How can markets can be highly efficient, even if they make errors?

Question

A Random Walk Down Wall Street (2015 11 ed, but an 2019 ed. is upcoming). p. 105 Middle.

  $\color{red}{\text{Markets can be highly efficient even if they make errors.}}$ Some are doozies, as when Internet stocks in the early 2000s appeared to discount not only the future but the hereafter. How could it be otherwise? Stock valuations depend upon estimations of the earning power of companies many years into the future. Such forecasts are invariably incorrect. Moreover, investment risk is never clearly perceived, so the appropriate rate at which the future should be discounted is never certain. Thus, market prices must always be wrong to some extent. But at any particular time, it is not obvious to anyone whether they are too high or too low. The evidence I will present next shows that professional investors are not able to adjust their portfolios so that they hold only “undervalued” stocks and avoid “overvalued” ones. The fact that the best and the brightest on Wall Street cannot consistently distinguish correct valuations from incorrect ones shows how hard it is to beat the market. There is no evidence that anyone can generate excess returns by making consistently correct bets against the collective wisdom of the market. Markets are not always or even usually correct. But NO ONE PERSON OR INSTITUTION CONSISTENTLY KNOWS MORE THAN THE MARKET. [I bolded]

Can someone please distinguish more clearly how $\color{red}{\text{'[m]arkets can be highly efficient even if they make errors'}}$? I don’t understand the differences between market efficiency and price correctness.

Answer 1

The theory of efficient markets is that no one can make rewards that are in excess of the level reflected by the risk they are taking, except by random chance.

So if markets can make mistakes, but not in a way that allows anyone to make disproportionate rewards except by random chance, then they can be highly efficient.

Answer 2

Suppose we have 100 jars, each with an unknown number of jelly beans. Denote these numbers $N_1$, $N_2$, $\dots$, $N_{100}$.

Millions of contestants are invited to submit their guesses for what these 100 numbers are.

For each $i=1,2,\dots,100$, let $G_i$ be the average of all the submitted guesses for the number $N_i$.

Let us refer to these 100 average guesses $G_1$, $G_2$, $\dots$, $G_{100}$ as the "market's guesses".

It is highly probable that every single one of the market's guesses is wrong. This is what Malkiel means when he says that "market prices must always be wrong to some extent" or that the market "makes errors".

However, the market's 100 guesses are probably much better† than any single contestant's 100 guesses. This is what Malkiel means when he says that the market is "highly efficient".‡

Altogether then, although the "market" may not get any single number correct (and is thus "always wrong"), it is, on average, "more correct" than any single contestant (and is thus "highly efficient").

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^_Footnotes.

^{_{†Where "better" can be quantified by say:}}

• ^{_{the sum of absolute deviations $\sum_{i=1}^{100} \left|N_i-G_i\right|$; or}}
• ^{_{the sum of squared errors $\sum_{i=1}^{100} \left(N_i-G_i\right)^2$; or}}
• ^{_{whatever other measure that seems sensible in this scenario.}}

^{_{‡Unfortunately, the term efficient means different things in different contexts and to different economists. My above answer is merely what I believe Malkiel meant by this term.}}