> That difference is partly due to different things being valued
This is misleading. All valuations are based on the discounted value of future cash flows. There are three variables at work here: today's cash flows, the growth rate of these cash flows and the discount rate. The market is simply saying that Amazon's growth prospects outweigh it relatively smaller size.
There is only one thing being valued by a rational investor: net present value of future cash flows.
Edit:
The only point I'm trying to make is that an investor, when they exchange money for a stock, is placing a bet on a single outcome: future cash flows. Of course there are plenty of ways to get those cash flows, but I find that most people get caught up in details like employee headcount and fail to grasp the single most important factor: compound growth.
Sure, but there are many ways to get future cash flows. A significant difference in the valuation of the two companies is that with Wal-mart, the expectation of future cash flows (and therefore present value) comes primarily from its present size, the cash flows that brings, and its expected ability to continue bringing in such flows. Whereas with Amazon, which has much lower current market share and cash flow, the market is "saying that Amazon's growth prospects outweigh it relatively smaller size". Hence the proportion of expected future cash flows that investors expect to come in the form of future growth is significantly higher with Amazon than with Wal-Mart. Therefore you would expect Amazon to have a lower current size and current headcount per unit present valuation, even if there were no differences in productivity.
What I was criticizing was just using the ratio of present market cap and present headcount as a meaningful metric, when comparing companies with very different growth expectations. That effectively becomes a restatement of the different growth expectations: Amazon has the same market cap as Wal-Mart but its present size is smaller in almost any way you could count present size (sales, headcount, etc.).
What I meant was that much investment is speculative, and that speculative investing is not solely, or even mostly, based on a purely rational model e.g. one that is based on a prediction of future cash flows.
It is usually based on betting on the the future price of the asset, independent of fundamentals. Some of these approaches are more justifiable than others: market momentum, qualatiative prediction of the company's valuation trajectory, trendy but questionable financial metrics, sophist technical analysis etc.
> There is only one thing being valued by a rational investor: net present value of future cash flows.
This only holds under the assumption of rational expectations.
Under the more reasonable assumption of heterogeneous expectations, it becomes necessary to think about what the market on average expects (or, possibly, other functionals of the agent population if the assumption of competitive markets is violated); the more so the shorter your investment horizon.
See for example
[1] F. Allen, S. Morris, and H. S. Shin. Beauty contests and iterated expectations in asset markets. Review of Financial Studies, 19(3):161–177, 2006.
which shows the failure of the law of iterated expectations (which is used to establish your original assertion) for the average expectations operator.
You then have
[2] P. Bacchetta and E. Van Wincoop. Higher order expectations in asset pricing. Journal of Money, Credit and Banking, 40(5):837–866, 2008.
who derive a gap between price and fundamental value (understood as the NPV formula that would prevail without the interference of higher-order beliefs) in the presence of heterogeneous expectations.
And last but not least,
[3] M. Kurz and M. Motolese. Diverse beliefs and time variability of risk premia. Economic Theory, 47(2-3):293–335, 2011.
who generalize this from the asymmetric information frameworks used above, where expectations are coordinated by the public signal, to a symmetric information setting where it is the correlation of beliefs that coordinates expectations.
In the end, this is all building on Keynes's original intuition that if agents hold diverse
beliefs about the future "the energies and skill of the professional investor and speculator are […] concerned, not with what an investment is really worth to a man who buys it ‘for keeps’, but with what the market will value it at."
So no, it is not necessarily the best strategy to only focus on NPV of cash flows. The shorter your time horizon, the more you depend on what "other people" expect too, whether you think them foolish or not.
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PS: Of course, if you believe that you have no predictive power w.r.t. what "Mr. Market" thinks (to borrow from Ben Graham's exasperated simile), then by all means your optimal strategy becomes to lengthen your horizon as far out as possible and concentrate only on NPV of cash flows, just as you said, in the spirit of value investing. I'm only pointing out that the optimality of this strategy hinges on both your investment horizon and your belief about your relative predictive powers w.r.t. "Mr. Market" and the fundamentals (leaving aside positive feedback loops or what Soros called "reflexivity" between price and fundamentals for now).
Rational expectations and heterogeneous expectations don't conflict with each other. Rational expectations only assumes that the aggregate expectation of the economy is an unbiased predictor.
Individual agents are free to be irrational, biased, and heterogeneous. In fact, heterogeneity is required in nearly any model, otherwise no trades will occur.
> Rational expectations and heterogeneous expectations don't conflict with each other.
Good point, although I didn't say they did. One can indeed view RE as a special case of heterogeneous expectations, and in fact that is essentially what I argue in a paper I am working on: That efficient markets are a region in the parameter space of more general market models, and that by traversing that parameter space one can generate different market outcomes. By way of illustration, take the public signal out of the above cited paper [1]. Without the coordination provided by the public signal the law of iterated expectations works again for the average expectations operator!
Regarding the source of heterogeneity, I don't agree with your citation of irrationality or biases. I am not an expert on behavioral economics but from what I understand, behavioral models seem very fragile to the insertion or presence of even a few rational agents, hence the need to erect "limits of arbitrage" by adding frictions, constraints, etc. It is possible to motivate heterogeneous expectations in a more robust way, see my reference [3] above and further references therein, for example. The basic idea is to generalize the economic system from ergodicity or even stationarity, so that heterogeneity is motivated epistemologically, rather than psychologically.
A rational investor knows how others value something and acts accordingly. What you described is one way to value something. If it was just you and me buying stocks, I would know how you act and get in front of your behavior to profit from it.
In finance you don't have to be the smartest person in the room to succeed, you just need to know the most about what everyone else is thinking.
This is misleading. All valuations are based on the discounted value of future cash flows. There are three variables at work here: today's cash flows, the growth rate of these cash flows and the discount rate. The market is simply saying that Amazon's growth prospects outweigh it relatively smaller size.