Scatter shot estimates of fair value

Portfolio management

Experts who are expected to agree

We are told forty two experienced money managers at an asset management company were given “a one page description of [a company’s] business; the data included simplified profit and loss, balance sheet and cash flow statements for the past three years and projections for the next two.” They were asked to estimate the fair value of the stock.

The outcome – the median noise or scatter in the estimates was 41%. At first blush, this is an astoundingly wide divergence. I imagine this was not some sort of bizarre outcome. It was probably a good indication of the divergent views you would find amongst analysts, money managers and other investors of the fair value of stocks.

In this post I propose to reflect on this phenomenon and think about what it means for investors.


Noise is the title of a book published in 2021 written by Daniel Kahneman, Olivier Sibony and Cass R. Sunstein. It is subtitled, A Flaw in Human Judgment. The money manager ‘noise audit’ is described on p. 28. Noise, for the authors, is said to be the scatter of outcomes you get when “people who are expected to agree end up at very different [judgements].”

They use the statistical technique of standard distribution to measure noise. This measures a typical distance from the mean.

Some explanation

In some ways the outcome was surprising. The forty two participants were given fixed two years earnings projections to work with. The discount rates they used, if they used any, give some room for difference. Their views about the future for the economy, wither interest rates, and so on, could have varied somewhat. Personally I don’t find it too surprising that there is wide divergence. For example, would it make a difference if the stock was Johnson & Johnson (JNJ), or Salesforce (CRM) or American Water Works (AWK) or even Tesla (TSLA)? You would expect to find a bigger range of opinions about TSLA. But, even amongst the others, investors representing different styles of investing would come at valuations differently.

For example, amongst forty two experienced money managers, you would expect to find some who specialized in growth stocks and others who specialized in dividend stocks and every other style in between. If I’m a growth stock aficionado, I may not put too much value on American Water Works. If I have made my career in big household name compounders like JNJ I might turn my nose up at TSLA or CRM.

I might also speculate that the mood of the market might have been different when each did their estimates. Three strong up days or three rough down days before each of the forty two carried out their tasks could well have made a difference.

And what about events in their personal lives at the time. Some might have recently received promotions and been feeling bullish. Others may have been have troubles at home and been feeling somewhat depressed. And finally, some may have been seasoned veterans and others might have been recent recruits.

Main message

Investors rely on estimates of fair value and target prices prepared by analysts. The main thing I draw from this study showing 41% median noise is that the reports I rely on probably exhibit the same scatter. I might get an analyst’s estimate of fair value of, say, $100. I have to recognize that the estimate might lie anywhere in a band of 41% centred on the median street assessment.

I have written elsewhere about the intelligent use of analyst’s reports. See How to get the most out of analysts’ reports

The main message from this 41% median noise is that when buying stocks we must be sure have a good margin of safety.

Wisdom of crowds

One tantalizing thought is the statistical phenomenon that when you take the average of guesses, of say forty two people, of the number of jelly beans in a jar, the average will come pretty close to the actual number. If we average the 42 money managers’ estimates of fair value, will we get an answer close to the true intrinsic value?

The answer is no, for a variety of reasons. The authors of Noise discuss wisdom of crowds at pp. 83 and 99. I have looked at this question and my post is Does Wisdom of Crowds apply to earnings estimates, price targets, value estimates and stock prices?

To begin with, wisdom of crowds works best with simple estimates of a number, like jelly beans in a jar, the weight of a dressed ox, the distance between cities, and so on. If expertise is needed, such as estimating insurance premiums by underwriters, or the fair value of stocks, it doesn’t work so well.

A kind of herding

But, there is a bigger problem. The main requirement for wisdom of crowds to work is that the estimates be made completely independently. The authors of Noise discuss the situation where people in a group are listening to each other when they make their estimates. As they point out: “But if they learned the estimates of other people – for example, the average estimate of a group of twelve – the crowed did worse.” See Noise p. 99.  What happens is that a kind of social influencing takes place producing what we might think of as herding that undermines the wisdom of the crowd.

On Wall Street, estimates and consensus figures are widely known. It can be career limiting to be out on a limb.

Bias and anchors

It gets even worse. When someone is estimating the fair value of a stock, the stock’s current price on the stock market acts as an anchor.

Kahneman writes: “Many psychological phenomena can be demonstrated experimentally, but few can actually be measured. The effect of anchors is an exception. Anchoring can be measured, and it is an impressively large effect.” (Kahneman, 2011 Thinking, Fast and Slow) p.123.  [Emphasis added]

It’s hard to imagine any analyst or investor forming an opinion about the fair value of a stock without, at the same time, taking a look at the current market price.

In Noise the authors use the example of people giving a dollar amount for how much they would pay for a bottle of wine. One group simply gave a figure. Another group was asked to write down the last two digits of their Social Security number and then asked if they would pay that for the wine. The Social Security number was irrelevant but acted as a psychological anchor. In one test, a group with a high anchor were prepared to pay three times as much for the same wine as a group with a low anchor.

When experts are estimating the fair value of a stock, the current price in the market has an impact in two ways. First, it acts as an anchor. Secondly, it acts as a Groupthink mechanism to produce herding behaviour. One thing we know is that investors can act as a herd.

More on bias

The interesting question is whether the 42 professional money managers in the ‘noise audit’ referred to above had access to market price data before they came up with their estimates of fair value. If they did, it is likely that market prices had an influence on their estimates. In that case, one would expect that the mean of their estimates would be biased toward market prices.

We also have to remember that sell side analysts are congenitally optimistic. Their reports reflect this bias.

So, if the money managers were aware of market prices, anyone trying to draw a wisdom of crowds conclusion from the 42 money managers estimates would have seen a biased mean. This bias would have been on top to the noise flowing from the scatter of estimates. In other words, the estimates would be all over the place and their mean would be off the mark.


The main message from today’s post is to take little at face value. Everything is uncertain. The main defence for investors is to have a sound investment process that includes things like only buying superb companies. Good companies won’t do because our assessment of their merits is so subject to noise. One should only buy with a substantial margin of safety. That’s because our estimates of fair value are so fraught with error.


Readers wishing to dig further into how to invest in an uncertain world:

Acting with imperfect information


Other posts on investment psychology

This post is part of a series. Readers are invited to read Investment psychology explainer for Mr. Market – introduction. This will give you a better understanding of some of the terms and ideas and give you links to other posts in the series.


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