nominal growth of the respective economy, e.g., the expected real growth of the economy plus the expected inflation.

Based on this assumption, I have calculated the risk premiums that were demanded by investors a year ago in stock markets of 13 developed countries. I used the five-year forecasts of inflation and GDP growth that are published by the economist intelligence unit (EIU) and the dividend yields of exchange-traded funds that follow the MSCI index of each respective country (except for the U.S., for which I used SPY, which follows the S&P 500 Index). As the risk-free rate of return, I used the yield of 10-year government bonds for each respective country. The results are presented in Table 1:

Table 1

Sources: Morningstar, The Economist, EIU and author's calculations

The average dividend yield last year in the stock markets of the developed countries that were examined was 1.5%. The average implied risk premium was 1.7%, and it varied between 0.3% in Spain to 3.3% in Britain.

What's the implication of these figures on the valuation of the respective stock markets a year ago?

In order to answer this question, I compared the implied risk premiums in Table 1 to studies that estimated the risk premium using historical data.

A study of long-term data in the U.S. has found that the risk premium, over government bonds, was 6.5% [History and the Equity Risk Premium; William N. Goetzmann & Roger G. Ibbotson; Yale ICF Working Paper No. 05-04, April 6, 2005].

Another study that looked at long-term data of several stock markets in developed countries has found a somewhat lower figure - 4% [Global Evidence on the Equity Risk Premium; Elroy Dimson, Paul Marsh & Mike Staunton; LBS Institute of Finance and Accounting Working Paper No. IFA 385, August 2003].

Regardless of which estimate we use, the risk premiums at the end of 2007 seem to be extremely low. These findings suggest that investors were overoptimistic at that time and that stock markets were overvalued. We can also see that the stock markets in continental Europe were more overvalued than the markets in the U.S. and Britain.

In the next stage, I applied the same analysis to the most current data. The results are presented in Table 2:

Table 2

Sources: Morningstar, The Economist, EIU and author's calculations

Within one year, the average dividend yield in the aforementioned stock markets rose to 8.4%. However, the current dividend yield is not uniform: It varies between 2.25% in Japan to 19.82% in Belgium. Respectively, the average risk premium rose to 8.8%, and it also varies between 3.3% in Japan to 19.6% in Belgium.

A further analysis of the stock markets in Table 2 shows that they can be divided into three groups. In the first group-the U.S., Canada, Spain, Switzerland and Japan-the risk premium has merely reverted to its long-term mean. In the second group-Austria, France and Australia-the risk premium is somewhat higher than its long-term mean. In the third group-Britain, Germany, Italy, Netherlands and Belgium-the risk premium is significantly higher than its long-term mean, suggesting an excessive pessimism that may lead to undervaluation.

One possible explanation to the high risk premium is the exposure of the index to the Financial sector. Investors may be expecting additional bankruptcies of financial institutions, and thus may attribute higher risk to stock markets that have high exposure to the Financial sector. In order to examine the validity of this explanation, I have examined the level of exposure to the Financial sector, measured by the weight of this sector in each index. The overall correlation between the exposure to the Financial sector and the risk premium is not high (0.33). Nevertheless, such exposure can explain the high risk premium in Italy (exposure of 46.7%) and in Belgium (exposure of 35.9%). Still, the stock markets of Netherlands, Germany and Britain seem to suffer from overpessimism and undervaluation.

So are we looking at a buying opportunity?

I think that a clear answer to this question was given recently by The Economist in an article that also dealt with valuation ratios (Think long):

On one hand:

"...for long-term investors who can screw up the courage to enter the stockmarket, the odds are looking more and more favourable."

And on the other hand:

"Valuation measures may be a great guide for five or ten years. But they are not much help over six months, let alone over the next day. And that is one reason why markets are struggling to find a bottom."

Elli Malki is an economic consultant and the editor of http://www.inbest.co.il/, an Israeli Web site that provides a decision support service for savers and investors. He can be reached at malki@netmedia.net.il This e-mail address is being protected from spambots. You need JavaScript enabled to view it.