# Beauty Contests And Market Bottoms

*By Nick Colas of DataTrek Research*

*Today we will discuss an early classic in the field of behavioral finance: John Maynard Keynes’ “Beauty Contest”. Its lesson is that market prices are set by what investors think other investors think. At present, that dynamic is creating ever-lower stock prices because of the increasingly consensus idea that the S&P 500 will bottom somewhere between 3,000 and 3,400. Those levels come from expectations of lower earnings due to a recession. The bottom will come when investors think other investors believe it has arrived.*

**For Story Time Thursday this week we have a discussion of an early behavioral finance concept called the “Keynes Beauty Contest”. **While distinctly out of step with modern values – the idea comes from John Maynard Keynes 1936 work “The General Theory of Employment, Interest and Money” - it is still a hugely useful paradigm today. Especially today, frankly …

**Richard Thaler published a wonderful analysis of the Beauty Contest in 2015 (link below), which quotes from the 1936 Keynes work to describe how it works:**

Imagine a newspaper contest “in which the competitors have to pick out the six prettiest faces from 100 photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole …”

“ … each competitor has to pick, not those faces that he himself finds prettiest, but those that he thinks likeliest to catch the fancy of other competitors, all of whom are looking at the problem from the same point of view …”

The analogy to equity markets:

Investors and traders look for investment ideas they think other market participants will find more attractive in the future.

The timeframe may be a day or a week for a trader and 6-12 months for an investor, but the idea is the same. Buy things that you expect other people will find more valuable at some future date. Any analysis worth pursuing must be in service to that goal.

**The hard bit about the Beauty Contest as far as its application to investing is that it is iterative.** It is not enough to pick faces you think the crowd will find attractive. Everyone else is doing that too. To win, you must run multiple cycles of “what will the crowd think?”

**Thaler’s article updates Keynes’ idea with a numerical version which explains why this is so challenging:**

“Guess a number from zero to 100, with the goal of making your guess as close as possible to two-thirds of the average guess of all those participating in the contest.”

“To help you think about this puzzle, suppose there are three players who guess 20, 30 and 40 respectively. The average guess would be 30, two-thirds of which is 20, so the person who guessed 20 would win.”

The naïve guess would be 50 – the midpoint between 1 and 100 – based on the assumption contestants are lazy and would just pick random numbers rather than latch on to the wrinkle of “two-thirds of the average guess”.

More educated guesses might be 33 (two thirds of that 50 naïve estimate) or 22 (on the assumption contestants have thought the problem through, but not iterated one level deeper).

**Math nerds will think of this as a Nash equilibrium problem, and Thaler makes the point the only viable answer using this approach is zero. **Iterate the last point’s math ad infinitum and you get zero. Yes, this assumes only math Ph.D.s are playing the game. But it is a logical conclusion nonetheless.

**We can use this idea to estimate what market participants think fair value on the S&P 500 is today:**

**The naïve guess is today’s close: 3785. **We’ve had a horrible first half of 2022, and maybe all the bad news is finally baked into stock prices.

**The second order guess might be 3,386, if we assume investors will think other market participants will key off either pre-pandemic highs and/or discount a modest earnings recession:**

This was the last S&P 500 high before the Pandemic Recession (February 19th, 2020).

It is also 18x S&P earnings of $188/share, which is roughly 15 percent (14.5 pct, to be exact) below current earnings power of $220/share.

While earnings typically decline 25 percent in a recession, perhaps any upcoming economic downturn will be milder than most. The 18x multiple is slightly richer than the 10-year average of 17x, but fair since investors tend to pay more for trough earnings as they anticipate higher earnings in a recovery.

**The third order guess could be around 3,000, if investors believe markets must discount a full-blown recession before there is enough general interest in stocks to make for a durable low:**

Assume an average hit (25 pct decline) to S&P earnings from a recession and you get $165/share versus the current $220/share earnings power.

Put an 18x multiple on that $166/share and you get an S&P of 2,970.

**Takeaway: fair value on the S&P – or any other stock market index – is a function of what investors think other investors think.** In bull markets those beliefs are iteratively revised upwards. In bear markets, such as now, those revisions trend lower until specific catalysts change investor perceptions. Then, the whole cycle starts all over again. At the end of a very difficult 6 months for stock prices, it is worth remembering that there is always a low and a next bull market. The goal now is to play defense until those arrive.

**Source: **Thaler article: https://www.chicagobooth.edu/review/keyness-beauty-contest