Fluid Dynamics, Boundary Conditions... and Google

John P. Hussman, Ph.D.
All rights reserved and actively enforced.

"The eagerness for quick riches is hard to squelch. Indeed, after an investing bubble, an echo bubble - where investors rush in to buy all over again - isn't uncommon. In market experiments conducted by George Mason University professor Vernon Smith, who shared in the 2002 Nobel Prize for economics, participants trade a dividend paying 'stock' with a very clear fundamental value. A bubble invariably forms, and then bursts. If the experiment is repeated with the same people, a bubble forms again. The second time, though, participants think they will be able to sell their positions before trouble strikes. Participants express surprise that they weren't able to get out before the second collapse."
- Wall Street Journal, March 7, 2005

"The general features of this solution are characteristic of the response of a bubble... The growth is fairly smooth and the maximum size occurs after the minimum pressure. The collapse process is quite different. The bubble collapses catastrophically, and this is followed by successive rebounds and collapses."
- Christopher E. Brennen, Bubble Dynamics & Cavitation, Oxford University Press, 1995.

That second passage is from a text on fluid dynamics that I happened upon last week. There are thought-provoking parallels between bubbles in physics and bubbles in finance. Market historians have long observed that financial bubbles are rarely resolved in a single collapse followed by a return to all's-well-with-the-world. Rather, crashes are typically followed by one or more "echo bubbles." Evidently, the speculative dynamics of the pre-crash run-up are too much to be dissipated all at once.

For example, the 1929 crash must have been terrifying, but stock prices staged a strong and convincing recovery in the aftermath of the initial decline. Still, by 1932, stocks had sunk to such profound depths that an investor would have had wistful regret for not having sold at the 1929 post-crash low. The same is true for the Japanese stock market, which endured a secular bear market of more than a decade, with numerous rallies of 40% or more punctuating the long decline. Needless to say, with the S&P 500 again at 20 times record earnings, and other multiples (price/revenue, price/dividend, price/book, etc) even more elevated relative to historical norms, my guess is that the U.S. market is still very much trapped in an echo bubble.

That said, although valuations are unusually elevated, and prices are extremely overbought, we also observe fairly good market breadth, and benign interest rate pressures. A defensive position is appropriate here, but with no strong negative catalysts outside of oil prices, there's no clear evidence that should lead us to necessarily expect a deep and sustained decline in the near-term (not to say it can't happen). Suffice it to say that we're defensive mainly for investment reasons, not short-term speculative ones.

Boundary conditions

Brennen's analysis of bubbles also stuck with me because of the following passage:

"It should be understood that the accurate evaluation of the bubble requires the solution of the mass, momentum and energy equations for the bubble contents, combined with appropriate boundary conditions."

Appropriate boundary conditions. And there it is. The difference between reasoned analysis and thoughtless extrapolation.

Boundary conditions essentially say, even if this thing fluctuates over time, we have a good idea what would happen here, here and here. These conditions are enormously useful in "pinning down" a solution.

For instance, investors who trade on margin are often destroyed by the belief that they can't lose, provided that the long-term return on stocks is higher than the interest rate they pay. But this ignores a crucial boundary condition: if a decline wipes out your equity in the short-term, the long-term never arrives. Bankruptcy is known as an "absorbing boundary," because once you get there you don't leave. Ask the guys who ran Long-Term Capital Management, who for all of their sophistication, didn't really factor that bit in.

Another important boundary condition is known as a "limiting condition." This is a way of saying, look, this thing may fluctuate over time, but we have certain expectations for how the behavior looks in the limit . For example, as soon as we apply the limiting condition that a company cannot become more than 100% of the entire U.S. economy, we discover that we can't use a single, permanent growth rate to price a stock, unless that rate is less-than or equal-to the long-term growth rate of the economy. The boundary condition immediately informs us that the growth process is essential to getting the story right (see the June 13, 2005 comment for more on this).

Which brings us, again, to Google.

Don't get me wrong. I really like Google as a search engine, I think the company is run by very smart people, and I don't have any investment positions in or against the stock. It's just that Google is a fascinating little laboratory to learn things about valuation. I continue to believe the discounted stream of cash flows the company will actually deliver to investors owning the stock over the long-term (the thinking investor's definition of "value") is ultimately worth somewhere in the $30's, say less than $40 a share. Add to that the idle IPO proceeds invested in cash and marketable securities, and for practical purposes, it's sufficient to say the stock is probably worth less than its lowest post-IPO print, which was at $95.96.

Let's think carefully about Brennen's remark: accurate evaluation of the bubble requires the solution of equations for the bubble contents, combined with appropriate boundary conditions.

How do we do that for Google?

Well, we know, for example, that the price/revenue ratio of the stock market as a whole has historically averaged about 0.8, and is currently way high, at about 1.4. So we know the price/revenue ratio that a company would have if it did, in fact, grow to the size of the U.S. economy. More realistically, we know that the highest price/revenue ratio for any stock with revenues over $100 billion is currently 2.4, that stock being General Electric. We also know that the two highest price/revenue ratios, among all stocks with revenues over $20 billion, are 6.9 and 5.1, for Microsoft and Cisco Systems, respectively. (Google currently sports a price/revenue ratio of 20.5 on $3.8 billion of revenues.)

So now we've got some appropriate boundary conditions.

What about the bubble contents? For those, let's assume that Google is in fact, the next General Electric, Microsoft and Cisco Systems; that investors buying the stock here are, in fact, getting in on the ground floor.

What sort of return can those investors expect over the long-term?

Let's see. OK, we know that total global advertising - television, radio, magazines, newspapers, billboards, and so forth represents about $350 billion at present, and is projected to grow about as fast as the global economy in the future, about 6.5% annually, according to PriceWaterhouse Coopers.

Total internet advertising is currently about 6% of that total, but let's project that 15 years from now, the internet share booms to 20% of all global advertising. Let's also assume that Google gets 75% of it. That's right, baby. 75%.

That puts Google's revenues 15 years from now at $135 billion a year, which is close to those of GE. Let's also assume that stock market valuations remain at a permanently high plateau, and that Google gets awarded the same rich price/revenue ratio of 2.4 that the market awards to GE, which again, is the most generous price/revenue ratio awarded to any stock with revenues over $100 billion.

We now have everything we need to calculate the expected return to investors:

Price_future / Price_today = (Rev_future / Rev_today) x (P/Rev_future / P/Rev_today)

= ($135 billion / $3.8 billion) x (2.4 / 20.5) = 4.159

Which implies an annual return on Google of [ 4.159 ^ (1/15) - 1 = ] 9.97% annually.

Bummer.

What if Google is the "next" Microsoft and Cisco Systems? Well, MSFT has about $38.9 billion in revenues, and CSCO about $24.2 billion. So $31.6 billion on average, with an average price/revenue multiple of 6.0.

Let's assume that Google gets there in just 10 years. Do the math:

($31.6 /$3.8) x (6.0 / 20.5) = 2.434, which implies an annual return of 9.30% annually.

Suffice it to say that even taking as given that Google is, in fact, the next GE, Microsoft and Cisco Systems, investors buying the stock at its current price aren't in for big returns.

Since I'd value the stock far lower than the current price, it's obvious that the Street and I disagree fundamentally about the dynamics of Google's sustainable long-term growth, the durability of its competitive advantage, the extent to which revenues will translate to earnings, and the extent to which earnings will funnel down to deliverable cash flow to shareholders. It strikes me that Q1 2005 results aren't a very representative benchmark for these, which makes me wonder whether future earnings and free cash flow won't be a lot smaller than analysts expect, but hey, that's me. Everybody deserves to dream.

In any case, when enormously optimistic growth assumptions still imply pedestrian returns, thoughtful investors might want to stand clear.

Market Climate

As of last week, the Market Climate for stocks continued to reflect unusually unfavorable valuations and still unfavorable market action. That said, I added a modest contingent call option position to the Strategic Growth Fund on weakness early last week, which moved the Fund to a local sensitivity ("delta") to market fluctuations of about 20%. In other words, locally, I would expect the Fund to experience about 20% of the fluctuations of the major indices, with additional fluctuations to the extent that our stocks perform differently than the market. That's not a substantial exposure, of course, and not enough to create concern if the market reverses to the downside, but it's a reasonable response to the fact that market internals have been sort of OK (you can sense my enthusiasm).

Overall, our investment position is still best described as defensive, though not "bearish." I am not at all convinced that the market has much, if any, upside potential, but I do my best to avoid making forecasts about market direction. The fact is that while valuations are awful and the indices are strenuously overbought, the market's internal action is not bad, and that reality is enough to prevent us from carrying a completely defensive position. Again, most of our exposure to market fluctuations is from call options (now in-the-money), meaning that we have "local" exposure to market declines, but not much "global" exposure - so even if the market drops abruptly, the most we have to lose from that call position is the small fraction of 1% of assets the Fund currently has invested in premiums.

In bonds, the Market Climate remains characterized by unfavorable valuations and relatively neutral market action. The spread between 6-month commercial paper and 6-month Treasury bills pushed to a fresh high last week, but I would still expect a clear spike to accompany any change in near-term recession risks. The Strategic Total Return Fund remains at a duration of just under 2 years (meaning a 100 basis point move in bond yields would be expected to impact the Fund by about 2% on the basis of bond price fluctuations).

On the currency front, the euro has declined to the point where it is now much more reasonably valued, though still slightly on the high side. As I noted in the December 20, 2004 comment, the euro was trading at about $1.33 but looked worth about $1.13 on the basis of price and interest rate parities (it recently moved as low as $1.20). Meanwhile, the yen still looks cheap. With the U.S. dollar clearly overbought and the current account deficit pushing new extremes, my impression is that we've seen about as much pressure as the foreign currencies are likely to see. On that basis, the whole commodities group, including oil and precious metals, could get some additional support from dollar weakness. Still, precious metals have already enjoyed a nice rebound (with the recent 18% jump in gold shares since May taking the gold/XAU ratio back under 5.0), so I clipped off a small portion of our position in the Strategic Total Return Fund late last week, in order to hold our position in these shares just under a 20% allocation.