Are U.S. stocks cheap? (October 2008, S&P 500 at 860)

The Natural Cadence of the U.S. Economy:

Between 1950 and 2000, corporate after tax profits have averaged 5% of GDP (historically they have hovered between 4% and 6% of GDP source1, source2 ), out of which approximately 40% of the profits have been paid out as dividends (net dividends) and 60% retained for reinvestment (source: using data from the BEA for nominal GDP and Corporate Profits).

The historical risk-free interest rates (1 year treasury bill) between 1950 and 2000 have averaged approximately 5%. (This also seems to be the case going back to 1900 in the modern industrial economies of Europe, the U.S. and Japan)

Nominal GDP growth during this time has averaged 7.3% per annum. As a rough approximation, corporate profits after tax should also have increased at this rate. Given that corporations retain 60% of their profits, this implies that the historical ROE is about 12% on average.

In other words, the structure and cadence of the modern U.S. economy suggests that over the long run, the natural order of things is for the economy to grow at 7.3% per annum in nominal terms and have a risk-free interest rate of 4.8%. Looking at each year's GDP by income, the corporate sector's post-tax profits account for 6% of GDP, of which it distributes 2.4% of GDP to its owners, and reinvests 3.6% of GDP for corporate sector fixed capital formation. The natural cadence of interest rates, risk premium and economic activity has allowed the corporate sector to this with an average ROE of 12%.


With this natural cadence, stocks are fairly priced when
the Market Capitalization to GDP ratio is around 80%

If we believe this economic cadence will continue into the future, then we can calculate the NPV of the U.S. corporate sector using the nominal growth, ROE, and profit as a % of GDP figures we have observed.

(a) Estimate 1: Given a required discount rate of 8%, the NPV of Book Value of all corporations after 40 years + NPV of all dividends received over 40 years is approximately = 18.64 times the current corporate profits, which = 93.2% of GDP (the average corporate profits is about 5% of GDP, this means that the NPV of the corporate sector is 5 x 18.64 = 93.2 % of GDP)

(b) Estimate 2: Given a required discount rate of 8%, half the NPV of Book Value of all corporations after 40 years + NPV of all dividends received over 40 years is approximately = 15.75 times the current corporate profits = 78.75% of GDP (the average corporate profits is about 5% of GDP, this means that the NPV of the corporate sector is 5 x 15.75 = 78.75 % of GDP)


Stocks are now fairly priced
(Oct 2008, S&P 500 at 860)

As of Oct 25, 2008, the Market Capitalization of the US stock market (based on the Wilshire 5000 index) is about 74% of 2007 GDP.

It looks like it is fairly valued (it's not overpriced, but neither is it a fire-sale price), but only if:

(a) you are a long term 20-30 year investor willing to accept 5-6% per annum returns (you should conservatively estimate expect returns to be less than the discount rate or economic growth rate, because your purchase price and selling price may be at different valuation multiples), and

(b) the cadence of US economy over the next 40 years will be similar to the period since 1950, so that the historical averages we are using in the valuation will remain valid over the next 40 years. This assumption would require that economic cadence is determined by the legal and capitalistic free-market structure of the U.S. economy, combined with the socio-political norms in the U.S. and universal human/psychological factors (all of which look likely not to change) and not by technology (which is improving at an accelerating pace as futurists such as Ray Kurzweil suggest).

(c) you think a 8% discount rate is sensible.


Will stock prices go down further?
(Historically, what is the cheapest that stocks have gotten?)

Yes, it's certainly possible. Investor psychology can cause markets to be severely undervalued or overvalued for prolonged periods of time. In the 1940s, the US stock market has at times had a capitalization as low as 40% of GDP. In the 1980s, during the high interest rates of the Volcker era, it was trading at about 50% of GDP (see Nick Nejad's blog post). So if history is a guide, investor psychology could make the markets could go down another 33%. (Historically, those two periods were also times when equities were out of favor with the public at large. The period between the 60s and 1974, and the period between the late 80s and 2000, were periods when equities were extremely popular.)

If we are moving into a period when equities are out of fashion in the zeitgeist, then it is conceivable that the market could fall till its value is only 50% of GDP (i.e. S&P 500 at around 580; or it could just stay stagnant as GDP grows until the ratio is about 50% (GDP would have to increase by 50%, ie. grow at 7% for another 6 years for this to happen).

The Wall Street Journal also has a neat table showing historical PE ratios of the market. Though PE ratios of the market in any one-two year period are not indicative of historical averages (because corporate profits as a % of GDP swing from year to year), they do suggest the possibility of the market going down by 35% if we return to the market PE ratios common in the 1980s. (2008 market PE ratio: approx 12; 1974 market PE ratio: approx 7)


Can we use this market capitalization to GDP ratio to assess the value of other equity markets?

This approach works for the U.S. equity market, because (a) the U.S. economy is extremely broad, robust, and resilient, and (b) the U.S. equity market is well developed and the publicly listed companies are representative of the overall U.S. corporate sector.

This is not true for all countries. For example, Brazil has a broad and deep economy, but a disproportionate amount of its market capitalization is for natural resource companies. Buying the index tracking fund there would not give you exposure to the underlying economy. As another example, Singapore has a small niche economy and a stock market that hosts many companies with businesses outside of the Singaporean economy. The market capitalization to GDP ratio in Singapore would tell you nothing about whether Singapore listed equities are overpriced or underpriced.


Buying stocks (or an index tracking fund) is a bet on the U.S. economy.
So should investors be concerned about the huge (and growing) U.S. current account deficits?

The 2007 current account deficit was about USD 731 billion, or about 5% of GDP. The impact of this to investors is that as the U.S. imports more stuff every year, the U.S. dollar will be under constant devaluation pressure.

(Side Note 1: The 2007 U.S. Net International Investment Position was about negative USD 2.4 trillion dollars, or about 15% of GDP. The NIIP has been deteriorating at a slower rate than the growth in cumulative current account deficits, suggesting that foreign holders of US dollars have been buying US assets whose prices generally decline over time, and/or that US investors have generally been buying overseas assets which generally appreciate in price over time. [see the BEA's "changes in selected major components of the international investment position" for details] But the U.S. NIIP is deteriorating nonetheless.)

(Side Note 2: As a comparison, Australia has a negative net international investment position of about 68% of GDP. This could theoretically be due to Australia borrowing more to fund its gross fixed capital formation which is about 25% of GDP, as compared to the gross fixed capital formation of about 18% of GDP in the U.S.)

If you are U.S. based investor who uses USD for day-to-day living, then this won't matter as long as the U.S. economy is able to start domestic manufacturing of items that were previously imported. My bet is that it will be able to do so. The resourcefulness and ingenuity of the capitalistic U.S. economy will rise to the occasion. You US dollar investments will return you US dollar dividends which will maintain their real value.

If you are a overseas based investor who used another currency for day-to-day living, then you would be concerned that even if you own all the companies the US, the US dollar dividends would be worth less and less, in real terms, in your local currency. However, my bet is that if the US dollar depreciates excessively, US companies will begin manufacturing things that used to be imported, and also export their wares as the depreciating dollar makes them more price competitive. This should limit the decline in the real value of your US dollar investments. But the quantum of the decline in real value of your US investments is hard to determine.