# Putting the gordon equation into practice

In his book "the investors manifesto", William Berstein explains how to use the Gordon equation to estimate expected real returns on stocks for stocks on the long run.

``````Expected return = Dividend yield + dividend growth rate
``````

The expected return is a real return. This means it is corrected for inflation. If I understand correctly, real return = nominal return - inflation.

Dividend yield is dividend of a stock divided by price.

The dividend growth rate must also be adjusted for inflation. It is hard (or impossible) to predict, but between 1870 and 2010 the inflation adjusted dividend grew with 1.32 % per year, on average (see Shiller, http://aida.wss.yale.edu/~shiller/data/ie_data.xls ). This is the number that Bernstein uses.

Now I am wondering three things

1. Some companies chose to buy back shares instead of paying dividends. Shouldn't I use the 1 / price earning multiple instead of dividend rate?
2. Companies can go bankrupt and the share holder can lose his money. Between 1870 and 2010, for sure some companies have gone bankrupt. Is this effect included in the dividend growth rate of 1.32 %?
3. Let's calculate expected real returns for some vanguard funds. For the moment we ignore costs. Is this a good comparison of expected real retruns?

Expected return = 1/PE multiple + 1.32 %

Data from https://www.vanguardinvestments.de/portal/site/de/en/mutualfund#funds_tab. PE multiples

``````       Fund                                         Index                   PE multiple *   Expected return
Vanguard Emerging Markets Stock Index Fund     MSCI Emerging Markets Index     13.3    8.8%
Vanguard European Stock Index Fund             MSCI Europe Index               20.4    6.2%
Vanguard Eurozone Stock Index Fund             MSCI EMU  Index                 23.9    5.5%
Global Small-Cap Index Fund                    MSCI World Small Cap Index      25.3    5.3%
Japan Stock Index Fund                         MSCI Japan Index                14.6    8.1%
Pacific ex-Japan Stock Index Fund              MSCI Pacific ex Japan Index     16.5    7.4%
SRI European Stock Fund                        FTSE Developed Europe Index     19.6    6.4%
SRI Global Stock Fund                          FTSE Developed Index            18.5    6.7%
Vanguard U.S. 500 Stock Index Fund             S&P 500 Index                   18.8    6.6%
Vanguard Global Stock Index Fund               MSCI World Free Index           19      6.6%
``````

(*) PE multiples of funds, not of the index.

It should be noted that this is an expectation, and not at all a guarantee. In general, to funds with lower PE multiples are more risky. Expected real return is not a measure of risk.