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We've been pointing out for a while that, based on a cyclically adjusted P/E ratio, the stock market is significantly overvalued -- say, 20% or so.

To arrive at this view, we use a "fair value" estimate for the S&P 500 of about 900, which is close to the one used by fund manager Jeremy Grantham, fund manager John Hussman, and others. This compares to the S&P's current level of about 1100.

But now Andrew Smithers, an excellent economist based in London, is telling us that we're way too optimistic, that fair value for the S&P 500 is actually in the 700-750 range. Smithers, therefore, thinks the stock market is about 50% overvalued.

Smithers constructs his estimate in two ways: 1) the same cyclically adjusted P/E ratio that we use, and 2) something called "Tobin's Q," which is a measure of replacement value. Like Yale professor Robert Shiller, Smithers charts these valuation measures for the last century, which provides some context for where we are today:

click to enlarge

Smithers CAPE and Q

The big story: Over the long haul, valuations revert to the mean.

Image: Smithers & Co.

Now, as always, the big caveat here is that valuation doesn't tell you much about what stocks are going to do over the near-to-intermediate term (1-3 years). To paraphrase Keynes, overvalued markets can keep on getting more overvalued for longer than you can stay solvent (and sane).

But valuation does give you a pretty good sense of what future long-term returns are likely to be (7-10 years). And all of these valuation analyses still suggest that long-term stock market returns are likely to be pretty crappy.

For a similar look at the market's valuation over time, here's Robert Shiller's chart, which charts the cyclically adjusted P/E ratio. Smithers' chart above plots the valuation measures against their own average. Shiller's chart below plots them against their absolute levels (ie. today's P/E is in the 20X range):

Shiller PE

Blue line = cyclically adjusted P/E; Red line = interest rates

Image: Professor Robert Shiller, Yale University

Lastly, here's Smithers' explanation for his valuation chart. It's complicated, but basically the idea is that near-term earnings are way too volatile to provide a meaningful read on the market's valuation at any given moment. Thus, to get a meaningful sense of valuation, you need to look at a fundamental measure that is more stable than quarterly earnings. The cyclically adjusted P/E, which averages 10 years of earnings, and Tobin's Q, which looks at assets, provide this. And as you can see in the chart, over the long haul, the market does tend to revert to the means.

Here's Smithers:

US CAPE and q chart

US q

With the publication of the Flow of Funds data up to 31st March 2010 (on 10th June 2010), we have updated our calculations for q and CAPE, which show very little change from our previous calculations.

Non-financial companies, including both quoted and unquoted, were 62% overvalued according to q at 31st March 2010, when the S&P 500 index was 1169. Adjusting for the subsequent decline to 1087 (10th June, 2010), the overvaluation had fallen to 50%. Revisions to data had little impact on q, with downward revision to net worth for Q4 2009 of 2.9% being offset by a downward revision to the market value of non-financial equities of 2.1%. Net worth for Q1 2010 fell slightly as equity buy-backs exceeded profit retentions.

The listed companies in the S&P 500 index, which include financials, were 58% overvalued at 31st March 2010, according to our calculations for CAPE, based on the data from Professor Robert Shiller’s website. Adjusting for the subsequent decline to 1087 (10th June, 2010), the overvaluation had fallen 46%. (It should be noted that we use geometric rather than arithmetic means in our calculations.)

Data for our calculations of q are taken for 1900 to 1952 from Measures of Stock Market Value and Returns for the Non-financial Corporate Sector 1900 - 2002 by Stephen Wright, published in the Review of Income and Wealth (2004) and for 1952 to 2009 from the Flow of Funds Accounts for the United States (“Z1”) published by the Federal Reserve. Data for our calculations of CAPE are taken from the data published on Robert Shiller’s website.

As net worth and cyclically adjusted earnings per share change little during a quarter, only changes in share prices are important for changes in the market value between our quarterly updates. The value of the market can thus be readily adjusted by viewers to this website. As the S&P 500 index changes, viewers can simply insert the new value and calculate the q and CAPE values, i.e:

With the S&P 500 at 1169 as at 31st March 2010, q was 1.6166 and CAPE was 1.5761.

To update as at 10th June 2010, when the S&P 500 was 1087, for q take 1.61 × 1087 ÷ 1169 = 1.50 and for CAPE take 1.58 × 1087 ÷ 1169 = 1.46.

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Source: Stocks Are 48% Overvalued - Andrew Smithers