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# Shillers PE10 and the PE (inverse of yield) of 10 year bonds

Í have been prompted to post this by John Lounsbury who has also been pondering recently this relationship between long term interest rates and stock prices. The graphs below clearly show the relative relationship between and changing preferences for bonds and stocks.

Background of charts

Shiller kindly shares his Irrational Exuberance spreadsheet from his website:
www.irrationalexuberance.com/

This post is based on the spreadsheet:
www.econ.yale.edu/~shiller/data/ie_data.xls

I derived the following charts from that spreadsheet by calculating a PEBond for the 10 year interest rates by calculating the inverse of the rate on the spreadsheet. I plugged numbers for the 3 months of 2010 where there are data that are not yet in the spreadsheet. I divided the PE10 (NYSEARCA:CAPE) by the calculated PEBonds for each month. I then graphed the data as a whole and then based on eyeballing it divided the whole series into 3 periods. PreWW1, 1917 to 1959 (by which time the Great Depression, 2 WW's, Korean war were finished and the cold war was well established) and from 1960 to 2010.3. I have added 10 period sma and polynomial curves (3 or 4 as indicated) using Excel.

A higher number above 1 reflects a greater preference for 10 year bonds, a lower number below 1 reflects a greater preference for stocks based on their relative prices. On that basis an investor would sell a high downturn and buy a low upturn.

This relationship reflects changing fear and optimism and only reverts to the mean on an infrequent and seemingly unpredictable basis.

Different Average Values for Different Periods

The average values for various periods are:
Average overall        0.75
(bonds generally preferred - reflects long periods of high
uncertainty and preference for bonds during the periods
after the great depression and around the two World Wars)
Average to 1917    0.58
(bonds heavily preferred most of the time)
Average 1918 to 1959        0.40
(on average bonds heavily preferred, but great volatility)
Ave 1960 to now        1.18
(stocks heavily preferred generally and increasingly so
from 1975 to 2000)
Average 1974 to 1988        1.13
(10 year rates above 9% - stocks generally preferred)

I believe the modern period is most relevant so will show it first, then the whole series, then the other two periods.

The Charts

A. The Modern Relationship

Ave 1960 to now        1.18
Average 1974 to 1988        1.13
(10 year rates above 9%)

It might be reasonable to expect that in view of the 2000/01 and 2008/09 crashes that the overall level of optimism may take some time to recover and that the trend might be something like 78 to 91, but stock prices will also be influenced by inflation/deflation, the level of bond prices, earnings levels/expectations, population growth and the overhang of unemployment and housing inventory. (My next post will be on the relationship between Shiller's monthly earnings and 10 year average earnings which is more directly useful for stock market analysis.)

B. The Whole Shiller Time Frame

The relative manias for stocks in 1930, 1968, 2000 and 2007 and to a lesser extent 1987 and 1989/90, are quite clear.

Average        0.75
Average to 1917    0.58
Average 1918 to 1959        0.40
Ave 1960 to now        1.18
Average 1974 to 1988        1.13 (10 year rates above 9%)

C. Pre 1917 and WW1

Average 1881 to 1917    0.58 (bonds heavily preferred most of the time)

D. 1918 to 1959  - The Volatile Period of Dramatic External Influence

Average 1918 to 1959        0.40

Shows the extreme preference for stocks in 1930 and for bonds  during the first and second world wars and how the transition to a preference for stocks progressed as the memory of WW2 reduced and people looked forward with optimism.

Conclusion
A graph of the relationship between 10 year interest rates and the PE and PE10 of the stockmarket is relevant to understanding stock market super cycles, as is the graph of the Shiller PE10. In the absence of events like the great depression and world wars in modern times there is a general preference for stocks over bonds, probably in recognition of the impact of even low general levels of inflation on bond prinicpals after 10 years and the expectations of real capital growth from stocks which has been realised until 2000 at least, partly assisted by household debt increases which leveraged GDP growth until recently. (See the work of Steve Keen for more on the relationship between increasing debt and GDP in both the US and Australia:
www.debtdeflation.com/blogs/

Acknowledgements:
Doug Short for his excellent historical record of US stock market and for introducing me to the work of Mebane Faber and QVM group on trend timing:
dshort.com
Mark Lundeen for his work on US stockmarkets and bear markets in particular:
www.gold-eagle.com/research/lundeenndx.html
Robert Shiller for his historical analysis and making his basic data available:
www.irrationalexuberance.com/
Steve Keen for his work on debt, GDP and economic crises:
www.debtdeflation.com/blogs/
John Lounsbury for encouraging this post
All the other excellent financial bloggers whose work I have drawn on and particularly those who post on SA.

Disclosure: Market Outlook, Bonds, Earnings