### Back-of-the-Envelope Equity Premium

Historically, corporate equity has returned about 6% more annually on average compared to government bonds. If I expected the equity premium to be that high going forward, I would be fully invested. In fact, I would be maxing out my HELOC to buy stock. But a 6% equity premium seems like quite an unreasonable expectation at this point in time. What might be a more reasonable expectation?

I’ve tried two methods to come to an answer. The first method assumes that dividends will grow at the same rate as GDP, then estimates expected real GDP growth, adds the dividend yield, and compares the result to the 10-year TIPS yield. The second method assumes that corporate profits will return to their historical fraction of national income, adjusts current earnings accordingly, adds the expected inflation rate, and compares the result to the nominal 10-year Treasury yield.

Method 1. To estimate real GDP growth (for the US), I take the trend labor productivity growth rate of 2.7% (based on my exponential smoother optimized for an 8-quarter-ahead forecast) and add an assumed labor force growth rate of 1%, so the estimated real GDP growth rate is 3.7%. The dividend yield on the S&P 500 is 1.95% according to this week’s

Method 2.

Not that a 1.78% premium is really all that bad for a long-term investor, but I have some short-term concerns that would make me willing to risk missing out on a few years of 1.78% excess returns:

So, by method 1, stocks are a good deal for someone with my preferences. By method 2, they’re not. Taking an average, (3.33% + 1.78%) / 2 =

I’ve tried two methods to come to an answer. The first method assumes that dividends will grow at the same rate as GDP, then estimates expected real GDP growth, adds the dividend yield, and compares the result to the 10-year TIPS yield. The second method assumes that corporate profits will return to their historical fraction of national income, adjusts current earnings accordingly, adds the expected inflation rate, and compares the result to the nominal 10-year Treasury yield.

Method 1. To estimate real GDP growth (for the US), I take the trend labor productivity growth rate of 2.7% (based on my exponential smoother optimized for an 8-quarter-ahead forecast) and add an assumed labor force growth rate of 1%, so the estimated real GDP growth rate is 3.7%. The dividend yield on the S&P 500 is 1.95% according to this week’s

*Barron’s*, and the 10-year TIPS yield is 2.32%. The calculation 3.70% + 1.95% - 2.32% gives an estimated equity premium of**3.33%**. It’s not nearly as “puzzling” as the historical 6%, but as a long-term investor, I still find 3.3% pretty impressive. If that’s the right figure, then I’m in.Method 2.

*Barron’s*reports the earnings yield on the S&P 500 as 5.74%. In 2005, after-tax corporate profits were 8.94% of US national income, compared to an average of 6.64% since 1948. Adjusting the latest earnings gives an earnings yield of 5.74% x (6.64/8.94) = 4.26%. The expected inflation rate is 2.5% (always). The 10-year Treasury yields 4.98%. The calculation 4.26% + 2.50% - 4.98% gives an estimated equity premium of**1.78%**. If that’s the right figure then I’m out – way out.Not that a 1.78% premium is really all that bad for a long-term investor, but I have some short-term concerns that would make me willing to risk missing out on a few years of 1.78% excess returns:

- With the premium so far below its historical average, I would expect some reversion. By reversion, I mean stock prices going down.
- Under this method, I’m assuming that corporate profits will revert to their historical fraction of national income. I’m guessing that when that happens, it won’t be a good time to own stock.
- I think Wall Street may be underestimating the chance of a recession.
- Nouriel Roubini provides a convincing set of parallels between today and 1987.

So, by method 1, stocks are a good deal for someone with my preferences. By method 2, they’re not. Taking an average, (3.33% + 1.78%) / 2 =

**2.55%**. At that price, I’m on the fence.Labels: capital, economics, finance, interest rates, macroeconomics, profits, US economic outlook

## 12 Comments:

Believe your Method 2 leaves out growth in earnings per share.

Let's suppose that S&P earnings per share grow "forever" in tandem with GDP -- perhaps 5.5% p.a. (3% real plus 2.5% for inflation).

A share is a claim on that future earnings stream, so its price today is just the value of those future earnings discounted back. For these numbers, that only works if the discount rate is 11.24% (=5.74%+5.5%)

If a share's discount rate is 11% p.a., then we expect its value to grow at about 11% each year. Which is an equity premium of ~6% above the long-term T-bond (~5%).

This is pretty standard stuff. Am I missing somethinG?

The previous post has a calculational error. It should read:

Believe your Method 2 leaves out growth in earnings per share.

Let's suppose that S&P earnings per share grow "forever" in tandem with GDP -- perhaps 5.5% p.a. (3% real plus 2.5% for inflation).

A share is a claim on that future earnings stream, so its price today is just the value of those future earnings discounted back. For these numbers, that only works if the discount rate is 9.76% (=4.26%+5.5%)

If a share's discount rate is 9.76% p.a., then we expect its value to grow at about 9.76% each year. Which is an equity premium of ~5% above the long-term T-bond (~5%).

This is pretty standard stuff. Am I missing something?

Growth in earnings should only be included if the source is something other than reinvested earnings, or to the extent that the return on those reinvested earnings is greater than the return on the original investment (which might be the case either because the return on capital is higher in the future or because the original equity was selling at a discount to its replacement cost).

If growth in earnings is merely due to reinvestment of retained earnings at the same rate of return, then it would be double counting to take into account earnings growth in addition to the full original earnings. For example suppose a stock has a 5% earnings yield and pays no dividends, and suppose the return on reinvested earnings is also 5%. Then earnings will grow at a 5% rate, but you are getting no dividends, and the value of the company is growing at the same rate, so the total rate of return is 5%, not 10%.

According to BLS data, US capital is actually getting less productive (as one might expect, given that the capital stock is increasing relative to available labor). It’s hard to say what the replacement cost might be, but stocks are selling at large multiples of book value, so I’m assuming they aren’t selling at a significant discount to replacement cost. Therefore I’m attributing all expected (real) earnings growth to reinvestment at the same rate of return.

Continuing my last comment…You could make a case that there are other sources of earnings growth, such as the value of land owned by corporations, which could continue to rise as the population rises even if there is no reinvestment, or the value of knowledge which can be costlessly spread over a rising population. So my method 2 could be understating the equity premium, but method 1 is probably overstating it (given what might be an optimistic assumption about productivity growth and failure to account for the inflation risk premium), so I’m still pretty comfortable with the range they give.

One of the big difference between now and 1987 is valuation. In 1987 the s&P 500 pe peaked at 22 just before the crash while my model said that given current inflation and interest rates the pe should have been 14. So the market was 50% overvalued and essentially all the crash did was eliminate that overvaluation -- it also caused the fed to abort the tightening that was in progress.

Now the s&p 500 pe is around 16

and my pe model say it should be around 16 so we do not have the big overvaluation currently that needs to be eliminated as we did in 1987.

In both cases I'm using trailing operating earnings rather then forecast eps. In 1987 I kept being told the market was OK because we were going to get a 33% gain in eps in 1988 and on that basis the market was not overvalued. They were right too, we did get a 33% increase in EPS in 1988 but that did not prevent

the 1987 crash.

Otherwise you analysis of the market is very good. Over the long run the market PE seems to have 5 to 15 years secular swings from below 10 to over 20 and back to below 10. We now appear to be on one of those long term down swings.

希望大家都會非常非常幸福~

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