Like many investors right now, I’m spending a lot of time trying to figure out whether the stock market has actually hit a stable ‘bottom’ or whether it still has further to fall. My dad and I had a long discussion last night about different methodologies for calculating what equity prices *should* be based on historical market behavior and the dynamics of the current situation. The two main factors that have driven the slide from the heights of October 2007 (DJIA @ 14,279.96 and S&P 500 @ 1,576.09) are the sudden de-leveraging of the financial markets (i.e. some major investors being forced to liquidate >75% of their positions) and the macroeconomic effects of a recessionary cycle (i.e. higher unemployment, lower consumer spending, deflation).

While theoretically possible, I believe modeling the impact of these two factors is a practical impossibility because they are so intertwined — de-leveraging sparked the recession and the recession is driving further de-leveraging. You could also do a technical analysis where you try to match current market behavior to past patterns and extrapolate what happens next based on what happened before. But that method requires making a bet on which past patterns to match against, i.e. is our current situation more similar to the Great Depression or all the recessions since. And that’s a big bet.

So, I propose a different (and much simpler) approach: assume a realistically sustainable growth rate over a long enough period and figure out where we would be if the market had grown at that pace. I picked 20 years as the period and charted the monthly percent change of the Dow Jones Industrial Average (DJIA) from 2,342.32 at the end of January 1989 to 8,131.33 at Friday’s close. The actual percent change is the blue line, and I plotted 3 other lines against it: 10% annualized growth in green; 6% annualized growth in orange; and 2% annualized growth in red.

Here’s what that period looks like in annual percent change for the DJIA and S&P 500:

And here’s the annualized rate of return for both the S&P 500 and the DJIA since 1989:

Over the course of this 20 year period, there were only 6 years in which the market declined *at all* (one of which, 2005, was basically break-even) and there were 10 years in which the market gained *more than 10%* and in 7 of those it gained *more than 20%*. Even after the tech bubble “burst” taking the market from 11,497.12 at the end of 1999 to 8,341.63 at the end of 2002 (a 27.4% decline in 3 years), the market would still have delivered a *10.1%* annualized rate of return over the prior 12 years. From where we sit today, it’s no wonder the DJIA declined 33.85% in 2008 (taking us to a still very respectable annualized rate of return since 1989 of 7.24%). But that doesn’t answer the question of how much further down it needs to go before we can consider the value of the equity markets stable.

That’s where the annual growth rate analysis comes in. It is still highly subjective — depending on what one believes to be a representative sample period and sustainable annualized growth over that period. But I like it because it helps me think about the broader market in terms I feel more comfortable making assumptions about, like what do I think is a reasonable rate of value creation for the economy as a whole over a given period. In the case of the 20 years since 1989, do I believe there’s a reason that the equity markets should have averaged ~10% annual growth while our Real GNP achieved only 2.76% annual growth over the same period? No, and obviously neither does the market at this point.

So, what is a reasonable expectation for a bottom? Your guess on the underlying assumptions is as good as mine. But if one believes technical advancements over the last 20 year period enabled us to double efficiency (i.e. extract twice as much profit from the same revenues), then the markets *should* have grown at around twice the rate of Real GNP. In that case, we would be expecting 5.51% annualized growth in the markets since 1989 as of the end of 2008. Starting from 1989 closing prices of 2,753 on the DJIA and 353.4 on the S&P 500, 19 years of organic equity growth pegged at 2x GNP growth should have closed 2008 at 7,634.38 and 979.95, respectively (actuals were 8,766.39 and 903.25).

**Update:** Dad accurately points out that GNP is a trailing indicator and equity prices are leading indicators. So, this analysis shouldn’t be considered anything other than directional. I find it helpful as one factor in my overall assessment of the current situation, but as Howard reminds us no one really has all the answers.

This final chart shows the actual level of the DJIA (blue) compared to what it would be if it was pegged at 1x GNP Growth (red), 2x GNP Growth (orange), and 3x GNP Growth (green). It is essentially the same as the chart at the top but now instead of arbitrarily picking annual growth rates, we have pegged them as multiples of Real GNP (i.e. ratios of business efficiency). As you can see, for most of the last 20 years the markets were assuming >300% improvements in business efficiency.

All the above charts and underlying analysis can be found in this spreadsheet.