You Can’t Count on 7%: Application

Let’s say that you want to invest in stocks. Let us say that you have a lump sum to invest and that you can leave it untouched for 30 years? Now let us suppose that you have just read You Can’t Count on 7%.
You Can’t Count on 7%

You look at 30-year returns at today’s valuations. The minimum 30-year (annualized real total) return is 3.2%. This is better than today’s TIPS with their 2% (plus inflation) interest rate. The likely return is 5.22%. It isn’t 7%, but it is a lot better than 2%.

But you remember reading this: “Or..we can wait for better prices.”

What should you do? Does it make sense to “wait for better prices?” YES, it does. Not waiting can make sense as well.

Hidden in the Text

Let’s look at what would happen if you were to wait up to ten years for favorable valuations. What would have to happen to make it worth your while?

This is from You Can’t Count on 7%:

“This is the regression equation for the 20-year stock return and the percentage earnings yield 100E10/P (using 1923-1972 data): y = 1.0849x-1.4488 where y is the annualized real return in percent and x is 100E10/P or 100/[P/E10]. The confidence limits are plus and minus 4%.”

When the most likely return y is 4%, the lower confidence limit is 0%. The upper confidence limit is y plus 4%, which totals 8%.

The break-even point is zero percent. The lower confidence limit equals 0% when y = 4%. Solving the equation: y = 4 = 1.0849x-1.4488 or 5.4488=1.0849x or x = 5.02%, where x is the earnings yield = 100E10/P = 100/[P/E10]. Solving, P/E10 = 19.9.

If P/E10 falls to 19.9, you are virtually guaranteed to break even in stocks (after adjusting for inflation) over the next 20 years. You are likely to earn 4% (annualized real return). You have a chance to make 8%.

Now lets solve for y = 5%. From the equation, y = 5 = 1.0849x-1.4488 or 6.4488=1.0849x or x = 5.94% earnings yield and P/E10 = 100/5.94 = 16.8.

If P/E10 falls to 16.8, you are almost guaranteed to make some money (1% plus inflation) over the following 20 years. You are likely to earn 5% (annualized real return). You have a chance to make 9%.

The next calculation is especially important. Remember that TIPS offer 2% interest (plus inflation). When y = 6%, the lower confidence limit equals 2%. You are virtually guaranteed to do at least as well as today’s TIPS.

Letting y = 6%, y = 6 = 1.0849x-1.4488 or 7.4488=1.0849x or x = 6.87% earnings yield and P/E10 = 100/6.87 = 14.6.

Historically, a P/E10 level of 14.6 has been typical. Prices are almost twice as high right now.

With P/E10 close to 14.6, you would be almost certain to do better with stocks than with 2% TIPS over 20 years. Your most likely return would be 6% (plus inflation). It could be as high as 10% (plus inflation).

Continuing with the equations with y = 7%, 8%, 9%, 10% and 11%:

When the most likely return is 7%, x = 7.79% and P/E10 = 12.8.
When the most likely return is 8%, x = 8.71% and P/E10 = 11.5.
When the most likely return is 9%, x = 9.63% and P/E10 = 10.4.
When the most likely return is 10%, x = 10.55% and P/E10 = 9.5.
When the most likely return is 11%, x = 11.47% and P/E10 = 8.7.

[The confidence limits are plus and minus 4%.]

Historical Valuations

Professor Robert Shiller posts P/E10 and other S&P500 data at his web site. Figure 1.3 shows P/E10 versus year. [The price-to-earnings ratio in Figure 1.3 is P/E10.]
Professor Shiller's web site
Professor Shiller's Online Data page

P/E10 was 8.7 in 1983. The last time that it was below 13 was 1986. The last time that it was 15 was in 1989. It was 16.8 in 1991. It was 19.9 in 1992 and 1994.

The 2003 low was 21. In May, it was 25.9. Today, it is 27.2. Before the peak of the bubble, P/E10 levels broke through 26 and 27 in 1996-1997.

If the rise and fall of P/E10 were symmetrical, P/E10 would fall below 15 around 2011. P/E10 would continue down to 8.7 in 2017. Historically, declines have been faster than rises.

The Benefits of Waiting for Good Prices

I will assume that you keep your money either in 2% TIPS or in a 0% inflation-matched alternative for ten years. Then you invest in stocks for 20 years.

Mathematically, the annualized total return r over the 30-year period is the solution to this equation:
(1+r)^30 = [(1+r1)^10]*[(1+r2)^20], where r1 is the annualized total return in the first ten years and r2 is the annualized total return in the next twenty years.

If r1 = 0.00% (i.e., only match inflation during the first decade):

If r2 = 0%, then r = 0.00%.
If r2 = 1%, then r = 0.67%.
If r2 = 2%, then r = 1.33%.
If r2 = 3%, then r = 1.99%.
If r2 = 4%, then r = 2.65%.
If r2 = 5%, then r = 3.31%.
If r2 = 6%, then r = 3.96%.
If r2 = 7%, then r = 4.61%.
If r2 = 8%, then r = 5.25%.
If r2 = 9%, then r = 5.91%.
If r2 = 10%, then r = 6.56%.

If r1 = 0.02 (e.g., as with TIPS):

If r2 = 0%, then r = 0.66%.
If r2 = 1%, then r = 1.33%.
If r2 = 2%, then r = 2.00%.
If r2 = 3%, then r = 2.67%.
If r2 = 4%, then r = 3.32%.
If r2 = 5%, then r = 3.99%.
If r2 = 6%, then r = 4.65%.
If r2 = 7%, then r = 5.31%.
If r2 = 8%, then r = 5.96%.
If r2 = 9%, then r = 6.61%.
If r2 = 10%, then r = 7.27%.

If P/E10 falls below 19.9 and if you only match inflation during the first decade, you should expect 30-year (real annualized total) returns between 0.00% and 5.25%. Your most likely return would be 2.65%. This is better than 2% TIPS.

If P/E10 falls below 19.9 and if you make 2% plus inflation during the first decade, you should expect 30-year (real annualized total) returns between 0.66% and 5.96%. Your most likely return would be 3.32%.

If P/E10 were to fall to 14.6, which is likely, your 30-year (real annualized total) return would be between 1.33% and 6.56% if you only matched inflation during the first decade. Your most likely 30-year return would be 3.96%.

If P/E10 were to fall to 14.6 and if you were to receive 2% interest (plus inflation), your 30-year (real annualized total) return would be between 2.00% and 7.27%. Your most likely 30-year return would be 4.65%.

How about Waiting Longer?

This is from You Can’t Count on 7%:

”This is the regression equation for the 10-year stock return and the percentage earnings yield 100E10/P (using 1923-1972 data): y = 1.5247x-4.5509 where y is the annualized real return in percent and x is 100E10/P or 100/[P/E10]. The confidence limits are plus and minus 6%.”

To assure ourselves of breaking even during a single decade, we need the value y to equal 6% since the confidence limits are plus and minus 6%. This requires an earnings yield x of 6.92% or P/E10 = 14.5. The range of uncertainty is high. The upper confidence limit is 12%.

To assure that we do at least as well as owning 2% TIPS during a single decade, we need the value of y to equal 8%. This requires an earnings yield x of 8.23% or P/E10 = 12.1. The range of uncertainty is high. The upper confidence limit is 14%.

P/E10 was 14.5 in 1988. It was 12.1 in 1986. If the rise and fall of P/E10 were symmetrical, P/E10 would fall to 14.5 in 2012. P/E10 would fall to 12.1 in 2014.

If we were to match inflation for twenty years and then receive a return of 0% for another decade, our (real annualized total) return would be 0%. If we were to receive a 6% return for the next ten years (which corresponds to a single decade in stocks starting with P/E10 = 14.5), our thirty-year (real annualized total) return would be 1.96%. If we were to receive a 12% return for the next ten years (which is the upper confidence limit), our thirty-year (real annualized total) return would be 3.85%.

If we were to receive 2% plus inflation for twenty years and then receive a return of 0% for another decade, our (real annualized total) return would be 1.33%. If we were to receive a 6% return for the next ten years (which corresponds to a single decade in stocks starting with P/E10 = 14.5), our thirty-year (real annualized total) return would be 3.32%. If we were to receive a 12% return for the next ten years (which is the upper confidence limit), our thirty-year (real annualized total) return would be 5.23%.

If we were to match inflation for twenty years and then receive a return of 2% for another decade, our (real annualized total) return would be 0.66%. If we were to receive an 8% return for the next ten years (which corresponds to a single decade in stocks starting with P/E10 = 12.1), our thirty-year (real annualized total) return would be 2.60%. If we were to receive a 14% return for the next ten years (which is the upper confidence limit), our thirty-year (real annualized total) return would be 4.46%.

If we were to receive 2% plus inflation for twenty years and then receive a return of 2% for another decade, our (real annualized total) return would be 2%. If we were to receive an 8% return for the next ten years (which corresponds to a single decade in stocks starting with P/E10 = 12.1), our thirty-year (real annualized total) return would be 3.96%. If we were to receive a 12% return for the next ten years (which is the upper confidence limit), our thirty-year (real annualized total) return would be 5.23%.

There is a wide range of outcomes from the stock market in a single decade. In spite of this, we have an excellent chance of doing better than today’s TIPS (which return 2% plus inflation).

Waiting is OK

It is OK to wait. It is OK not to wait. It is safer to wait.

You should get a buying opportunity if you decide to wait. P/E10 was 10.0 in 1985, fifteen years before the bubble’s peak. Judging from Professor Robert Shiller’s graph, there is a good chance that we will see P/E10 equal to 10.0 by 2015.

You may experience regret if you wait and stocks do well for the next two or three years.

We have assumed that you would leave your money untouched for thirty years if they were in stocks. That is a long time, especially if the market drifts sideways and downwards for a decade of more.

What if you do everything wrong? What if stocks do well enough in the next two or three years to draw you into the market and then it heads down toward much lower valuations. You need to guard against such a possibility.

Have fun.

John Walter Russell
August 4, 2005