Growth and punishment: The vector space model

After processing more than 1500 data points on the performance of thirteen technology companies, patterns are beginning to emerge. The steps so far:

The final step is to plot the changes in the relationship between pre- and post-crisis for the set of companies normalized to the same starting point and then classifying them: 

The chart shows how the “average P/Es” changed after 9/30/2008 vs. how the companies performed during those periods. An evocative categorization is suggested for the four quadrants.

One way to read the data would be as a degree of effect of the crisis. For example, in the case of HP, its P/E dropped by about 6.5 while its average growth decreased by 41 basis points giving an average of 0.16 drop in P/E for every basis point reduction in growth. That would be a fairly modest impact. In the case of HTC, the impact would be even less. The effect on P/E was zero even though growth dropped by about 78 basis points. At the same time the impact on Microsoft was severe with the P/E dropping as much as for HP even though its growth only moderated by 5 basis points.

Therefore the “slope” (or angle in vector parlance) of each of the lines in the chart above may be interpreted as the severity of discount in value that the crisis invoked. Those values are shown the following chart:

A strong bar on the right half of the chart implies severe impact, a bar around the middle implies minimal impact and a bar in the left represents an inverse relationship where the market priced in opposition to performance[1]. What should be considered along with this chart is the quality of earnings and consistency of performance (which are shown in the posts linked above.)


As noted in a previous article, there are really only six companies which had strong separation between pre- and post-crisis valuations: Apple, HP, RIM, HTC, Microsoft and Google. They are also the companies which had strong P/E drops (except for HTC). As a group they are also the companies with the best growth stories historically. This is perhaps the reason for the drop. Basically, because these were strong companies they “had the most to lose”. The market “punished” them more severely than the weaker companies because the weak had already been discounted.

The other observation is that Apple and RIM are not treated particularly differently. The drops in P/E are at about 1 for every basis point drop in growth. This means that the the degree of value lost is about the same as a function of growth loss. Microsoft seems to have been the most affected. We can argue that it is perhaps weaker than the others strategically so this is reflected here, but I doubt it’s weaker than RIM. Microsoft is also in contrast with Google which seems to have been given a lot of benefit of the doubt.

Nonetheless, this framework offers some hints on how technology companies have been treated after the crisis. There is no rightness or wrongness about this treatment but it may indicate potential for significant reaction in the opposite direction if and when macroeconomic conditions improve. These vectors are, in a way, proxies for volatility or “beta” in terms of correlation to the overall market. The greater the beta, the more amplification to market movement; the greater the slope value

As always, Apple is the canary in the coal mine as far as sentiment is concerned. What should be watched is the pricing reaction as Apple moves from a net reduction in growth to a net increase in growth. How will P/E react? The argument on this site so far has been that growth is exceptionally strong for Apple and it’s not being reflected in the price. However, in this analysis we’ve stretched the time frame and did a longer retrospective. On this new time scale growth is not yet at the levels Apple enjoyed in the heady days of 2005/6. Perhaps this growth will return and when it does we’ll get to see which way Apple’s vector moves.



  1. An inverse relationship with value can happen for various logical reasons, for example that a company has volatile performance which is depending on anomalous events.
  • Anonymous

    Thanks Horace and Dirk – a most illuminating article….in fact, a real eye opener.
    It seems as though the market group-think goes along the lines of..(regarding failing company)”Oh, you’re still here? OK we’ll do nothing” and…(for a successful company)”Yes, we see you are making tons of money but we’ll just bleed you a little to make you try harder” A trial by fire indeed. The case for LG looks a bit odd in this context.
    Is it the case for Apple that it must simultaneously exhibit both growth ‘and’ profit for a reflected change in PE or is there some sort of artificial restraint being applied to keep the rest of the sector looking healthy?

    • Ian Ollmann

      So, I’m noticing that the “P/E drop per basis point of net income reduction” plot seems to be roughly correlated with my notion of the relative margins of these companies. While Horace is probably on track here, perhaps the market is more forgiving of declining earnings for the low margin players because they are really living on the edge.

      In any case, the story I’m seeing here is that AAPL P/E is down because earnings growth is down. Since P/E reflects expectations of future earnings potential, this seems reasonable to me, and the sort of simple explanation that can be attributed to a broad market. I’d call it mystery solved! I was surprised to see Apple in the punished for failure box. (Failure? What failure?) But if declining growth we’ve been seeing, then it all seems much clearer.

      If true, one predicts we then expect tepid stock movement until Apple makes a convincing case for accelerated growth.

  • Begs the question of “why”…

  • Anonymous

    Using simply the summary plot above, those companies that have been ‘rewarded’ are Samsung, Acer, Nokia and LG. One other has not been ‘punished’: HTC. I may be being simplistic, but all the others are North American (that includes Sony in this case).

  • Sacto Joe

    One small nit to pick: HTC doesn’t appear to have suffered “strong P/E drop”. It’s change is virtually zero.

    More importanly, there is a second “vector” that is highly relevant, and that is to measure change in gross income versus net earnings. For example: Apple’s gross income increased 82% last quarter over the year earlier quarter, while Dell’s gross income was effectively flat. Since Dell’s net earnings increased 75% YOY and still only came to 5.7% compared to its gross income, it actually represents a tiny amount of growth. Apple’s net earnings increase YOY by 122%, and yet its earnings equal 27% of its income. That is a huge difference between the two companies.

    • Sacto Joe

      Horace, this would be a good application of your three axis graph, simultaneously comparing growth in income, net earnings and stock price for these 13 companies. And just for the sake of inerest, I’d also add Amazon….

    • Re. HTC, you’re right. I edited to note that.

      Your point about the quality of earnings is also very valid. Alas, time did not permit us to weed out the spurious data. The labor required to go through this much data is significant.

  • Sacto Joe

    Regarding P/E, if Apple is at $400/share when it announces its earnings in a few weeks, which appears likely right now, and if as I suspect its earnings equate to about $30/share for the whole fiscal year, then Apple will have dropped its P/E from about 15.8 to about 13.3, or the equivalent of about a 16% drop in “value” in the space of a few months. To me, the “culprit”, in Apple’s case, is clear; investor’s perceptions of Apple’s potential earnings is comletely out of whack.

    • Sacto Joe

      Sorry – “are” completely out of whack.

  • Av9114

    Either the graph is mislabeled or you are using the term basis point incorrectly (1% = 100bps). I suspect the latter as 1 basis point of earnings growth is insignificant and your graph would then imply that no companies net income has changed by more than a percent and a half.

    • The graph is mislabeled. There should not be a “%” after the numbers in the vertical axis.

  • Talltrash

    Horace, it would be interesting to see this graph using Earnings Yield substituted for P/E.


    • Earnings yield is the inverse of the P/E ratio.

    • Earnings yield is the inverse of the P/E ratio.

    • Earnings yield is the inverse of the P/E ratio.

  • plist

    I never see it discussed, but it appears to me that weekly stock options and “Max Pain” effect are also a big part of AAPL’s inability to move absent any big news, such as blowout earnings.

    Its a tail wagging the dog type phenomenon, Fortune touched upon it. Haven’t heard much else. But if AAPL is closing near Max Pain 90% of the time that there are no major news announcements…that would seem to be significant.

  • MOD

    To me this shows that Apple is in the middle of the pack as far as PE declines are concerned. The graphs to not explain why the group (together with its peers) declined.

    Granted there was a financial crisis, but these are high tech companies, not financial companies.

    That the “acceleration” of earnings decreased is not saying much. There is still acceleration (exponential increase of earnings), and earnings themselves, which in and of themselves (without exponential increases) ought to justify a higher PE.

    Why is the market comparing this group with the financial companies.

  • KGB

    Terrific effort, Horace & Dirk!

  • Steve

    Too wonky for me. Simplicity inspires me. Complexity confuses me, repels me, and devalues your work.

    • MOD

      I kind of agree. We need an “Iphone” of a graph.

    • It is too complicated. Amazing how hard it is to simplify.

  • Ian Ollmann

    Ho, Ho! We are schooled again!
    Thank you Horace.

  • Eric

    Perhaps the two contrariwise labels should read “Punished despite growth” and “Rewarded despite failure”.