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Using Interest Rates to Estimate Market P/E

Reading various forecasts for the stock market, I often come across a fair market value for the S&P 500 based on the average P/E ratio over a given period of time. This average P/E, usually between 15 and 16, is then used to determine the  current fair value, or the value the market will likely return to in the "near future". However, using this strategy often leads to investors missing out on major market movements while waiting for the market to return to some chosen market average.

I believe there is an alternative method that may provide a better indicator as to whether the stock market is under or over-valued. Interest rates, particularly those available from relatively risk-free government securities, play a significant role in the valuing of investment assets such as stocks.

A book published in 2006 by Aswath Damodaran includes a regression analysis from 1960 to 2005 showing a strong positive relationship between short and long term government securities and the inverse of the P/E ratio, or earnings yield. Using this regression line, it is possible to come up with an estimated trailing 12-month P/E ratio at any given period of time. Looking back over the past 20 years, and using operating earnings for the S&P 500, I calculated the predicted P/E ratio (based on short and long term government rates at the time) against the prevailing P/E ratio at the end of each quarter. 

From 1989 through mid-2002, the prevailing P/E ratio at the end of each quarter was consistently higher than the P/E ratio predicted by rates on government securities (the regression line). I attributed this difference to strong long term earnings growth expectations and relatively little market uncertainty. After mid-2002 however, the situation reversed, and the prevailing P/E ratio of the S&P 500 was consistently lower then the P/E ratio indicated by rates on government securities, which I attributed to increased market uncertainty and lower long term growth prospects. Using these data points, one could see the two periods when market conditions were at their extremes: the fourth quarter of 1999, when the difference was a record negative 13.1 percentage points and the market was near its stop, and the fourth quarter of 2009, when the difference was a record positive 14.5 percentage points and the market was close to its bottom.

Using this method to determine where the markets should be now, I use projected 2010 S&P operating earnings of about $69 (assuming 23% growth in 2010), and a P/E ratio, derived from this regression line, of approximately 19. Actually, the regression line results in a P/E of 25, which I reduce by 6 percentage points due to current market uncertainty and modestly restrained growth prospects. With this, I get to a market price of 1311, which I discount back one year by 12% for a current market value on the S&P of about 1154.

Disclosure: SSO, a leveraged ETF that is long the S&P 500