Stock splits and stupidity

Stock splits are back in style. Nvidia, Chipotle, and Broadcom all recently announced splits.[1] How should we think about splits? In this post, I’d like to focus on how not to think about them.

In a perfect world populated by rational investors with frictionless trading, there’d be no need for us to think about splits at all, because no one would ever look at nominal share prices. Instead, we’d look at cumulative total return indices for each security, which would have the added benefit of reducing confusion about dividends, as argued by Hartzmark and Solomon (2022).

Unfortunately, we don’t live in a perfect world. Instead, we live in a world of investors with varying cognitive abilities who focus on nominal share prices. Today, I want to discuss research suggesting that splits have real consequences for investors and for market values.

Before going any further, I need to ask you the following three questions:

1. John has a nickel in his left pocket. He takes the nickel out of his left pocket and puts it in his right pocket. How many cents does John have?
2. Sally has a nickel. She trades it for five pennies. How many cents does Sally have?
3. A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How many cents does the ball cost?

If you failed to answer “five cents” to all three questions, then understanding splits may be difficult for you, and perhaps a career in finance is not your best fit.

The first two questions are my attempt to capture “conservation.” In child psychology, conservation is the idea that altering the appearance of an object does not change its basic properties. For example, if you cut a cookie in half, you don’t increase the total amount of cookie.

Swiss psychologist Jean Piaget studied the ability of children to understand conservation, and found that by age 11, children had mastered the logic. Evidently, Piaget failed to study CEOs. Thus, it falls to me to announce the winner of the coveted Jean Piaget Award for Financial Innumeracy. The award goes to Park Soon-jae, CEO of Alteogen:[2]

Alteogen, a Korean developer of biobetters, Tuesday said it has decided to gift 0.2 bonus shares for every one common share to shareholders to compensate for the plunge in stock prices from short selling.

“We feel apologetic to the shareholders who have suffered great damage from the drop in the stock price due to short sales,” said Alteogen’s CEO Park Soon-jae denying any changes in the company’s fundamentals

As background information, “free bonus shares” in Korea are the same as “stock dividends” in the U.S. The statement above is describing a 1.2-for-1 split for shareholders of Alteogen.

Consider this hypothetical scenario. You own a restaurant, and you hire a manager to run the restaurant, call him Fred. Fred comes to you and says, “I feel apologetic that you have suffered great damage from the drop in profits due to the hobgoblins that live in the floorboards. Here, as compensation, let me gift you all the cash in the cash register.”

In this scenario, Fred is completely clueless because:

1. There are no hobgoblins in the floorboards.
2. Fred does not own the cash in the cash register, and thus he cannot “gift” it to anyone.
3. You already own the restaurant including the cash in the cash register. How are you made better off by getting something you already own?

Moving now from CEOs to investors, let me describe another cognitive error involving splits. You could describe this error as “nominal illusion,” “money illusion,” or “non-proportional thinking,” but I will just call it “confusion.” It is best illustrated with another hypothetical scenario. Suppose every week you go to the grocery store, where they sell milk in one-gallon containers for $6. One day you arrive at the store, but now you find half-gallon containers that cost $3. Is the milk now “cheaper” and thus a better bargain?

Apparently, for many stock investors, the answer is yes. They view lower priced stocks as more attractive because these stocks have more “room to grow” (Birru and Wang (2016)). A variety of evidence suggests that lower stock prices attract retail investors, and their increased buying is one explanation for the fact that when company ABC announces a stock split, the price of ABC goes up.

Consider a world dominated by confused investors. Suppose a stock is trading at $50 and then does a 2-for-1 split. In a world with only rational investors, the stock price would fall to $25. But $25 would be an irresistible bargain for cognitively challenged investors, and they buy. As a result, when the split takes place, the price does not fall all the way to $25 but instead goes to $26. In this world, a stock split causes the total value of the firm to rise by 4%.

Another way to describe this behavior is that investors are “anchoring” on the previous price level, or are “under-reacting” to the stock split, treating it like a 1.9-to-1 split instead of a 2-for-1 split.

Now, I know this behavior seems implausibly stupid. But if there’s one thing I’ve learned, it is that there does not exist behavior so stupid that it cannot possibly be observed in the wild. I call this the Postulate of Infinite Stupidity: there is no such thing as implausibly stupid.

Is there evidence in favor of the confusion hypothesis? Yes. Duffy, Rabanal, and Rud (2023) conduct a laboratory experiment involving an artificial stock market with splits. They find that when a stock has a 2-for-1 split, the total market value goes up due to buying by confused investors. In fairness to these experimental subjects, we don’t really need to invoke the Postulate of Infinite Stupidity to explain their behavior. It is understandable that when you perform an unfamiliar task involving abstract math for the first time, you might screw up.

And that brings me to question (3) about the cost of the ball and the bat, which comes from the cognitive reflection test of Frederick (2005). Duffy, Rabanal, and Rud (2023) administer a similar test to their experimental subjects and find that people who score poorly on the test are more likely to buy in response to a split. Thus, we have hard evidence that, at least in the lab, the stock price reaction to splits is driven by cognitively challenged buyers. If you do a stock split, you’ll attract some low IQ buyers.

Moving now to the real world, Shue and Townsend (2021) study another implication of non-proportional thinking. Their idea is that investors focus inappropriately on share price levels when processing information. Investors conceptualize news in dollar per share terms instead of percent terms. For example, investors frame “good earnings news” as “stock price should rise $1.” The implication is that low-priced stocks react more to news and thus are more volatile. Here is what they find:

We find a sharp discontinuity around stock splits: total return volatility, idiosyncratic volatility, and market beta increase immediately by approximately 30% after a 2-for-1 split. Further, the volatility does not return to pre-split levels, even after six months.

Now, I am not trying to argue that stock splits are a bad idea. There are many costs and benefits of stock splits, and investor confusion is only one part of the story. It’s also worth noting that the Shue and Townsend (2021) results do not necessarily have normative implications. For example, their findings suggest that the volatility of Nvidia will go up, due to its recent stock split. Is that a bad thing? I don’t know; perhaps Nvidia had artificially low volatility before, and thanks to the split its volatility has now reached appropriate levels.

One thing is for sure. Many market participants get confused by simple corporate events and struggle with basic math. If they can’t handle splits, what else are they getting wrong?

Endnotes