Financial Physics

Financial Physics Model
Unified Theory of the Stock Market

The behavior of the 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. In this chapter we will build a total stock market return model based on two variables – one reflecting the fundamental valuation (Fundamental Model) and the other reflecting the behavior of investors (Emotional Model).

This is an attempt to unify two ideas – one is investment return based on true fundamentals of economics and the other is emotional return based on the emotions of investing. Corporate earnings and dividends have provided a steady underlying stock market return over the long term. These fundamentals of economics are the result of growth, productivity, and prosperity in our resilient American economy. Whereas emotional returns on stocks represent the impact of changing public opinion about stock valuations – it changes from month to month and daily from optimism to pessimism.

We will show that the stock market return is determined by the interaction of just two parameters; investments return represented by the earnings growth and dividend yields of our corporation (Fundamental Return) and Emotional return (Emotional Return) represented by the price that investors are willing to pay for each dollar of earnings.

Our belief is that we are at a crossroads of Finance and Physics. We call it Financial Physics. Financial Physics represents a framework of a few key variables and their impact on the stock market’s overall direction. It is not a magician’s illusion – it’s a Fundamental Physics!

Conventional wisdom often ignores the fundamental factors that drive the market. In this model, we will attempt to analyze the market based on simply three variables:

  • earning growth
  • dividend yield
  • change in the price-earnings (P/E) ratio

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

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

Investment Return = Fundamental Return + Emotional 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 Emotional Return, which is how much investors are willing to pay for each dollar of earnings. This is known as price-earning (P/E) multiple. Emotional return is driven by price to earnings expansion or contraction.

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

Fundamental return is almost predictable and a positive factor. Emotional 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 emotional 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)

Figure I

Stock Market Total Return

In general, a growth investor focuses on the first component (Earnings Growth, an income investor on the second component (Dividend Yield), and a value investor on the third component (Low P/E).

To validate the predictability of our Financial Physics model we will analyze the stock market performance for the past one hundred 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 in chapter III.

Stock Market Total Return:

Let’s analyze the annualized stock market total return in context of Fundamental Return (earning growth plus dividend yield) and Emotional Return (Change in the P/E multiples) for the last 100 years, 40 years, 20 years, 10 years and 5 years.

100 Years of Historical Return:

figure II

Investment return

For the last century the average annual stock return was 9.6%. This return was virtually identical to the fundamental return of 9.5% - consisting of 5% from earnings growth and 4.5% from dividend yield. That tiny difference of 0.1% arose from behavioral return. Depending on how one looks at it, emotional return contribution was merely statistical noise. In the long run, reality rules.

50 Years of Historical Return:

Since 1950 through 2004, S&P 500 overall produced 12% annualized return – see the table 1 below.

TABLE 1
Total Stock Market Annualized Return (50 Years)

Period
Earning
Growth
Dividend
Yield
Fundamental
Return
Starting
P/E
Ending
P/E
Emotional
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 Emotional return came to 0% per year, resulting in the actual total return of the stock market to be an identical 11.2%.

Table 2
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%
Emotional 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 – emotional 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 2, from 1962 to 1981, the P/E ratio of the S&P 500 Index changed from 22 to 8 – resulting in a emotional 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 emotional return, raising the annual fundamental return of 10.3% to a market return of 15.3%

5- 15 Years of Historical Returns:

Table 3 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.

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.

TABLE 3
Total Stock Market Annualized Return

Period 
Earning
Growth
Dividend
Yield
Fundamental
Return
Starting
P/E
Ending
P/E
Emotional
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%

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 Emotional 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, during this period from 1965 to 1981, stock market significantly lagged earnings because of price-earnings multiple contraction.

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.

Yearly Stock Market Returns from 1981 – 2000

Interest Rates and P/E Multiples

Emotional 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 the more interest rates rise, the less future cash flows of a company are worth in today's dollar.

Table 4 indicates historical trends:

TABLE 4
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.

We have seen that in the long run, fundamental returns, the earnings and dividend generated by American business, are almost entirely responsible for the total return delivered in our stock market.

However, over short periods such as a year or even several years, emotional return based on the change in P/E multiple can be significantly influenced by the prevailing interest rates.

What we have learned from Financial Physics Model?

Financial Physics Model consisting of primarily two variables; Fundamental Return and Emotional 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 100 years, 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, Emotional 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.

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

TABLE 5
Contribution of Fundamental & Emotional Returns
To the Overall Market Return

 

Fundamental Return

Emotional 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 emotional return and they are very predictable. But as the time horizon of investment decreases, emotional returns begin to play a significant role in the determination of overall stock market returns and become a major contributor to the market noise.

My advise to investors is to ignore short-term noise of the emotional reflected in our financial markets and focus on the productive long-term economics of our corporate business.

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!