The behavior of stock market is inherently so complex that no single variable can predict how the market is going to behave next or what would be its future returns - at least not on a regular and consistent basis over a long time. Given that the computing horsepower on Wall Street rivals NASA, the single variable, if it exists, would have been found already. But it hasn’t. The reality is that not only is market behavior a function of multiple variables but these variables are also interacting, and they do so imprecisely; the exact same data set at different times sometimes produces different results.

As millions of investors vote every day with their wallets the stock market, in the short run, becomes very noisy and chaotic. However, as any physics student would tell you - one need to distinguish between noise and signal and learn how to ignore the former and enhance the latter. In physics one also learns how to handle a complex mathematical problem by breaking it down into a set of manageable components, solve them each separately and then try to put them back together to get a complete solution. Additionally, any student of stock market would tell you that over the long run, the stock market is a weighing machine not a voting machine. Our belief is that we may use this crossroads of Finance and Physics that we call Financial Physics. Financial Physics represents a framework of several key variables and their impact on the stock market’s overall direction. It is not a magician’s illusion – it’s a Fundamental Physics!

Our belief is that as mysterious as the stock market seems, its returns may be determined by just two simple returns; fundamental return and speculative return.

Add them together and you have the stock market total return.

Investment Return = Fundamental Return + Speculative Return - (1)

The first term, Fundamental Return, is determined by adding Earning Growth and Dividend Yield.

Fundamental Return = Earning Growth + Dividend Yield - (2)

The second term is Speculative Return, which is how much investors are willing to pay for each dollar of earnings. This is known as price-earning (P/E) multiple.

Speculative Return = Change in P/E - (3)

Fundamental return is almost predictable and a positive factor. Speculative return, on the other hand, reflected in the change of price-earning ratio (P/E), is unpredictable. Fundamental return does not change day to day, however speculative return can significantly influence day to day market noise.

Thus the Stock Total Market Return can be simply expressed as:

Investment Return = Earning Growth (ΔE) + Dividend Yield + Change in P/E (ΔP/E)

In general, a growth investor focuses on the first component, an income investor on the second, and a value investor on the third.

To validate the predictability of our Financial Physics model we will analyze the stock market performance for the past fifty years to see how well these three variables fit into the equation. It will also give us an indication about how much each of the three variables contributed to the total stock market return in the past. Given the mathematics of the market place, it would be extremely challenging to predict the future. We will however, attempt to isolate the variable that will have most influence in the future stock market return. Based on our Financial Physics model, we will try to predict the market performance for the next decade.

Stock Market Total Return:

Let’s analyze the annualized stock market total return in context of Fundamental Return (earning growth plus dividend yield) and Speculative Return (Change in the P/E multiples) for the last 50 years, 20 years, and 10 years respectively.

50 Years of Historical Return:

Since 1950 through 2004, S&P 500 overall produced 12% annualized return – see the table I below.

TABLE 1
Total Stock Market Annualized Return (50 Years)

Period	Earning Growth	Dividend Yield	Fundamental Return	Starting P/E	Ending P/E	Speculative Return	Total Return
1950-2004	6.0%	4.0%	10.0%	7.2	20.6	2.0%	12.0%

We can see that it has been mostly driven by growth in earnings which accounted for 50% of the total return. Next contributor was dividend yield – accounted for 24% of the total return. And the last but not the least, is the valuation change - accounting for 16% of the total return.

40 Years of Historical Return:

Now let’s analyze the total stock market returns for about the past 40 years –symmetrical 20 year spans of 1962 to 1981 and from 1982 to 2001 (see the table II below).

If we look at the last column of the table first, we can see that for the total period of 40 years, the rate of earnings growth plus the dividend yield came to a total of 11.2% per year, while the speculative return came to 0% per year, resulting in the actual total return of the stock market to be an identical 11.2%.

Table II
Total Stock Market Annualized Returns (40 Yrs & 20 Yrs)

	1962-1981	1982-2001	Total Period (40 Years)
Earnings Growth	7.0%	6.5%	6.75%
Dividend	5.1%	3.8%	4.45%
Fundamental Return	12.1%	10.3%	11.2%
Speculative Return	-4.6%	5.0%	0%
Total Market Return	7.5%	15.3%	11.2%

In this case of 40 years of history, the earnings growth accounted for 60% of the total return, while dividend yield accounted for 40% of the total return and there was no contribution from the valuation change accounting for 0% of the total return.

It appears that in the long run, earnings and dividends call the market’s tune. It seems market is very efficient in the long run. However over the short term – and even over some extended period – speculative return (change in the P/E multiple) can be the driving force.

20 Years of Historical Return:

If we look at the first column of the Table II, from 1962 to 1981, the P/E ratio of the S&P 500 Index changed from 22 to 8 – resulting in a speculative return of minus 4.6% annually. This cut the fundamental return of 12.1% to a market return of 7.5%.

In the second column, from 1982 to 2001 period, the P/E ratio changed from 8 to 22 – adding 5% per year in speculative return, raising the annual fundamental return of 10.3% to a market return of 15.3%

5- 15 Years of Historical Returns:

Table III shows the anatomy of total stock market return (composed of earning growth, dividend yield, and change in P/E multiples) over three different periods since 1950.

TABLE III
Total Stock Market Annualized Return

Period	Earning Growth	Dividend Yield	Fundamental Return	Starting P/E	Ending P/E	Speculative Return	Total Return
1950-1965	5.2%	4.8%	10.0%	7.2	17.8	6.1%	16.1%
1966-1981	7.0%	4.1%	11.1%	17.8	8.0	-5.2%	5.9%
1982-2000	6.4%	3.5%	9.9%	8.0	26.4	6.9%	16.8%
2001-2004	3.8%	1.8%	5.6%	26.4	20.6	-6.9%	-1.3%

As we have noticed before, stock returns tend to reflect growth of earnings and dividend yield, but there are often extended cycles where P/E multiple change can significantly enhance or undermine return. This table show annualized return of the S&P 500 comprised of these three variables.

From 1950 to 1965, for example, corporate earnings grew at a 5.2% annual rate, and dividend yield contributed 4.8%; combined these two produced a Fundamental return of 10%. However, during this period, price-earnings multiples expanded significantly from 7.2 at the start of the period to 17.8 at the end resulting in the speculative return of 6.1%. If we combine these two returns, we see stock market annualized return of 16.1%.

In contrast to this, if we look at the period of from 1966 to 1981, earning grew at a favorable 7.0% rate and dividend yield contributed 4.1%, while price-earnings multiple declined from 17.8 to 8.0 which reduced the average gain by 5.2%, resulting the stock market total return of 5.9%. So from 1966-1981, earnings outpaced equity price because of the collapse in P/E over the period, undermining stock returns.

As we can see from the figure below, stock market significantly lagged earnings because of price-earnings multiple contraction.

Figure I
Yearly Stock Market Returns from 1965-1981

From 1982 to 2000, earnings grew at 6.4%, dividend yield contributed at a 3.5% rate, while P/E multiples surged from 8.0 to 26.4, contributing 6.9% rate. The SP 500’s annualized return for this period was 16.8%. Thus in the great bull market from 1982-2000, stock price grew much faster than earnings, as the P/E multiple on the S&P more than tripled, accounting for 41% of the market total return over that period.

Figure II
Yearly Stock Market Returns from 1981 – 2000

What we have learned from Financial Physics Model?

Financial Physics Model consisting of primarily two variables; Fundamental Return and Speculative return, fairly well explains stock market total returns over both long and short term periods. Since the model is fundamentally based rather than statistically based, this should reasonably assess its validity and accuracy.

We can also see that over the 50 years, 40 years, 20 years or 5 years – fundamental returns have always had a positive contribution to the total return. On the other hand, Speculative returns, were always unpredictable, with both positive and negative contributions.

The historical average rate of fundamental returns seems to be clustering around 10% per year. This reflects earning growth on average of 6% to 7% per year. Add to this, 4% to 3% dividend yield, and one ends up with about 10% fundamental return per year. This is very predictable and consistence at least historically on a long term basis.

On the other hand, speculative return can be significantly influenced by the prevailing interest rates. Interest rates are primarily driven by inflation. Higher interest rates and higher inflation tends to depress P/E. One major reason for this is that more interest rate rise, the less future cash flows of a company worth in today’s dollar. The table below indicates the historical trends:

TABLE IV
Interest Rates and P/E Multiples

Period	10-Year Treasury at the Start	10-Year Treasury at the End	S&P 500 P/E at Start	S&P 500 P/E At End
1966-1981	4.47	14.09	17.8	8.0
1982-2000	14.09	5.57	8.0	26.4

For example, the period 1966-1981, the ten year treasury yield rose from about 4.5% to 14.1%, and the price-earning multiple contracted 5.2% rate from 17.8 to 8.0. During the following period, the ten year treasury yield contracted from about 14% to 5%, resulting price-earning multiple expansion at an annual rate of 6.9% from 8.0 to 26.4.

By taking into account the absolute contribution to the total return by each of the two main variable; fundamental return and speculative return over different time periods, one can construct the following table and chart.

TABLE V
Contribution of Fundamental & Speculative Returns
To the Overall Market Return

	Fundamental Return	Speculative Return
40 Years 1962-2001	100%	0%
20 Years 1962-1981	72%	28%
20 Years 1982-2001	66%	33%
5 Years 2001-2004	44%	55%

We can see that over the long period, fundamental return contributed more to the total return than speculative return and they are very predictable. But as the time horizon of investment decreases, speculative returns begin to play a significant role in the determination of overall stock market returns and become a major contributor to the market noise.

In the long term, market looks as calm and beautiful as an ocean when watched from a distance, but it becomes more and more turbulent and chaotic as one approach closer and closer to the ocean!

Figure III
Contribution of Fundamental & Speculative Returns
To the Overall Market Return