Financial Physics

Financial Physics Model
Forecasting Future Returns

Looking ahead, stock market return will continue to depend on prospects for earning growth, dividend yield, and valuation change. Thus separating fundamental return and speculative return would be a valuable tool for considering reasonable expectation for future stock market return.

Future Fundamental Return:

As we have seen previously, fundamental return is a sum of two factors – earning growth and dividend yield. As profit increases, the stock portfolio appreciates in price. As one earns dividend yield, portfolio increases its value even more. As we analyzed the earning growth and dividend payout, we will find that in the long run, both items are logically connected to the GDP (Gross Domestic Product).

Earning Growth:

If one assumes that the S&P 500 index is an excellent proxy for the market as a whole - there is a historic and permanent relationship between S&P 500 index earning growth and real economy growth - GDP growth. The business factors that drive earning growth are the same factors that drive GDP growth. GDP at its heart, after all, is the sum of the revenues of all U.S. businesses. As business revenues grow, business earnings grow, and GDP grows.


On a macro-economics sense, over the long run, GDP growth depends on two main factors – the population growth, and the productivity growth rate. Population growth plus productivity growth produce GDP growth. As population growth, the workforce grows and more people working, produces more output. Productivity is defined by output per person per hour. As the world is becoming more and more digitize, and as we automate more and more of our activities, it is raising the productivity more rapidly than we once thought possible.

Over the last seven decades, real GDP (not adjusted for inflation) has grown around at 3.5%. Past GDP growth of 3.5% a year has been driven by population growth of about 1.0% and productivity growth averaging about 2.5%. In future population growth is likely to slow down, perhaps by a little. However, in our view, this will be compensated by increase in the productivity growth due to the globalization and digitization of our new world.

pop growth

If we assume that in future also, GDP will maintain its present growth rate of 3.5% a year and if we add to that an annual inflation rate of about 2.5%, one gets about 6% growth in the nominal GDP. This essentially represents the real and nominal (real + inflation) sales growth of 3.5% and 6% respectively for S&P 500 index in the future.

And if one takes a look at 50-year chart of after tax profits as a percentage of gross domestic products, one finds that the this rate normally falls between 3% and 7% with an average rate of net profit margins of about 6% as a percentage of GDP. As of March 31, 2006, after –tax profit margins were 8.5% of GDP. This is the highest after-tax profit margins seen in over 75 years. Only in 1929 were after-tax profits higher, when they peaked at 9.07% of GDP.

after tax profits

And thus, we can safely predict that in future, the average rate of earning growth will cluster around 6% a year.

Long Term Earning Growth Forecast

Items Real
Average % Growth Per Year
GDP Growth
Nominal GDP Growth
Corporate Product(Sales)
S&P Earning Growth

Dividend Yield:

There is also quite a consist link between corporate dividend payout and the total size of the U.S. economy. The chart below shows the year-after-year relationship between dividend yield and GDP. We see that, year after year, corporate dividends paid to shareholders by firms listed on NYSE are almost equal to 2% of GDP. The sort of firm that makes into NYSE exchange are larger, older, more established and, therefore, somewhat more likely to pay dividend. Whichever way we slice it, with logic or with data, the chart points out that Dividend yield over time are fairly steady with respect to the GDP. This ratio is almost entirely independent of the overall value of the stock listed on the NYSE stock exchange.

This is an important finding, though it is often not very obvious. The total dividend cash flow paid to shareholders by companies listed on the nation’s stock market is quite constant. To reiterate the key point; total dividend payouts run somewhere around 2% of GDP.

For the present $10 Trillion U.S. Economy (GDP) and therefore U.S. Corporate Sales Revenue (U.S. GDP) and at a 6% after-tax profit margin, U.S. corporate on aggregate are generating about $600 billion profit annually. Out of which, it is paying out about $200 billion annually to its shareholders as a dividend (2% dividend payout of U.S. GDP). Thus at present, U.S. corporate are paying out as dividend to shareholders about 40% from their earnings.

Historically, in aggregate, the S&P 500 companies have averaged about 7% earning growth (real + inflation) over a long period of time while paying out half (50%) of those profits annually in dividends.

Total Fundamental Return:

Thus if we combine the corporate earnings growth of approximately 6% (real GDP growth rate of 3.5% and about 2.5% inflation rate) with dividend yield of approximately 2.0% of GDP - over the long run, stock market should enjoy a total fundamental return of about 8.0% on a compound annual growth rate (CAGR) basis.


Fundamental Return: Real GDP Growth Rate + Inflation Rate + Dividend Yield 3.5% + 2.5% + 2.0% = 8.0%

This 8% future fundamental return seems to be less than the historical average rate of fundamental returns of around 10% per year. This is due to the fact that over the seventy years, average dividend yields on S&P 500 stocks have been 4.0% while recently on aggregate, dividend yields in today’s market have sunk into the 1.5% range.

Future Emotional Return:

As we mentioned before, emotional return can be significantly influence by the interest rates. Interest rates effect on valuation is the same way gravity acts on matter. The higher the rate, the greater the downward pull and lower the financial valuation. Higher the interest rate lower is the P/E. We can see from the Table IV, how higher interest rates depresses the P/E and hence its contribution to the total market return. That’s because the rates of return that investor need from any kind of equity investment are directly tied to the risk-free rate they can earn from government bonds. So if the government rate rises, the prices of equities must adjust downward, to a level that brings their expected future return into line. Conversely, if government interest rates fall, the move pushes equity price upward.

Interest rates are primarily driven by inflation. Over an extended period of time, higher is the inflation; higher would be the Interest Rate. Inflation rate and interest rate are like twin sisters, they follow each other; they track closely.

figure 12

Over the past 50 years, the difference in magnitude between interest rate and inflation rate has fluctuated between 1.5% to 6% at the extremes, and has averaged about 3% over this period. For example, if inflation is 3%, long term bond yielded an interest rate of 6%. If inflation increases to 5%, one would expect a 30-year bond to yield 8%. Higher inflation causes a loss of purchasing power. Investors will simply pay less for the shares in a high-inflation environment, but more in a low-inflation environment.

There is a “Rule of 20” which says that the sum of P/E and inflation should be close to 20. The present P/E of S&P of about 17 and inflation of 2.5% makes it very close to the fair value.


One of the most important factors that drive inflation is the amount of money that the government makes available to the economy. It does it by raising or lowering the short term interest rates. When Fed raises interest rates, it makes less reserves available to the bank, thus effectively taking money out of the system. This is the reason everyone watches the move made by Federal Reserve Chairman so closely. One can see from the chart below that the federal funds rate have been recently creeping up from 1% to 5%.


In a very simple Federal Reserve Board model, which estimates the fair value of the market, one compares stock earning yields (inverse of P/E in percentage) with the 30-year bond yield. For example, P/E of 20 for S&P 500 provides stock would provide earning yield of 5% which compares favorably with the present 30-year bond yield of 5%. If the long term bond is yielding 4%, then according to the Fed model the equivalent P/E should be around 25. But if interest rates rise to 6%, then the P/E should decline to about 16. It means when interest rate increases from 5% to 6%, Fed model expects P/E multiple to drop by 20%. This may cause the market to decline by about 20%

However, we would make one more adjustment to the earnings yield on the S&P 500 to make it truly comparable to bonds. The 5% yield on 30-year Treasury bond is guaranteed, but it does not increase whereas, the S&P 500 earnings do grow at an annual average nominal (real + inflation) of about 7% (the 50-year average). Therefore, we need to adjust the earnings yield of the S&P 500 to take into account that it is growing at 7%.

If we examine the historical relationship between guaranteed bond yield and stock yield, we find that usual difference between a bond yield and stock earnings yield is about 1%. For example, if investors can get 5% on a guaranteed bond they are willing to accept 1% less meaning 4% earnings yield on a stock. The reason for this is that if you have a 4% stock earnings yield and it is growing at 7%, it will equal your 5% bond yield in about 3 years. Anytime thereafter, the stock earnings yield will increase by 7% per year. If you project this over several years, there is quite a difference and that’s why investors are willing to accept an initial lower earnings yield on stock.

One can see from the long term interest rate trends from Chart VII – the current interest rates are two decade low. Thus in our view, the probability of interest rates going down and P/E rising in any meaningful way for the next decade is remote. Indeed, most still expect interest rates to rise, which implies P/E to fall.

s&P 500

In our estimate, the present S&P earnings yield of 6% (P/E ratio of roughly about 17) is reasonably priced when compared to the present long term interest rate of 5%. If, for the next 10 years the present interest rate remains at 5% and the present P/E ratio of 16 does not change, then the contribution from the speculative return will be zero.

If however, in the scenario where the inflation picks up and the interest rates rise to 8%, the P/E ratio will fall from 17 to about 8. In this case, the speculative return would contribute about minus 3% per year.

fig 16

Future Stock Market Total Return:

In the case where the long term interest rates of 5% and present P/E ratio of 16 does not change, then the contribution from the speculative return will be zero and the market total return will be the same 8% provided by the fundamental return.

In the case where the interest rates rise to 8%, the P/E ratio will fall from 16 to about 8, then speculative return would contribute about minus 3% per year; this will cut the 8% fundamental return to 5% market return.

Thus our Financial Model predicts future stock market annualized return to be in the range of 5-8% for the next decade.

Contribution of Fundamental & Speculative Returns
To the Overall Market Return
For the Next Decade

Next Decade

Fundamental Return

Speculative Return

10 Years



fig 17

The great bull markets of the last two decades we saw from 1982-2000 when market produced 16.8% annualized return on stocks was more an anomaly than normal. During that period interest rates dropped from 14% to 5% and consequently P/E multiple surged from 8.0 to 26.4. The tripling of price/earning ratio was a windfall that one should not expect again in the future at least in the near term. In the next decade, our belief is that the primary driver of the stock market return will remain to be Fundamental Return comprising of earning growth, inflation, and dividends.

In our next section of Stock Selection Methodology - we will extend this model to screen individual stock based on these variables and then attempt to construct a portfolio for an optimum future performance.