After the stock market nearly doubled following  Federal Reserve Chairman Alan Greenspan's talked about "irrational exuberance" about four years ago, he avoided making any more comments about stock values (aside from skittishness) when he presented his comments to Congress this past week. 

However, the Federal Reserve uses a simple rule of thumb for evaluating stock values that has become known as the Fed Model.  One of the open secrets is that the model currently indicates that stocks are significantly undervalued.

This model is not designed to forecast future stock market values.  All it does is determine whether prevailing conditions justify higher or lower stock values than currently persist.  Furthermore, the model is simple. 

Look at the yield on a representative government bond.  Then invert the current stock price relative to next year's projected earnings.  If the .04 current yield on the five year bond is larger than forecasted earnings divided by current price, then stocks are over-valued.  If it is less, then stocks are cheap. 

After the recent seven day sell off that drove stock prices down by more than 10 percent, stocks have become cheap according to this model.  However, stocks have remained expensive or cheap for long periods of time.  At the height of the technology bubble, the model suggested that stock values were almost 50 percent too high.  Now they may be as much as 15 percent too low. 

There are several problems with such simplicity.  First, what is the correct bond yield to compare to earnings yields.  Second, how much risk premium should be received by stock holders to compensate for the large fluctuations that their holdings suffer.  Third, how forward should stock investors look to determine the relevant earnings.  

Unfortunately, we now have a fourth issue.  What is the quality of the earnings?  Are they created from book keeping, inflation, asset sales, or actual production. 

One reason why I like the Fed Stock Valuation Model is that it reflects what I have been using in the past two decades. 

I believe historical ratios of earnings to prices is only useful to the extent that bond yields are consistent with historical norms.  Most casual stock market analysts know that prices average about 16 times earnings over time.  Today, stock prices are nearly 20 times earnings. 

What they fail to realize is that the ten year government bond over the same history that created the 16 price earnings average reflected an average yield of almost 7 percent.  With those ten year bonds currently yielding 4.7 percent, price earnings ratios should be substantially higher to reflect the same current value of future earnings. 

I always use yields on long term bonds in my analysis.  Since the quantity of 30 year government bonds will be restricted over time according to current Treasury policy, the freer floating 10 year bond has become my long term benchmark.  In contrast, the Fed uses a bond of shorter maturity. 

I avoid the forecast problem by using trailing earnings in my analysis.  Of course, the stock market is forward looking (although one wonders how forward when a single quarter's performance significantly alters the market value of an enterprise).  Currently, stocks are selling about 23 times trailing performance. 

However, an economic recovery has barely begun.  From about 6 months into that expansion until about 24 months of expansion, profits grow by a multiple of GDP.  Over time, they converge on the growth of GDP.  As mentioned many times in this column, one of the long term constants in economics is the share of income going to owners of capital versus providers of labor. 

Thus, earnings will do very well in the next two years and then slow substantially.  (That slowing was delayed for more than five years in the 1990s, but that may have been the result of special conditions). 

This means that stock values probably should have a higher multiple relative to trailing earnings until normal income shares are restored.  Instead, my model shows that stocks are unusually low relative to trailing earnings in the prevailing interest rate environment. 

Moreover, I use operating earnings from the national income accounts.  This already removes asset sales and inflationary effects from the numbers.  While cheating might be reflected in these numbers, the companies would not only be committing fraud but also tax evasion.  While a number of companies have misinformed their investors, they might not have misinformed the tax collector. 

Indeed, a comparison of tax based estimates with the investor reported profits suggests that misstated profits are not as widespread as most investors currently believe (although most of the information is not yet available to draw that conclusion).

Anyway, my model currently believes stock values are understated relative to current earnings by about 12 percent.  If earnings rise significantly, as most economists expect, we might be undervaluing American enterprises by more than 25 percent by the end of next year if stock values do not rise.  If Greenspan had mentioned that the Fed's  stock valuation model reached similar conclusions, as it apparently does, one wonders how large a stock market rally could have occurred this past week.