Yesterday I looked at John Hussman’s method for estimating the long-term returns on stocks. The long-term return on a security consists of two parts: income (from dividends or interest payments), and capital gains (from price changes). **For any future stream of income, the higher the price you pay , the lower the annual rate of return you will earn. **

Hussman provides the following equation to mathematically estimate the total return on stocks over any future time horizon (annualized):

(1+g)(Original Yield/Terminal Yield)^{1/N}– 1 + (Original + Terminal)/2Where Original Yield is the original dividend yield (in decimal form), Terminal Yield is the dividend yield expected at the end of the holding period, N is the holding period in years, and g is the growth rate of dividends over the holding period.

Here’s my calculation. If I assume a dividend growth rate of 6 percent (about the long-run average*), the current S&P 500 dividend yield of 2.1 percent (from multpl.com), a terminal S&P 500 dividend yield of 4 percent (Hussman says that the dividend yield on stocks has historically averaged about 4 percent), the expected nominal return over ten years is **2.4 percent **annually.

**(1+0.06)(0.021/0.04) ^{1/10} – 1 + (0.021 + 0.04)/2 = 0.02435**

Ugly.

If I use multpl.com‘s mean and average long-term S&P 500 dividend yields of 4.46 and 4.39 percent respectively it gets uglier still, so I’m not going to bother.

Over 20 years the nominal return rises to **5.7 percent**, and over 30 years **6.8 percent**.

Still too ugly.

Hussman last calculated the 10-year S&P 500 total returns to be about **5.2 percent** annually, and offers the following:

As a rule of thumb, a 1% market decline in a short period of time tends to increase the prospective 10-year return, not surprisingly, by about 0.1%. However, that approximation is less accurate over large movements or over extended periods of time, where growth in fundamentals and compounding effects become important.

The market is approximately flat since Hussman wrote his article on May 21, so the market decline should have had no impact. To get to Hussman’s 5.2 percent with my inputs, we have to assume a 9 percent growth rate (bullish!):

**(1+0.09)(0.021/0.04) ^{1/10} – 1 + (0.021 + 0.04)/2 = 0.05248**

Or a terminal yield of 2.9 percent (still bullish):

**(1+0.06)(0.021/0.0288) ^{1/10} – 1 + (0.021 + 0.0288)/2 = 0.05194**

I’ve got no idea why my calculation differs from Hussman’s. I’m all ears if anyone has any suggestions. Either way, even with outrageously bullish assumptions, 5.2 percent is not a great return. It’s about half the historical return of 10 percent. There are other methods of calculating expected returns that I’ll look at tomorrow.

* Hussman says:

Historically, earnings, dividends, revenues, book values and other stock market fundamentals have grown at a rate of 6% annually.Earnings are the most volatile of these, sometimes growing from trough-to-peak at rates approaching 20% annually, and sometimes plunging from peak-to- trough at rates approaching -20% annually. In fact, historically, earnings have been even more volatile than prices themselves. When measured from peak-to-peak or trough-to-trough however, earnings show exactly the same sturdy 6% annual growth rate that other stock market fundamentals exhibit. Over the past century, the highest growth rates over any 30-year period were 6.3% annually for dividends, and 7.8% for earnings (trough to peak).