Speaker 1: We were down nearly 3,000 points on the Dow.
Speaker 2: The single largest point drop in history.
Speaker 3: The worst Dow point loss ever.
Speaker 4: The Dow and S&P having its worst one-day point drop ever.
Katy Milkman: On March 16th, 2020, the Dow Jones Industrial Average fell by nearly 3,000 points as investors came to grips with the implications of the coronavirus pandemic. Media outlets around the world ran dramatic headlines, calling it the biggest point drop in the Dow's history. Those media outlets weren't wrong. The 2020 plunge was the largest point drop in the Dow's history. But in percentage terms, it was much smaller than the Black Monday crash of 1987.
In this episode, we look at how we often fail to make important transformations with data, like thinking in percentages. We do this when considering things like fuel efficiency, the value of our homes, how investors should respond to news, and how to protect wildlife habitats.
I'm Dr. Katy Milkman, and this is Choiceology, an original podcast from Charles Schwab. It's a show about the psychology and economics behind our decisions. We bring you true stories involving tough choices, and then we explore how they relate to the latest research in behavioral science. We do it all to help you make better judgements and avoid costly mistakes.
Damon Lesmeister: These forests have massive trees that reach over 300 feet in height and can be 10, 20 feet in diameter.
Katy Milkman: That's Damon.
Damon Lesmeister: My name is Damon Lesmeister.
Katy Milkman: He's a wildlife biologist working in Oregon.
Damon Lesmeister: I work for the U.S. Forest Service with the Pacific Northwest Research Station.
Katy Milkman: Damon specializes in studying the northern spotted owl.
Damon Lesmeister: They're a medium-size owl. They have this round head. Their breast feathers have sort of a spotted look to them. Their eyes, from a distance they look black, but if you look very closely, they're actually very dark brown. There's some striping on the tails, and they're mostly brown. It's not common to see them unless you're in the deep forest.
Katy Milkman: While they're tricky to spot, they have a distinctive call.
Damon Lesmeister: They have a four-note location call. They evolved this to be able to establish territory so that they can communicate with their neighbors and be able to sort of defend that space. But they have other calls also. They may enter in sort of this duet within pairs. And so they're communicating back and forth with one another. And then they have other call types that they use just at the nest themselves. And so there's at least a dozen different types of calls that spotted owls use in various different sort of communications.
Katy Milkman: Northern spotted owls usually mate for life. And once they pick the perfect home, they settle in.
Damon Lesmeister: They establish and maintain territories if it has all the suitable conditions. So all the forest structure for nesting and roosting and prey base, and if they have a mate, then those spotted owls will maintain that territory as long as they can.
Katy Milkman: Unfortunately, that territory is under threat.
Damon Lesmeister: As a scientist, we're sort of trained to be very measured in the way we communicate and careful about making predictions. But I will say that the projections for northern spotted owl populations in Washington can only be described as quite bleak.
Katy Milkman: Things are bleak for the owls because their population has been dropping dramatically in recent decades.
Damon Lesmeister: Since the monitoring program really officially began in the early 1990s, we've observed consistently the populations declining. Our study areas in Washington in particular have had the highest rates of decline.
Katy Milkman: In some areas like Cle Elum, Washington, scientists have seen a dramatic decline. Thirty years ago, researchers counted 47 nests. Last year, they counted only one.
Damon Lesmeister: I'm sure they didn't realize this at the time in 1992, but that was the peak. You fast forward to 2021, we observed seven individuals on the study area. Six territories met our definition of an occupied territory. We had one pair and we had one nest last year and one fledged young.
Katy Milkman: So why are so many northern spotted owls struggling?
Damon Lesmeister: Habitat is really the big driver of what is the threat for spotted owl populations.
Katy Milkman: Northern spotted owls can't survive in any forest. They need to live in old-growth forest. These are areas untouched by logging or frequent fires, and there's less and less old-growth territory these days. So it's getting harder and harder for northern spotted owls to find suitable habitat. On top of all that, the northern spotted owl is facing another threat, one that looks and sounds quite similar.
Damon Lesmeister: There's some very early records of barred owls going back decades, but really starting in the early nineties or so started to document this sort of odd bird that was very similar to northern spotted owls. They are about 18% larger. Of course, they're barred. The breast feathers are more like streaks rather than spotted. Barred owls inhabited the forests of the Eastern U.S. It's a forest bird, but they can use a lot of different types of forests, and they can survive in this quite well, but they also are more generalist in their diet. They have smaller home ranges. So that has an important effect because now you can get more barred owls in a smaller area. So they are generally a much more aggressive species. And so, all of these different characteristics of barred owls have really exacerbated the population declines of northern spotted owls.
Katy Milkman: So barred owls are bad news for northern spotted owls. They're bigger, more aggressive, and less picky about their diet. Damon and other scientists set out to understand exactly how big of an effect barred owls were having on their spotted owl cousins. To do that, they listen to the forest soundscape. They use passive bioacoustics, essentially deploying recording devices and microphones to capture the sounds of the animals without disturbing the animals themselves.
Damon Lesmeister: Sound is really important for spotted owls. It's a way that these animals are sort of leaking information into the environment about themselves. As of today, we have over three million hours of sound that we've recorded in the forest of the Pacific Northwest.
Katy Milkman: Sadly, things don't look good.
Damon Lesmeister: We estimate there are certainly fewer than 3,000 spotted owls that remain.
Katy Milkman: Less than 3,000 northern spotted owls for the entire Pacific Northwest region. Some areas have only one owl or a handful. It's particularly hard for the population to recover in those places.
Damon Lesmeister: There's definitely cause for concern in spotted owl populations. They're quite imperiled. We have plenty of evidence to suggest that they're in this extinction vortex at least in some areas where the population may be beyond being able to be sustained at its current level. There's so few spotted owls that remain.
Katy Milkman: In 2015, researchers decided they needed to take drastic action. They made the very difficult decision to cull a portion of the barred owl population.
Damon Lesmeister: The decision was made to use lethal removals. Dave Wiens of the USGS led this research into removing barred owls, and then we were working on our side to see what effects those barred owls' removals would have on spotted owl populations. So it was a collaborative project led by multiple different federal agencies.
Katy Milkman: The study took place from 2016 to 2019.
Damon Lesmeister: There were total of 2,485 barred owls removed during this study.
Katy Milkman: You may find this number distressing. I certainly do. 2,485 is a lot of owls, and it seems like a heavy-handed response. In fact, there have been several petitions against the practice, questioning the ethics of killing one animal to save another. And I certainly empathize strongly with the people who signed those petitions. Government conservationists in several areas have explored non-lethal ways to manage barred owl numbers like relocation. But unfortunately, those approaches generally don't work. As unappealing as it is, there's evidence that lethal removal of barred owls is effective.
Damon Lesmeister: At the beginning of the study, this was in the control area. We had 11 occupied territories by spotted owls. There was nothing happening with barred owls, just monitoring what's happening. At the end of the study, 2019, there was one occupied territory of those 11. So we had a territory-level extinction events, 10 of them, that happened during that time.
Katy Milkman: So in these control areas where no barred owls were removed, northern spotted owls only survived in one out of 11 locations.
Damon Lesmeister: In the treatment area, this is where barred owls were being removed. We started in 2015 with three occupied territories by spotted owls. So we started actually pretty low where the barred owls were ultimately going to be removed. And then by the time we got to the end of the study, 2019, there were six.
Katy Milkman: Six territories may not seem like a lot, but that's a 100% increase. Imagine what this would mean for the spotted owl population on a larger scale.
Damon Lesmeister: As hard as those decisions are to be made, there were the first signs that this could be helpful for spotted owls. Now you wouldn't say that we've had population recovery and those sort of things, because there's multiple things that need to happen in order to have a recovering population, but at least demonstrated through this study that the first step in population recovery, we have evidence that this can help us get there.
Katy Milkman: But even if this method helped a few northern spotted owls, it seems like there was a big cost, right? Barred owls live across much of North America and number in the millions. So it's hard to pin down an exact population number for these animals. But bird conservation organizations like Partners in Flight estimate there are about 3.4 million barred owls. Remember, 2,485 barred owls were removed during the study. That sounds like a lot, but it likely represented removing about 0.07% of the barred owl population, less than one 10th of a percent.
Damon Lesmeister: So you've got this invasive predator that is incredibly common, so we could remove many thousands of them, and with no real appreciable effect on the population. And so as spotted owls are continuing to decline, every one of those individuals are increasing in importance. In my view, the forest is less without spotted owls. And if society, if we choose, we want this species, we want this iconic bird to persist in the landscape, we will have to manage barred owls. That will absolutely be a necessity. We know that left alone barred owls will cause the extinction of spotted owls.
Katy Milkman: Damon Lesmeister is a research wildlife biologist with the U.S. Forest Service and holds courtesy faculty appointments with Oregon State University in the Departments of Fisheries and Wildlife and Forest Engineering Resources and Management. I have links in the show notes and at schwab.com/podcast.
The effort to save the northern spotted owl is a great example of how researchers kept two owl populations in perspective when they were faced with a really difficult decision. Removing nearly 2,500 barred owls for that study may sound like a lot, especially when it helps a far smaller number of northern spotted owls. And it definitely is. I don't want to minimize the loss of even one such majestic creature. But to make well-reasoned decisions, a conservationist needs to think not just about the absolute numbers of animals at stake, but about their population sizes. There are roughly 3.4 million barred owls compared to less than 3,000 northern spotted owls. Northern spotted owls represent only 0.09% of the combined populations.
Whatever your moral compass may tell you about the decision to cull barred owls, you can likely see the important logic of proportions behind it now that we've talked you through the math. But when you first heard just how many barred owls were being removed to protect a tiny number of spotted owls, your immediate reaction probably resembled mine. It sounds instinctively like a miscalculation, and that's the logic we're going to talk about today. Sometimes our minds should think proportionally, but we default to thinking in absolute numbers, and that can have a real cost whether we're trying to conserve an endangered species, consider the fuel efficiency of different cars, or make investment decisions.
Kelly Shue has studied the effect of non-proportional thinking on financial markets. She's a professor of finance at the Yale School of Management.
Hi Kelly. Thank you so much for joining me today.
Kelly Shue: Oh, thank you very much for having me. It's my pleasure to be here.
Katy Milkman: I am really excited to talk to you about non-proportional thinking, but I wanted to actually start by just asking you if you could define "non-proportional thinking." What does that term mean?
Kelly Shue: So non-proportional thinking is when investors think about stock price reactions to news in dollar units rather than in percentage units. So they should be thinking in percentage units. So, for example, if there's a good news that a skilled new CEO has arrived, they should think this firm's value should go up maybe 1% in response to this news. The wrong way to think about it, and that would be non-proportional thinking, is they would think, "Well, other times when firms had similar good news, they went up about a dollar. So this firm should also go up in value by a dollar per share." And the reason this is the wrong way to think about it is because firm share prices—and dollar units in general for shares—is basically meaningless. You could take the same firm, divide it into a different number of shares, and have a different share price.
So one way to think about it is suppose you had two identical firms, same size. One is trading at $20 per share, and the other is trading at $40 per share. The $40 per share firm has a higher share price simply because it's divided into half the number of shares. It would be wrong, if due to the good news of a new CEO arriving, you think, well, the $20 per share firm should go up by $1, and also the $40 per share firm should also go up by $1. That's the wrong way to think about it. That's non-proportional thinking. Because if you think that way, then the $20 per share firm by going up a dollar has gone up 5% and the $40 per share firm by going up a dollar has only gone up 2.5%. When really they should have the same percentage return to this good news.
Katy Milkman: That was a really clear explanation. Thank you for laying that out. I am definitely going to dive deep into your awesome research on non-proportional thinking in the stock market. Before I even ask you more details about that work, I wanted to talk a little bit about the underlying psychology, and I think you've argued that this feels closely related to denominator neglect or ratio bias. And I was wondering actually if you could explain what those biases are and if you'd be willing to talk a little bit about how they've been studied before and motivated this work.
Kelly Shue: Yeah. So our research on non-proportional thinking is motivated by this earlier research in psychology, talking about denominator neglect or ratio bias. That's the tendency of people to focus too much on the numerator and not enough on the denominator when they're thinking about things that are ratios or percents. So I think the most interesting and important example is actually in the medical context: There's a paper by Yamagishi in 1997 that finds that when cancer is described as killing 1,286 people out of 10,000—so that's basically a 12.8% kill rate—people think that's riskier than when you say, "This cancer kills 24 out of 100 people," even though that actually translates to a higher, 24% mortality rate. So people should be thinking about the mortality rate, 12% versus 24%, but instead they're drawn to the headline numbers of numerators: 1,286 people dying, or 24 people dying.
Katy Milkman: It's so interesting. And so could you talk a little bit more about the exact research you've done looking at what the implications of this are in the stock market and how you studied this in that context?
Kelly Shue: Sure. So we took this bias about denominator neglect and we thought, well, in finance and in the stock market, people should be thinking about returns. And "returns" is basically a ratio. It's the dollar change divided by the share price as of the previous day. But if people neglect the denominator and they only focus on the numerator, which is a dollar change, then what they would do is they might react in the same dollar units for stocks that are otherwise identical, but trading at different share prices.
So in particular, low-price stocks might have greater return reactions to news. And the reason it happens is suppose we think news should move stocks up by a dollar. That $1 divided by a lower share price is going to translate into a greater return movement for lower-price stocks. So we tested this in financial markets, and I think the clearest test that we do is we focus on what happens before and after stock splits.
Katy Milkman: A stock split is when if you own two shares of a stock, suddenly that would become four shares because everything's being divided in half. If you owned two shares worth $40 each, now you own four shares worth $20 each, that would be a stock split, an equal stock split. Am I summarizing that adequately?
Kelly Shue: Yes, that is exactly what a stock split is. Nothing about the firm has changed, but the number of shares doubles—share price is half of what it used to be. So a $40-per-share firm becomes a $20-per-share firm. And now we have double the number of shares. And what we would predict is, suppose investors engage in non-proportional thinking. Then in response to some good or bad news, they might have thought, "This news should move up the share price by $1." Well, that same news should move up the share price by only 50 cents after the stock split. But suppose investors don't realize that. They might think the same news should continue to move up the share price by $1 after the stock split. This will translate to much bigger return swings. So, in other words, bigger return volatility after the stock split. And that's exactly what we find in the data. Even for very large publicly traded firms, what we find is share-price volatility goes up by about 20 to 30% after a stock split, and it remains elevated persistently after that for months up to a year.
Katy Milkman: So by volatility, you're basically saying the share price just bounces around more than it used to because people are overreacting relative to the way they would've for this exact same situation at a different price point.
Kelly Shue: Exactly. And the reason we focus on volatility is the firm is continuously getting news. Some of the news is good, so the share price will move up. Some of the news is bad, share price will go down.
Katy Milkman: Like a big, new patent or something, earnings outperformed expectations, CEO has switched to someone who we think is brilliant, or something along those lines. It's so fascinating. And one of the things I wanted to ask you is why do you think it is that people are overreacting in this way or underreacting depending … and I guess we don't really know which is correct, but what do you think it is that leads to this particular non-proportional thinking bias?
Kelly Shue: I think we can go back to how information is displayed to investors. So if we look at The Wall Street Journal, The Wall Street Journal used to only publish dollar-price changes for stocks. So they would say some stock went up $1.50. You can figure out the percentage change, but you have to do that work on your own because what was most salient to its readers is the dollar change.
Katy Milkman: So basically the world feeds us this sort of denominator neglect by telling us numerators in the context of the stock market and probably in lots of other of contexts too. And that is a likely culprit for our focus. So if all of the world's newspapers and news shows and apps started telling us about returns in percentage terms, instead of in terms of the numerator, maybe that would reduce this bias.
Kelly Shue: I believe so. I think the tendency of news sources to report changes in value in terms of dollar units, I think that's a historical artifact. And if we instead always showed percentage movements, we would start thinking in the units that are showed to us on the news.
Katy Milkman: How did you get interested in studying this topic?
Kelly Shue: So I got into this topic because I grew frustrated by looking at the CNBC ticker and how it was always showing the dollar reactions to news, and I would have to do this calculation. My coauthor Rick Townsend and I, we were also talking about how silly it was that people were talking about the Dow index having the largest point drop in history when the Dow index is now at a much higher level than it was 10, 20, 50 years ago. So the fact it had a very large point drop is actually not a big deal. It had far larger percentage drops in its previous history.
Katy Milkman: That's fascinating. So basically you as a finance professor saw something that the communicators were getting wrong and then wondered, could this actually have implications for financial markets? And that's what led you to do the work.
Kelly Shue: Exactly.
Katy Milkman: So this is a podcast for people who are interested in making better choices, both when it comes to their finances and everyday life. So if we abstract away for a minute from thinking about buying and selling stocks, what do you think the takeaway is from understanding non-proportional thinking and denominator neglect might be more generally for people in their day to day lives?
Kelly Shue: I think the overall message, and this applies outside of finance, is people have to be very careful about thinking about problems in the right units. So, in financial markets where everything should be thought about in percentages or as a ratio, to think only in the numerator leads to a major mistake. Similarly, when you're thinking about the mortality risk of a cancer or any type of disease, you want to be thinking in percentage units, not just how many people died. You want to think about the population that was assessed over. But there's also what seems like the opposite bias. People should also be careful in a related context in which they should only be thinking about numerators.
So there's a famous example by Tversky and Kahneman that shows that people are more willing to travel 20 minutes to a different store to save $5 on a $15 calculator than they are to save $5 on a $125 calculator. And this is a mistake because what you should be comparing is your cost of traveling to a different store with your savings, which is $5. You should not think about $5 divided by $15 or $5 divide by $125. So I think people should try to think very carefully: "Should I be thinking about a ratio, or should I just be thinking about the raw dollar amount that I'm saving or the raw dollar amount that I'm getting?"
I think one variant of this that hits very close to home because I also do research on housing purchases, and I also recently bought a house myself, is I think people are kind of reluctant to do a little bit of effort to, let's say, make $10,000 more on a house sale or to save $10,000 on a house purchase because they reason $10,000, that's not very much relative to the total value of a house, which might be a hundred thousand dollars or more. But really you should be thinking about what's the cost of putting in a little more effort versus $10,000, just the level $10,000, and not think about it as a ratio.
Katy Milkman: Oh, I love that. That was a really good example. Kelly, thank you so much for taking the time to talk to me today. This has been really interesting.
Kelly Shue: Oh, thank you very much for having me on the show. This is my pleasure.
Katy Milkman: Kelly Shue is a professor of finance at the Yale School of Management. You can find a link to the paper on non-proportional thinking that she coauthored with Richard Townsend in the show notes and at schwab.com/podcast.
One thing to consider with stock performance is that it's not just what percentage the stock or even the entire stock market went up or down that matters. It's what's the impact on your portfolio. On the Financial Decoder podcast, Mark Riepe and his guests often discuss traps that make it difficult to evaluate your investments in aggregate. You can check out episodes like "How Should You Measure Your Portfolio's Performance?" and "Does Your Portfolio Need Adjusting?" at schwab.com/financialdecoder or wherever you get your podcasts.
As Kelly mentioned, it's important to think about problems in the correct units. While it's easy to focus on how many barred owls were lethally removed to protect spotted owls, the proportion was pretty small relative to the overall population. Similarly, a large point drop in the financial markets might rattle your nerves, but calculating the actual percentage drop may help you weather a downturn with less anxiety. Non-proportional thinking, or focusing on absolute numbers rather than percentages, is just one way we get mixed up when we should be carefully calculating and comparing ratios.
In another study that demonstrates how mixed up people get when we need to make simple proportional calculations, Rick Larrick and Jack Soll, two Duke professors, proved that posting a vehicle's fuel efficiency in gallons per mile rather than miles per gallon could help consumers make better decisions about car purchases and environmental impact. That's because the improvement in a car's gas mileage doesn't scale linearly in miles per gallon, but we think it does. Most people think buying a new car that improves your gas mileage from 34 to 50 miles per gallon will save more gas over 10,000 miles driven than buying a new car that improves gas mileage from 18 to 28 miles per gallon.
50 minus 34 equals 16, which is bigger than 28 minus 18, which equals 10. People are just doing the simple subtraction problem, but moving from 34 to 50 miles per gallon isn't a simple subtraction problem. It saves only 94 gallons over 10,000 miles, while going from 18 to 28 miles per gallon saves 198 gallons, more than twice as much. We think these ratios are linearly related when in fact they aren't. Gallons per mile, though, can be compared in the straightforward way our brains expect, which is why it's a better metric. A simple lesson from all of this is that we aren't very good at figuring out when to focus on numerators, when to focus on denominators, when the numbers we're working with can simply be compared linearly, and when we need to take the inverse of a ratio to allow for simpler linear comparisons. We get all mixed up the minute there are relevant proportions in our line of vision. So what can you do?
Before reacting to any bit of news that comes in numerical form, whether it's bad news about the price of a stock, the miles per gallon you'll get if you trade in your car, or the number of people who've died from a disease outbreak, remind yourself to stop and think carefully about the relevant quantity, rather than acting on your gut reaction. Do you need to consider the denominator? If you want to make comparisons, are the numbers in the right units, or might you need to invert them? Don't be embarrassed to slow down and take out a pad of paper to jot down some notes. Our intuitions about numbers often lead us astray. Thinking slowly and logically can save you from meaningful mistakes. When in doubt, running your calculations by a few thoughtful friends or colleagues as a sanity check to be sure you haven't neglected something important is a great idea.
You've been listening to Choiceology, an original podcast from Charles Schwab. If you've enjoyed the show, we'd be really grateful if you'd leave us a review on Apple Podcasts. You can also follow us for free in your favorite podcasting app. And if you want more of the kinds of insights we bring you on Choiceology about how to improve your decisions, you can order my book, How to Change, or sign up for my monthly newsletter, Milkman Delivers, at katymilkman.com/newsletter.
Next time, the riveting story of a near disaster at the height of the Cold War. And you'll hear about how stress affects decision making from psychologist Modupe Akinola. I'm Dr. Katy Milkman—talk to you soon.
Speaker 8: For important disclosures, see the show notes or visit schwab.com/podcast.
