Valuing the S&P 500

Brian Sturgess - June 2013


Speed Read
  • Three models used to measure the relative valuation of US equities all suggest the S&P 500 is moderately overvalued.
  • An alternative method, adjusting the S&P 500 to account for inflation also suggests that the real value of the market is moderately overvalued.
  • The deflated S&P 500’s average value has been close to the trend rate of growth in real GDP growth with periods of underperformance from 1974 to 1994 and outperformance from 1995 to date.

The relative value of the S&P 500
Three approaches are used to assess the value of the equity market as a whole relative to other assets. These models can be categorised as follows: Shiller’s Cyclically Adjusted Price-Earnings model (CAPE), Tobin’s Q (QR) and the Equitisation Ratio (ER). All of them measure the percentage under or overvaluation of the S&P 500 market index in relation to the ratio of the current value to the long-run average of the relevant variables. None of these methods seek to advise investors on precise market timing, but only on the relative long-term value of equities. Two of the methods – QR and ER are assessed on a quarterly basis given the frequency of required data releases while CAPE can be calculated every month. All three methods are suggesting that the US equity market has entered an overvaluation phase since 2009. The longer term picture of the percentage valuation of the S&P in relation to long-run averages of CAPE, QR and ER are shown from 1952 to the end of 2012 in Chart 1 and from the start of 1998 to the end of 2012 in Chart 2. Details of these models are contained in a paper by Sturgess (2012) which is available at World Economics








Deflating the S&P 500
Another means of assessing the current relative value of the United States equities market can be made by adjusting for the effects of price inflation over time. Chart 3 compares the value of the nominal S&P 500 Index from 1970 to date against the same data in constant prices using the GDP deflator to estimate the real value of equities. The GDP deflator is employed to do this instead of the usually quoted Consumer Price Index (CPI) because the former index measures inflation in the prices of all goods and services, including capital goods and goods for export, produced domestically by the private and the public sectors. In contrast the CPI measures changes in the cost of purchasing a fixed basket of consumer goods including those domestically produced and imported. Given the broad range of sectors represented in the S&P Index the GDP deflator is preferred as a means of deflating the nominal values of equities. It has also been used by Sturgess (2013) to estimate real government long bond yields.




Taking price inflation into account subdues the rise in the value of the S&P 500 from 1970, but some historical market land marks are still visible. The impact of the overpricing of equities during the period of the so-called ‘dotcom’ bubble which peaked in 2000 is still pronounced in the constant price data series as is the subsequent severe market correction following the financial crisis of 2007-08. However, the S&P in May 2013 was still only 82% of its real value thirteen years ago and 5% below its peak value before the financial crisis. However, comparing the real value of the S&P 500 against real GDP growth over time discussed below also suggests, in basic agreement with the CAPE, QR and ER models, that the US equity market is overvalued.


The S&P and Real GDP Growth 
The long-run behaviour of the real value of equities should be broadly in line with the growth in real GDP. In terms of cumulative growth rates the annual compound rate of growth of real GDP from 1970 to 2013 was estimated at 2.8%, while the real growth in the value of S&P 500 was slightly higher at 3.2%. Chart 4 plots trends in the deflated S&P 500 series and in real GDP over this period and it suggests that the market is currently around 20% overvalued. Chart 4 also shows that the average long-term relationship is balanced by two significant periods when the real S&P 500’s performance deviated significantly from the trend in GDP growth. There was a long period of consistent equity market underperformance from 1974 to 1994 and then a volatile period of outperformance from 1995 to date punctuated by the sharp fall in the market after 2007 occasioned by the financial crisis. 





References
Sturgess, B.T. (2012), When to buy and when to sell equities, World Economics Journal, Volume 13 (3), July-September, pp27-46, http://www.world-economics-journal.com/Contents/ArticleOverview.aspx?ID=525

Sturgess, B.T. (2013) Bond yield comparisons are seriously distorted by using consumer price index deflators, World Economics, February: http://www.worldeconomics.com/Papers/Bond%20yield%20comparisons%20are
%20seriously%20distorted%20by%20using%20consumer%20price%20index%20deflators_0421e952-4e4b-4415-b8a7-1331abc84697.paper






Notes
[1] The long-run average values used were 0.76 for QR, 0.69 for ER and 0.19 for CAPE.
Specifically from 1 January 1970 to 5 May 2013 using Professor Robert Shiller’s database at www.econ.yale.edu/~shiller/data/ie_data.xls‎ and rebasing the index to January =100

[2] The historical GDP deflator data and estimates for 2012 and 2013 were obtained from the IMF at http://www.econstats.com/weo/V005.htm.

 [3] The GDP deflator is receiving official support from regulatory bodies for comparing investment returns. In March, 2012 a report by PricewaterhouseCoopers to the UK’s Financial Services Authority recommended using the GDP deflator instead of the Retail Price Index for projected rates of return on a variety of asset classes. See: http://www.fsa.gov.uk/static/pubs/other/projection-rates12.pdf