Buffet, Hussman, and Some Math

Much has been written of late regarding the stock market’s valuation after an amazing 5-year run.   More specifically, there have been several articles appearing recently addressing the concept of Market Cap to GDP as a valuation metric.   Such articles include “Market Cap to GDP:   The Buffett Valuation Indicator” by Doug Short and “The Federal Reserve’s Two-Legged Stool” by Dr. John Hussman.

Short’s article harkens back to a 2001 Fortune Magazine interview within which Warren Buffett called the Market Cap to GDP measure “probably the best single measure of where valuations stand at any given moment.”   Dr. Hussman, in his weekly commentary, went into great detail calculating expected forward market returns over a number of time frames based upon Market Cap to GDP.   They are both good reads, and I encourage anyone interested in the topic to look them up.

Warning:   At this point, this article is going to get wonky.   Not NASA wonky, but “more-algebra-than-is-remotely-interesting” wonky.   If you’re not one to wonk, feel free to skip to the conclusion.

In his article, Dr. Hussman (hussmanfunds.com) explains that expected market returns can be broken into two components:   capital gains and dividends.   Capital gains are driven by two other factors:   “the growth in nominal GDP and the reversion in the ratio of market capitalization to GDP towards its historical norm.”

The first driver is somewhat direct:   GDP growth translates into capital growth.   The second driver, reversion to the mean, is the “wag” assumption in the calculation.   The “wag, ” however, is not without historical confirmation; despite the fact that timing the commencement of the reversion is next to impossible.

Now for the algebra, to estimate the annualized expected return E(r) of the stock market for the next 10 years, courtesy of Hussman (with the formulas presented differently by me):

Inputs:   Long Term Average GDP (LTAGDP)                          6.3%

Current S&P 500 Dividend Rate   (DIVRATE)                          1.86%

Historical Market Cap/GDP Ratio (HMCGDP)                        0.630

Current Market Cap/GDP Ratio (MCPGDP)                             1.251

Using these inputs, on can calculate the expected future returns of the market, assuming mean reversion of the market cap to GDP ratio as follows:


Plugging in the inputs, we get the growth component delivering E(r) of -0.75%.   Add to that the dividend rate of 1.86% and you arrive at an annualized E(r) for the market for the next 10 years of 1.11%.

Not very exciting.

To make a basic test of validity, Hussman ran the same equation from 2009.   The inputs from then were as follows:

Inputs:   Long Term Average GDP (LTAGDP)                          6.3%

Current S&P 500 Dividend Rate   (DIVRATE)                         3.60%

Historical Market Cap/GDP Ratio (HMCGDP)                        0.630

Current Market Cap/GDP Ratio (MCPGDP)                             0.600

Note that the MCPGDP was less than half of where it presently resides (1.251).

Plugging these numbers into the formula you arrive at an annualized E(r) for the market for the next 10 years of 10.42%.

That’s pretty darn good.

Here’s where I take the Hussman calculations one step further in order to see if the E(r) of 1.11% is reasonable in light of where we came from at the market’s nadir in 2009.

We determined above that, from 2009, the 10-year annualized E(r) was 10.42%.   We also know that the past 5-years’ annualized returns have been 20.19%.   If we believe that the 10.42% annualized return is close to being accurate, what does that portend for the next 5 years?   To calculate that, I began by valuing $100 invested in 2009 compounded by the known 20.19% annualized return.   That looks something like this:

$100(1+.2019)^5 = $250.81

I then calculated what we should expect that $100 investment to be after 10 years, using our E(r) of 10.42% as follows:

$100(1+.1042)^10 = $269.45

So…   We expect to have $269.45 after 10 years, but we’ve already risen to $250.81 in 5.   That leaves us to calculate what annual return we should expect over the next 5 years to reach are target.   That is calculated as follows:

(269.45/250.81)^0.2 – 1 = 1.44%

Once again, not very exciting


IF…   you, like Buffet, believe that Market Cap to GDP is the single best measure of market valuations, and

IF…   you, like Hussman, believe that the mean reversion formula can roughly project forward returns, and

IF…   you’ve stuck with this blog long enough to make it this far,

THEN…   we are in for an intermediate period of sub-par index performance.

Obviously this is only one metric to look at when attempting to determine market over/under valuations.   But, I like it.   It confirms what can be expressed more simply without all the math:

After 5 years of equity demand being pulled forward, reflected by a 20.2% 5-year annualized return, we might expect lower returns over the next 5 years as markets return to their normal long term averages.

– LL