Last week Felix wrote an interesting post on the valuation of high growth big cap tech, specifically Apple and Google. The debate in the comments was equally interesting. Felix thinks AAPL should *not* be worth more than GOOG, as recently become the case when the former’s market cap surpassed the latter’s. GOOG grows faster than AAPL, he points out, has higher margins, and is increasing market share in its core (web advertising) market while AAPL is losing share in its (iPod/iTunes); unlike AAPL, GOOG has a dominance in its fast-growing core market that amounts to a monopoly, option value from its many ventures, and finally no management succession risk. That should be worth a premium valuation.

All these points are either true or could be plausibly argued. So how can this be, given that the market prices in all knowable, digestable information (Felix is a great fan of indexation and presumably holds to a very dilute version of the efficient markets theory)? Why is a company with all these attributes trading at a discount to this relatively deficient one?

Baruch knows the answer. He gets *paid* to value high growth big cap tech. While he personally covers neither AAPL nor GOOG, in the vast expanse he calls his mind this does not disqualify him from opining about both companies firstly from the point of view of a Spinozist but secondly, from time to time, as a stock operator or “punter”. You will remember that from the first perspective, he likes neither of them very much. From the second perspective, Baruch has said he would actually be long AAPL here. In fact, the fund he works for is an owner in size. As for GOOG, it is a smaller position than the benchmark, an “underweight”, in the argot. Had he his druthers, moreover, Baruch would strongly consider a GOOG short.

There are two central concepts to tech investing — expectations, and the 2nd derivative of growth. Both of these concepts combine in interesting ways. Let’s deal with both, the role of expectations first.

Consensus expectations are important in any stockmarket sector. But the delta or surprise or the change in expectations after excellent quarters, for tech companies, tends to be higher than in other industries, and it is that change which really drives stock prices. Stock analysts tend to the conservative, especially in tech, given the volatility of earnings. There is rarely an incentive for them to stick their heads above the parapet. Indeed it is more often that analysts with buy ratings on a stock will have *lower* earnings numbers going into quarters than their peers, so they don’t inadvertently raise the average of published sell side expectations, “the consensus number” as calculated by Bloomberg or Reuters. It also allows them to write notes starting “XXXX comfortably beat our estimates, validating our positive view on the stock”, rather than “XXXX was in line, and you may well ask why I keep on supporting this piece of crap”.

The clever investor knows that tech is the definition of Talebian *Extremistan*, yet all the analysts live in *Mediocristan*, so buy side guys tend to have higher expectations than consensus when they own stocks, and lower expectations when they don’t or are short. This is why well-owned stocks, whose prices have risen into the earnings report, can fall even after the report has trounced consensus, and reviled, over-sold, shorted names who have missed consensus may even shoot up 5-10%. In either case, they under- or over-shot the “Whisper number”, the consensus of the powerful buy side names who may be long or short those stocks in size. Good luck finding out what the whisper is, as publishing it would immediately invalidate it. You’ve probably got to call a sell sider who talks to these bigger guys, and try and wheedle it out of her, and even then she may not know it.

Obviously the whisper influences stocks before they report, and explains much of the intra-quarter share price movement. That is a very likely reason for the disparity, Felix: underlying whisper numbers for GOOG are moving down, below the published growth rates and PEs and margins that you cite, and for AAPL they are moving up.

As for growth, we all know tech investors are fools for growth. Explosive growth beyond consensus rates shrinks PEs over time. You will find the pricey stock everyone laughed at you over saying “oh look at that idiot Baruch buying XXXX at 35x 09” will suddenly look a lot cheaper after everyone raises their eps 20% after a blowout quarter. Moreover, the growth will then expand your PE subsequently, as all the punters think, well they killed all the analysts last time, we know consensus tends to undershoot, mediocre beings that these analysts are, they’ll buy the crap out of it even more, your stock is at 40x a much higher consensus, and hey presto, you’re sitting on a 40% gain.

For assessing the ability of these stocks to meet and even blast through whisper numbers, nothing matters more than the second first derivative of growth, the rate of change of the growth rate. Distressingly, growth companies largely see declining growth rates, except at the very start of their product cycles (when they are largely still privately held), and it is this tendency that analysts tend to follow in their models. Accelerating growth rates upset this, however; the mean-reverting analysts get discombobulated and their estimates increasingly irrelevant.

Let’s put it all together. AAPL’s underlying growth rates are increasing with iPhone. And none of the analysts have 10m iPhones for Q3, but maybe a few buy side guys are thinking it may be possible. The published growth rates Felix has access to do not reflect this. GOOG’s growth rates are falling as their market share of total adspend grows, but the overall pie shrinks due to the non-recession we find ourselves in. The larger and more successful it is at growing in its market, the closer it gets to a crossover point at which penetration gains no longer offset the economic losses. We don’t know when that might happen, but it might be next quarter. Sure it’s a monopoly, sure it’s the fastest growing monopoly we know, with option value up the wazoo. But we simply know it too well. It no longer surprises us and may have downside risk.

AAPL’s average earnings surprise (the amount it beat consensus) in the last four quarters was +11% and every quarter was a beat. GOOG’s was +2% and missed twice. There are no statistics as to how they did against the whispers. Investors think consensus has a pretty good idea about GOOG’s quarterly prints, but know it’s probably wrong about AAPL’s. They may also suspect AAPL may be at the start of a mega product cycle with iPhone that could compensate for the decline of the iPod/iTunes franchise and accelerate the overall growth rate far beyond the static consensus. That’s real option value. And while it could change in a second, that’s why it’s worth more than GOOG right now.

You mean the first derivative of growth, the second derivative of earnings, right?

no, the growth of the growth rate. all revenues. i’m not specifically talking about earnings growth rates, although that is also very important and i guess it could equally apply. the main question is: are growth rates increasing or decreasing? if increasing, all sorts of good things happen, and the stock is likely to go up a lot via the mechanisms i describe above.

maybe it’s the first derivative of growth. oh dear, that would be embarrassing.

I agree with Felix. I think you mean the second derivative of revenue over time, which is, of course, the first derivative of growth. It’s like the acceleration of revenue vs the velocity of revenue.

Dweebs!! Pedant alert! I can see this comment stream becoming a tedious discussion of what “2nd derivative” means, rather than the clear educational value of my post. Soon as I get home I am changing the title. Us tech guys CALL it the “second derivative.” So that’s what it is.

Anyway, ramster, what do you mean by the “acceleration of revenue” rather than the “velocity”? do mean “of revenue growth” than “of revenue”? i don’t know what the “velocity” of revenue is. Does that mean e.g. y-y growth in revenues?

because whatever that number is for AAPL, say 38% last quarter, that number is going up in the collective minds of investors, and this is why AAPL is worth more than GOOG.

Well I never denied being pedantic. Consider 3 cases

1) flat revenue: first derivative (i.e. growth) is zero. The second derivative is also zero.

2) steady growth in revenue (e.g. 38% a quarter). First derivative is a non-zero constant but the second derivative is still zero.

3) increasing growth in revenue (e.g. 10% in Y1, 20% in Y2, 30% in Y3, etc.). First derivative of revenue is increasing linearly. Second derivative of revenue is a non-zero constant.

In my analogy, scenario 2 represents revenue velocity but not acceleration. Scenario 3 is acceleration. I believe scenario 3 is what you’re talking about when referring to the second derivative.

From social conscious perspective:

AAPL does not have no productive, but has destructive value.

Of course, that is from different perspective than pure marketing hot product.

Stumbled on to your blog.

Good luck

yeah, that’s right. scenario 3. revenue growth increasing, makes stocks go up.

so technically that is first derivative? rats.

Since earnings/revenue is the underlying issue, then the first derivative or the rate of change is the growth rate, hence first derivative.

But ya i get your post, good stuff :)

There are other stocks in the universe than AAPL & GOOG. And once you introduce the third derivative,

alltechs will get filtered out.Go out and discover the real growth stocks.

This comment thread is amusing, especially after reading your “About” page where you called Leibniz a fool. At least Leibniz would get the derivative right.

Fascinating to read that there is a Spinozist investing blog though. Spinoza was one of my favorite classes in college, and I was pleasantly surprised to see him quoted by Benjamin Graham in The Intelligent Investor and the part of Security Analysis I’ve managed to slog through so far.

Good point about the power of accelerating earnings and beating whisper numbers, but I second the poster above who expressed ennui about the two mega caps. Why not turn your attention to the tiny stocks that have a chance of taking off (I’ve mentioned a couple of candidates on my blog)? That’s a lot harder, but as Spinoza said in his Ethics, “all things excellent are as difficult as they are rare”.

No “rats” necessary, really: the number you talk of is the second derivative of revenue, but the first derivative of growth, which is itself the first derivative of revenue.

So yes, I guess I, too, am a pedant.

Your point remains valid, and thanks for it.

Patton, you make my morning. I may change the title of the post back. Take that, Ramster! Pow! The second derivative of revenue!!

Dave, everyone knows Newton invented calculus, and that Leibniz copied him, the sad, derivative, flighty nincompoop that he is or was. In fact, the latest, unpublished, biography makes the charge that he had problems with long division. Anyway, as Patton points out, I was right all along.

Interestingly, Spinoza was a trader before he became a philosopher, probably dabbling in West and East India stock, as well as commodities like raisins. I don’t think he did very well, he was trading in a hole.

As for ignoring the smaller stocks, one of the things I want to avoid with this blog is making it too “stocky”, and reducing it to a tip sheet, open to the accusation of punping and dumping the stocks I own and write about. I am fully aware that there are more interesting stocks in the world than the big cap techs, and it is mid cap tech and growth (ex biotech) that we specialise. Looking for these smaller stocks is my day job. Oh the stories I could tell.

That’s why my posts are more about generalities (how I think people value stuff, for instance), in other words the epistemology of investing, and refer to the biggest, most popular stocks everyone, including my friends, talks about, like AAPL and GOOG. In fact, I don’t formally look at AAPL and GOOG at all.

Whack! (reed on knuckles)

Derivation can only be delineated in terms of “time”? Hmmmm…

Baruch, you have not begun to fight!

I come to expect more precision in my spectacles. You might consider an appellation to the eminent Brook Taylor to reconcile your desire to balance the importance of a first derivative with a second.