Undoubtedly, this is the subject of the last three months: do we have a bubble in the stocks markets? The question is obviously not new and has been raised a million of times in the past without any consequences in terms of policy and futures cycles. However, the question is gaining more attention nowadays, and especially from monetary authorities. In the past, the corollary question that policy makers were interested in was: “Do we have to care?” And surprisingly enough, there was a consensus among economists and practitioners. Most research, including Ben Bernanke’s research ten years ago, showed that the Fed shouldn’t take asset prices into account when setting interest rates.  But, the tide may have turned. “This crisis has demonstrated that the cost of waiting to clean up asset bubbles after they burst can be very high” said recently William Dudley, ex-Goldman Sachs economist; new president of the New York Federal Reserve. Indeed, in the financial media and even at the Fed, everybody tends to agree that not deflating the housing bubble was a fundamental error of monetary policy.  As such, it’s not surprising that some prominent economists, including Nouriel Roubini asked the Fed to focus on “properly calculating asset prices and the risk of asset bubbles”. But, back to the original question: can we identify a bubble? Mr. Dudley claims that “Asset bubbles may not be that hard to identify—especially large ones”. “Not that hard”, lets’ clarify this.

As the Internet pioneer AOL (at one point Time Warner and AOL represented $350 billion, twice the value of Google, and is now known as one of the worst mergers of all time) begins a new chapter Thursday, I’ll focus on the dot-com bubble today. A follow-up post will be devoted to the current crisis.

When academics want to test for the existence of a bubble, they use as a reference model the so-called Discounted Cash Flow (DCF) approach. The DCF states that today’s price is equal to future discounted dividends plus a terminal value (where the discount is based on “an appropriate rate of return”).  Sophisticated professionals may recall that this is how John Hussman recently described the management of his funds (he used to be an academic professor).  As John explained in his Weekly Market Comment, an investment security is a claim to a long-term stream of cash flows. And, given this benchmark, a bubble is said to exist when the price of stocks changes at a rate that is not coupled with the growth rate of dividends.

Now, the difficult part, obviously, is to correctly forecast this “stream of future dividends”. But as we want to look back at the dot-com bubble, this is not really our problem since we do have the data (we’ll see below that this is not as insurmountable as one could imagine).

How do we know that the prices in the U.S. stock market were “well-coupled”? Well, we just need to graph the couple Price-Dividends and look for a change in the dynamics of these two variables. Let’s open our eyes on the period 1993-January 2004.

The first phase 1993-1997 (April) corresponds to a sustainable or constant increase in the S&P500 price. This constant coefficient linking dividends with the price index is dependent on both the dynamics of the dividends (or simply put the link between today and tomorrow’s dividend) and the discount rate (remember the one that should be appropriate).

On the other hand, from April 1997, one could observe the start of a decoupling phase where the price no longer grows in line with dividends (or if you want the regression line has changed). This is where the bubble component kicks in and increases the slope of the linear relation, before price started growing exponentially (in February 1998).

This graph enables us to separate out overvaluation from changes in fundamental values. Note that the bubble component is sometimes called “rational speculative” since the size of the bubble or the magnitude of the overvaluation may be dependent upon current dividends. The latter could then turn into something irrational, completely debased from the fundamentals (the exponential phase). One could notice that the relation only stabilizes mid 2003, which coincides to the beginning of the Fed 1% interest rate policy, before the markets starts a new stable dynamic (which we will study in an upcoming post).

Now, let’s do something more useful, that is do the same analysis in real time, by comparing past dividends with current price. Our analysis is similar to what Robert Shiller does when he computes the cyclically adjusted PE ratio by taking a 10 year average for earnings. In our case, we only consider 1 year as dividends are less cyclical.  One may criticize this approach for a valuation perspective, but in our case, we’re only interested in the change of dynamics, thus, we should be immune to this criticism.

Interestingly, the results are pretty similar to what we’ve observed before, with coupling and decoupling phases. The only difference is about timing, as the first decoupling phase seems to have occurred in October 1997 while the second and decisive decoupling phase occurred later in September 1998.  The results are not very surprising as this relation is based on a backward looking measure for dividends.

But, overall, the argument still remains: as early as the end of 1998 one could have spotted that stocks were starting to get overvalued, signaling the birth of a bubble. Now, had you tried to speculate against the market at that time, you may have lost your shirt (as the market reached its highest point in August 2000); remember what Keynes said, “The markets can remain irrational longer than you can solvent”. But, you could have reduced your market risk exposure…