**This blog post was originally published on the MoneyGeek.ca blog by Jin Choi. The website no longer exists, but Jin has graciously allowed us to re-publish his research for the benefit of future investors forever.**

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Wouldnt it be nice to know how much stocks will return over the long term? Such information would be very useful, as it would allow us to better plan for the future. If you save for your retirement based on the assumption that stocks will return 9% per year, but they return only 5% per year, you could be in trouble.

Predicting stock market returns might sound difficult, and indeed, those who study stock market data find that market returns fluctuate randomly in short time spans, even up to a few years. However, those fluctuations tend to even themselves out over longer periods of time, such as over a decade. This happens because human emotions tend to dictate the short term fluctuations in stock prices, but over time, stock prices always gravitate back towards their true value.

There are several models that try to predict long term stock market returns. These models all work by attempting to capture the true value of stocks, but they employ different methods to do so.

On MoneyGeeks Stocks page, Ive implemented three of those models for the Canadian stock market. In the rest of this article, I will explain the rationale for one model in particular, called the Gordon Growth Model.

The premise of the Gordon Growth Model is simple. If you hold a stock forever, the only cash flow you will receive is from its dividends. Therefore, you can calculate the rate of return youll get from a stock using only expected dividend payments.

Now, calculating the rate of return this way can be tricky because actual dividend payments can fluctuate wildly. But if we make some simplifying assumptions, the calculation becomes much easier. Specifically, if we assume that a companys dividend grows by at a constant rate forever (a dubious assumption but bear with me), the rate of return that we can expect from the stock can be reduced to the following formula:

Rate of return = Next years dividend yield + Growth rate of dividend per share

For most individual stocks, its dangerous to use the above formula because its unlikely that their dividends will grow at a constant rate forever. However, the constant dividend growth assumption becomes more reasonable when we look at the stock market as a whole.

Lets say we buy a basket that contains small fractions of all stocks that comprise the Canadian stock market. We can achieve this, for instance, by buying a Canadian stock market ETF, such as XIC.TO (read my free book to learn more about ETFs). We can expect to receive stable dividends from our basket of Canadian stocks, because even if one stocks dividend goes down, we can expect another stocks dividend to go up.

Once we accept the assumption that dividends will grow at a constant rate forever, we just need to figure out next years dividend yield and the rate of dividend growth to forecast the long term stock market return.

Of these two components, figuring out next years dividend yield is easy - we just need to add the total amount of dividends paid by Canadian companies and divide it by the total value of all Canadian stocks. As dividend yields normally fluctuate slightly, Ive taken the 5 year historical average. As of the time of this writing, that rate is 2.4% per year.

Figuring out the rate of dividend growth is trickier. There are different ways of going about this.

The most obvious method is to examine the historical trend of total dividends paid by all Canadian companies, and project that trend into the future. While you may find the simplicity of this method appealing, this method has some problems.

One problem is that it doesnt take share counts into account. If total dividend payments go up by 5% but if the total number of shares issued by Canadian companies goes up by 8%, then the dividend per share goes down by roughly 3%. In this example, the dividend growth rate we should use is -3%, not +5%.

The other major problem is that the growth in total dividends reflects the companies willingness, not their ability, to pay dividends. Because of the popularity of dividend investing, stocks that pay dividends have come to be valued higher than similar stocks that dont pay dividends. Realizing this, Canadian companies have increased their dividend payments substantially in recent years. This trend is unsustainable, so we shouldnt expect it to continue into the future.

A better way to forecast dividend growth is to assume that dividends will grow at the same rate as earnings per share, and then use the following formula to forecast earnings per share growth:

Earnings per share growth = (Earnings - Dividend payments)/Shareholders equity

Let me briefly explain why the above formula works. Oversimplifying things a little bit, shareholders equity measures the amount of money that belongs to Canadian companies. The more money that companies possess, the more profits theyll generate. Shareholders equity goes up by the amount of money the company earned, less what they paid out in dividends. Earnings are expected to grow at the same rate as shareholders equity, hence the formula.

Examining data from 2010 to 2015, the earnings per share growth as implied by the formula is about -0.6%. If we plug this number back into our previous formula that forecasts future stock market returns, we conclude that Canadian stocks could return +1.8% per year going forward. Note that you can see this number in the Canadian Stock Market Overview section in MoneyGeeks Stocks page beside the Gordon Growth Model label.

At first glance, this may sound alarming. If we believe the model, Canadian stock returns will be no more than the rate of inflation we've experienced in the past few years.

However, I think the model is more pessimistic than warranted. The reason why the model is forecasting negative future returns is because it expects dividend growth to be negative. The negative dividend growth in turn is the result of low earnings by Canadian companies in recent years.

If we assume that Canadian companies will continue to post terrible earnings, then I would agree with the model and expect negative returns going forward. However, Canadian company earnings have been unusually low in the last few years as the result of plunging commodity prices such as oil and gold. I dont expect the crash in commodity prices to continue indefinitely, so I believe Canadian earnings will post positive, not negative growth.

You may then wonder whats a more reasonable earnings growth rate to assume. Unfortunately, there isnt a perfect way to tell.

One alternate way is to assume that dividend growth will follow the historical Canadian GDP growth. This method, labeled the Grinold and Kroner method in MoneyGeeks Stocks page, is forecasting 4% per year returns for Canadian stocks. Unfortunately, this method has its flaws, which I wont get into right now.

But even if we assume positive dividend growth in the future, its hard to escape this conclusion: future Canadian stock returns wont live up to the 9% per year it has generated over the past 100 years.

I realize this is disappointing news for some. It means that many of us will have to save more than we planned if we are to achieve our financial targets. But its far better to face reality and prepare than to ignore reality and be unprepared for the future.

**This blog post was originally published on the MoneyGeek.ca blog by Jin Choi. The website no longer exists, but Jin has graciously allowed us to re-publish his research for the benefit of future investors forever.**