Wall Street Goes Crazy: The Numbers

The S&P 500 jumped 5.54% today. How weird is that?

Yikes. Stocks up 5.54% in one day. How often does that happen? And does today provide fresh evidence that investors are irrational?

Answer to first question: Very, very rarely. Here is a list of the biggest up moves in the S&P 500 index since 1950.

In those 72-plus years there have been only 14 bigger one-day rallies. Frequency: Something less than once in every five years.

A statistician, though, might insist on a two-sided test. Throw in the big one-day crashes and see how often the market moves either up or down by a large amount before you decide how striking a price shift is.

Comparing ups to downs gets a little tricky. To be consistent with your arithmetic, you should always compare the high number in a pair of prices to the low. Thus, a 25% up move ought to be seen as the same kind of earthquake as a 20% down move. (Having one right after the other puts an index back where it was.)

On that score the great vibration looks somewhat smaller. The frequency of up or down moves corresponding in magnitude to a 5.5% up move has been higher, occurring somewhat more often than once in every two years since the beginning of 1950.

Here are the bad days:

As to the second question: I am of the opinion that most investors are either irrationally exuberant or irrationally despondent much of the time. So here I offer three ways to see the recent volatility as the sign of the market’s mental illness.

1. If investors did what they are supposed to do, they would take a random walk along Wall Street, plucking their moves from a log-normal distribution. The standard deviation of daily moves since 1950 is 1%, so a jump like today’s (in either direction) represents just about 5.4 sigmas. It should occur only once in 14 million days of trading. That’s once every 112,600 years.

Clearly, buyers are not walking randomly. They are moving in herds.

2. If people were behaving themselves, they wouldn’t be any jumpier nowadays than they were in the previous century. Take note that most of the big down moves, and almost all of the big up ones, have occurred in the past 23 years.

Short attention spans and get-rich-quick schemes are now the norm. I blame Sam Bankman-Fried and Robinhood.

3. If securities prices reflected expectations for future corporate earnings, they might, plausibly, take a sharp turn upward when the threat of a recession is diminished. Perhaps that threat receded today with hints that the Federal Reserve would become less hawkish in fighting inflation.

So, less recession equals higher earnings equals higher stock prices. But in this scenario of a more feverish economy, real interest rates should go up.

What happened today to real interest rates? Take a look at the market for Treasury Inflation Protected Securities. Their real rates lurched down, from 1.70% to 1.43% for the ten-year bond.

Very meshuggah.