Financial Mathematics Text

Friday, December 7, 2012

Are stocks a good value relative to alternatives?

To explore the question about stocks we'll need some criteria and we'll need to look at some various metrics. For simplicity, I will be assuming that "stocks" means the "market" and more specifically the S&P 500. All data and conclusions will be relative to that. The main alternative investment we'll look at are Baa rated corporate bonds.

The first two metrics we'll look at are the dividend yield and Shiller Cyclically Adjusted Price to Earnings (CAPE or PE10). (Data is obtained from here.)

CAPE or PE10 = Current Price / Average of the last 10 years of earnings

Figure 1 keeps an updated version of this and many other interesting charts.

As can be seen in Figure 1, there's a pretty good correlation between CAPE and total stock market returns. As of right now, the stock market is priced higher than historical average. As a result, we might expect lower than average returns. Using a simple linear model (between CAPE inverse and total returns) we can predict about 6.5%. This is somewhat lower than historical averages for the stock returns.

There's more to this story of course. One question we might ask is why prices get as high (or low) as they do. One way to look at this is by examining Moody's Baa bond rates (data provided by FRED). In recent years there's been a decent correlation between Baa yields and CAPE.

Figure 2

Currently, Baa yields are at about 4.5%. So that needs to be taken into consideration when evaluating expected future stock returns. For much of the recent period, Baa yields were higher than CAPE yields.

Another metric we can look at is the dividend yield. I personally subscribe to the view that the real value of stocks (like bonds) is the stream of cash payments (dividends) that the stock pays to its owners. This is counter the view that the stock is worth what someone else is willing to pay for it (sometimes derogatorily referred to as the "Greater Fool" theory).

John Hussman has a simple model for estimating returns using dividend yields (see here).

The idea is pretty simple. Your returns will be related to the dividends you receive, the annual growth rate of those dividends and what the market (in the future) will be willing to pay for the dividends. This last idea is related to an idea of "mean reversion".

We'll define the dividend yield as:

Dividend Yield = Last Year's Dividend Payments / Price

Currently, the S&P 500 offers a dividend yield just over 2%. Historically it has averaged approximately 4.5%

So what does the model project?

Figure 3

These are projections for 10 years. They depend upon a current dividend yield of 2%, a growth rate (on the vertical axis) and a final dividend yield (on the horizontal axis).

What about the colors? The red represents projected returns of less than 4.5% (e.g. you can do better investing in Baa bonds). The yellow represents 4.5% to 6% (better than Baa bonds but perhaps not an adequate risk premium). The green represents greater than 6% expected returns.

I've boxed off the 3-5% region. In recent years, SPY has had a growth rate in dividends of about 5%. Historically dividends have grown around 3%. So that should give some idea as to where future growth rates might be.

If I had to make some guesses, I would probably assume that the dividend growth rate might be about 4% and the terminal dividend yield would be about 2.5%. As a result, expected returns  would be about 4%: Baa bonds would be a more attractive alternative.

In conclusion, we've looked at a couple of models for estimating future stock returns. Both models project lower than historical average returns. But this is hardly an exact science. Furthermore, the low interest rate environment means that investing in bonds might not be a good alternative to investing in stocks.

Of course there are alternatives. There are international stocks as well as the option of picking US stocks other than simply investing in the "market".

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