Monday, January 23, 2012

GDP Growth vs All Ords Growth

Updated 25, 26 January and 8 and 16 Feb, 2012
(8 Feb update looked at 1974 to 87 period of exceptional performance and added scattergrams of  changes in All Ords vschanges in GDP and changes in All Ords vs changes in 10 Year Bond Yields )
(16 Feb update just above the Scattergrams section, including the last table re All Ords and GDP (indexed from 1998) and the following paragraphs) 

Originally posted 22 January, 2012.

This is a post I am continuing to develop and which examines 3 primary questions.

1. What is the relationship between stock market growth and GDP growth?

2. Does the stock market growth have a high correlation with GDP growth?

3. Do changes in the relationship between GDP and the stock market allow timing of the market, at least in bubble recognition?

From looking at the data there is nothing obvious about a correlated pattern of timing on a quarterly basis of growth in GDP and growth in the stock market. (Click graphs for larger images.)

Seeing the lack of correlation on a quarter by quarter basis in the graph made me decide to check the degree of correlation over periods of different numbers of quarters using statistical methods.  The table below is the result of looking at all periods possible of the numbers of quarters shown over the period of  52 years from 1959 to 2011:

# of Qtrs 4 10 20 50 100
Ave RSQ 0.555 0.460 0.461 0.645 0.841
Median RSQ 0.638 0.468 0.450 0.754 0.888
Std Dev 0.348 0.326 0.320 0.278 0.124

The conclusion is that over short periods of say 1 to 5 years there is little correlation, and over long periods of say 30 to 50 years there is increasingly strong correlation.

That wasn't what I expected, so I continued to test different hypotheses with the data looking at relationships. It made me think of a post I had read about someone who modeled complex systems and who then looked at the relationship between stock market and GDP but more from looking at average relationships between the two.

 That lead me to ask myself, "What should the relative growth of equity be compared to the growth in GDP to provide an incentive for capital and business formation?"

My first guess, perhaps based on my unremembered modeller friend's work, was that equity should grow at a, say, 50% higher rate than GDP because this would provide people and businesses with a reward sufficiently greater than the mere passive growth in GDP so that there was a real incentive to take risk and borrow funds to form and grow businesses. So I modeled that using GDP data from the RBA statistical tables. It didn't make much sense as there seemed to be a dramatic change between 1983 and 1987.

In this first chart below I have multiplied All Ords growth each quarter by 0.6667 (same as dividing by 1.5) and subtracted GDP growth for that quarter. Clearly in the period to 1978 or so the All Ord quarterly growth didn't get  near 1.5 times GDP growth, while say 1978 to 1987 had a much higher ratio and from 1988 to end 2011 the All Ords grew at a bit better than 1.5 times GDP growth (based on eyeballing the slope of the trends during those periods.

I played with the ratio to get the long term growth of each of the All Ords and GDP equal from 1959 to 9/2012. That showed a lower than average proportion of equity growth to GDP growth to the mid 70's, a very much higher than average ratio from 1974 to 1987, relative stability from 1988 to 2001, an increasing ratio from 2002 to 2007 and a falling average ratio from 2007 to end 2011. The graph below illustrates these changes.

I did notice though that the peaks and troughs in stock market performance were fairly obvious. (I note that:
1. the period of change corresponds with the period during which inflation was defeated with interest rates lagging deflation down over time till inflation entered the 2 to 3% range now targeted
2. from my reading of Steve Keen's work that the period of 1986 to 2007 is the period of dramatic growth in household and total debt in Australia , both as percentages of GDP, and
3. that the period from about 1990 to 2007 saw the skewing of income shares in favour of the top 10% and even more so the top 1% on some countries)

In looking at using different ratios of equity growth to GDP growth I noticed that a ratio of 1 made sense of the period from 1959 to the late 70's.

I also worked out that a ratio of  almost 2 (1.96 to be precise) made sense from 1987 to 2011. Note the peaks of 87 and 2007 are aligned as are the bottoms of 1991 and 2009.

The ratio that made sense of the period from 1978 to 1987 was 6.6 times! This was a period of huge adjustment.

With a ratio of 1.5, equity holders increase their wealth exponentially unless gains and/or wealth (I need to give that more thought) are subject to progressive taxation. At a ratio of 1 I expect that equity holders get more wealthy far more slowly, unless there are taxation concessions for capital gains.

Notes on 68 to74 and 74 to 87
1974 was a very bad year for the stock market.

There are 3 major things to remember about 1973 and 1974:
1. The first oil shock occurred in 1973. Oil increased from about USD 15 to USD 100 per barrel in 2007 USD, a 600% rise.
2. From Feb 74 to Sept 74 the PE of the Australian All Ords fell from 10.7x to 5.4x
3. There was an inverted yield curve steepening for the same period. 90 day rates increased to 1.32 times 10 year government bond rates. (In March 2009 they were only 0.7 of the 10 year rate).
4. From 1960 to 74 the stockmarket grew at only the same rate as the GDP.

The period from September 1974 to September 1987 was the "golden years" of the Australian stock market.

1. This was in spite of oil prices continuing to rise significantly.
2. The yield curve became more normal with 90 day rates falling to 0.95 of 10year rates
3. The huge difference was that PE ratio.s rose from 5.4 times to 21.1 times. This dramatic re-rating would, all other things remaining equal, cause an increase from an opening indexed amount of 100 to 390.
4. In addition to the dramatic change in PE ratios, GDP grew by 48% over the same period, leveraging the impact of the rise in PE ratios.

1987 was then a very bad year for the market as it fell 50% in the matter of a few weeks. Looking back with hindsight we should not have been surprised as the exponential rise of the preceding few years was simply incredible and not sustainable. Depending on exact choices of starting and finishing months the All Ords has grown about 1.9 times as fast as GDP from 1987 to 2012.

In 2007 we had endured a sustained increase in crude oil prices back to over $100 in 2007 USD terms, similar to the 1973 first oil shock and the stock market crashed again.

In conclusion, the re-rating of PE's as governments proved to markets that they were going to return to a low inflation, low interest rate world was the major thing giving rise to the golden years of Australian stock markets, assisted by GDP growth.

Another approach

I thought I might look backwards and forwards using stable periods for indexing and trend determination. I chose December 1998 as the base date for indexing to make GDP equal to the All Ords on an indexed basis. I chose the date because it was where 10 year government bonds first approached 5.0%, a rate they have have been around from that date to date, although the average over the period is 5.59 and the yield was 3.67% at 31 Dec 2011.

I used Excel to calculate the growth rates of GDP and the All Ords from that Dec 98 to Sept 2011:

GDP All Ords
Start date Dec-1998 Dec-1998
Start value 230535 2813
10YGB 5.03% 5.03%
End Date Sep-2011 Sep-2011
Periods 51 51
Periods pa 4 4
End Value 335767 4070
10 Year bond 4.22% 4.22%
Rate pp 0.74% 0.73%
Rate pa nom 2.96% 2.91%
Relatiivity 1 0.982
Inverse 1.018 1

We have had a period of 51 quarters where GDP grew marginally faster than the All Ordinaries, which is very similar to the period of the 60's and early 70"s before there was dramatic growth as inflation and interest rates fell.

This can be shown graphically.

By looking at the All Ords against GDP we can again see how obvious the mini-bubbles of 1987 and 2007 were. When looking at the chart, remember that interest rates were in a very substantial long term down trend before 1998, so the real focus on this chart is post Dec 1998. The implication from looking at the chart is that while nothing is certain, and corrections can overshoot to the downside, at present levels, absent a recession the stockmarket could reasonably be expected to grow in capital value at the rate of GDP growth, say 3% plus give a running yield, which I understand is normally in the order of about 2% of GDP. We can also see that over the long term the average rate of growth in the stock market has been higher than the GDP growth rate. The fall in Bond Yields should also help drive up PE ratio of stocks.

The one thing that looks quite clear from the chart above is that the excessive prices (based on comparative GDP growth) of 2005-7 have been rectified by a combination of GDP growth and price stock falls. Stocks are now in a fair value range, subject to no major change to GDP growth and no major realignment of interest rates, or other major shock like a disorderly default of Greece.

As I write the recent rises in the All Ords have changed the growth rate over the period from Dec 1998 to 1.1 times the rate of growth of GDP (assuming trend growth of GDP from September), still well below the average since 1960.

The diagram below shows more clearly the relationship between GDP and the All Ordinaries since December 1998. 

It seems that bottom and top picking might also be assisted by looking at the relative growth of the All Ordinaries compared to GDP, but with an awareness that if there is a transition in rates of infaltion/deflation or interest rates needed to sustain target inflation, then there might be a realignment of PE ratios over a period of years if those new interest rates are sustained. This could be happening now in the US and non-PIIGS europe. By looking at the difference in the exchange rates in the text box, but not reflected in the chart above, we see that the relative profit for Australian investors has been  against USD investors. This is also true against GBP, EUR and many other currencies to greater and lesser degrees, making us ask the question "Is a good time to diversify internationally to Emerging Cream?" (see later article).

Scatter diagrams: GDP and 10 years bonds vs the All Ords

On a period by period basis there is relatively little relationship between the All Ords and either of GDP or 10 year bond rates.

I was expecting that the chart above would show a pattern that correlated falls in the 10 year bond rate with rises in the All Ords, and rises in the 10 year bond rate with falls in the All Ords. It is not the case within the single period of 1 quarter.

I was expecting that large falls in the All Ords would have been correlated with falls in GDP, but virtuall all quarters with lower GDP than last quarter showed a rise in the All Ords. There did not seem to be a likelhood of a greater correlation by adopting say a 1 quarter lag, at least from eyeballing the columns of data.

The change in the All Ords is not highly correlated with changes in either GDP or 10 year bond yields for any single quarter or for quarters generally..

Looking Forward

The question now is whether the ratio which equalises GDP growth rates and the All Ords growth rate has  changed or the All Ords growth is merely at a temporary low compared to the GDP growth.

If the last 4 years has seen a change, it is to a rate of 6.6 times again, but this time to reduce the relative size of losses in the stock market compared to growing GDP! (In the period 78 to 87 it was a measure of relative outperformance of the stock market compared to GDP, not underperformance as it is now.)

Alternate theses are that
1. GDP is set to fall significantly and the stock market has anticipated it, (given the obvious costs of austerity in unemployment and social upheaval I can't see this being a sustained outcome for a country with a fiat currency.)
2. the relative reward to equity vs labour will be reduced and profits and the stock market will fall accordingly or has already anticipated the fall in share of revenues going to equity, or that
3. the stock market, having shrunk compared to GDP since end 2007, will shortly resume its relationship of growing at almost twice the rate of GDP.
4. Some combination of the above.

It is highly unlikely that the Australian stock market will grow at less than the rate of GDP growth for more than 4 quarters (see discussion of correlation and R-squared near the top of the article and relative ratio of growth in 70's being 1), although Japan shows that is possible after a dramatic bubble even over 20 years previously in an economy facing demographic headwinds.

Note re mathematical analysis:
I expect I might need to examine the periods of 1959 to the late 70's completely separately to the period of 1987 to 2008 or 2012 so that the first period is not affecting the second. Intuitively I think that the trend from 1987 to 2012 being essentially horizontal on the graph is sufficient, but I need to prove this to myself with further work when the spirit moves me!

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