Old School Grahamian Formula Investing

Over the last few years, we've been testing some technical methods by which to time stock market cycles. Our ultimate objective has been to enter the market (i.e. Standard & Poor's 500) at near market peeks and to exit the market at near-market troughs, without staying too long out of the market or missing any major market moves. There are various techniques or "formula timing" indicators that we follow, but below we will discuss a long-forgotten formula timing strategy developed by Benjamin Graham and evaluate whether it can still be relied on and what signals it offers investors today.

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The formula

The Benjamin Graham formula timing method involves determining a "central value" for the market as well as an upper and lower valuation range based on historical interest rate and fundamental data.

• A central value, or fair value, of the S&P 500 can be estimated by capitalizing the average earnings per share over the previous k years by an "equilibrium" multiplier equal to 1 divided by n-times the yield on AAA-rated corporate bonds (in Graham's model k=10 and n=2).

• Growing positions in the S&P 500 is recommended when the index is less than 80% of the estimated central value and reducing positions is recommended when the index exceeds 120% of its central value.

A summary of the formula is provided below:

Central value = (k-Year AVG EPS) x (1/(2 x AAA-Corporate Bond Yield))

Results

Results of using the above formula are presented below for the 20-year period from 1995 to 2014, as shown in the figure. If the formula had been followed consistently since 1995, we would have been out of the market from 1995 all the way through to 2014 and wouldn't have seen one solid entry point.

Figure 1: Central Value and Valuation Range (Black) and S&P 500 (Red)

To us, this is clearly not a satisfactory result and highlights the deficiencies in using the parameter values of Graham's old formula (k=10 and n=2) in more rapid growth and modern-day interest rate environments.

To address this problem, we varied the parameters one by one using an optimization procedure to determine what values would produce a "best fitting" central value. Results are shown below. The optimization procedure called for parameter values of k=7 and n=0.8.

Figure 2: Calculation of central value

Figure 3: Central Value and Valuation Range (Black) and S&P 500 (Red)

The results presented above are more satisfactory - but still aren't phenomenal. On one hand, the formula appears to signal growing overaluation leading up to the bursting of the tech bubble in 2000-2001, which would have helped investors sell out before the market top; it does not unfortunately provide a clear buy signal near the market bottom of 2002. This type of failure in the model was actually flagged by Graham in the 1940s in which he stated that "...while it may be sufficiently dependable to be worth using for its overall results [over long periods of time], like all others of the kind, it is not fully dependable."

It happened that the model signaled fair valuation in 2005 and 2006 and signaled overvaluation in 2007. Had an investor been guided by the formula, he/she might have sold out in 2007 and avoided incurring massive losses in 2008.

Unlike after 2001, Graham's formula did provide a buy signal at the end of 2008 - a contrarian buy signal of course (very appropriate for Graham!). The formula signaled fair value in 2009 and 2010 and again called for puchases in 2011 and 2012. As of December 2014 the formula again signaled fair valuation, and at current rates and based on updated earnings, the market appears to remain fairly valued.

Conclusions

Considering all results presented above, Graham's formula appears somewhat outdated based on his suggested parameter values. Using our optimized parameter values, however, does enhance the formula a bit. Like any formula timing method, we would not rely on it exclusively, but we do think that it offers some insights that deserve continued observation moving forward.

This article first appeared on GuruFocus.

• Warren Buffett Recent Buys

• Warren Buffett's Current Portfolio

• This Powerful Chart Made Peter Lynch 29% A Year For 13 Years