A boy who ran to the piano when he heard his parents come home became a father who runs to the nursery when he hears his wife come home. The mathematics of being watched explains why, what it costs, and why it reaches from cleaner fish to fund managers, with a test on the stock market that no one could run until the rules change.
When the person who judges you gives a warning before arriving, what they see is your performance, and the performance teaches them nothing. A watcher who arrives at random, with no warning, sees the true share of your time; a watcher who is heard coming sees whatever you rush to show. In the language of queueing theory, random arrivals see time averages (Wolff, 1982). Warned arrivals see the sprint.
The same arithmetic says why the habit survives. If praise follows what is seen, the reward for one more hour of the real thing is one minus the share of visits that come with a warning. With a perfect warning bell it is zero. And the fear that started it never fades, because a fear can only be unlearned on a trial, and a sprint never lets the trial happen.
This is my story twice over, once at a piano bench when I was a boy and once at a nursery door this year, and it turns out to be the story of a great deal of life: of fish that behave better when other fish are watching, of patients who take their pills most faithfully around the doctor's appointment, of drivers who brake for the speed camera and speed up after it, and of fund managers who tidy their portfolios before the quarter's holdings are printed.
That last one we can test. We measured the stock market's own sprint: since 2017, small companies have done about 30 basis points better than the S&P 500 on the last trading day of a quarter than on an ordinary month-end, and given back about as much the next day. It is a small habit, and two years carry much of it. It exists in a world where funds' holdings are made public once a quarter. In 2024 the Securities and Exchange Commission adopted a rule to make them public every month, starting with the largest fund families on November 17, 2027. Then, in February 2026, it proposed to keep publication quarterly after all. If the parents start coming home every month instead of every quarter, the model says the quarter-end sprint should fade and ordinary month-ends should start to look like quarter-ends. If the Commission keeps the old schedule, the experiment is cancelled, and nothing should change. We set the test down here, with its dates, before anyone can know the answer, including the regulators.
My son Solomon arrived this year, and with him came a month off from my day job. Technically I am on sabbatical. That month gave me the time, at last, to become the writer I had always dreamed of being, and to put to work the nearly two hundred mathematical models I had carried in my toolkit for thirty years without really using them. Vista Research, its Library of decision models and every one of these inquiries are possible only because Solomon was born. In a sense, he is the co-author of all of them.
I have spent much of that month on this work, with great joy and an incredible feeling of accomplishment and productivity, especially now that so much of the process runs on its own. I also want to spend meaningful time with my son, and I do, and I enjoy it. The trouble is a matter of timing. Whenever I hear my wife coming home, I drop everything, slam the laptop closed and run to the nursery. I like being there anyway. But I run at that moment because I want her to see me there. Underneath it is a fear: that if she comes home and finds me working, I will be criticized for not being more fatherly. (I just realized, while writing this, that before Solomon came I often found myself running to look as if I were doing the dishes or tidying up when the garage door opened.)
I wondered where that fear came from. Then I remembered the piano.
The market half of this inquiry came from a rule. In 2024 the Securities and Exchange Commission voted to make mutual funds' holdings public every month instead of every quarter, and in February 2026, in a proposal summarized in the Commission's own fact sheet of February 18, 2026, it suggested taking that back. A rule about how often the parents come home was too good to leave alone.
When I was a boy I was supposed to practice the piano every day and be ready for my weekly lesson. I developed a reflex. Whenever I heard my parents coming home, I ran to the piano and started playing, so that it would look as if I had been practicing the whole time they were away. I had a rough idea of how much I was supposed to practice, and I took that number seriously, in my way. I simply scheduled the practice for the moments when my parents could see it.
I hated criticism, and I had a conditioned fear that if they didn't see me practicing I would be told I should be spending more time at the piano. So I gave my parents what they could observe. It worked, if the goal was to avoid a lecture. It was not my parents' goal.
What makes this a little funny, and a little tender, is what happened next. The boy who sprinted to the piano became a serious musician on another instrument. As I wrote in my book, The Scholars' Treasure, "there was always my clarinet. I was so good at it, so driven to practice and perfect that craft" (Chapter 3, page 40). I became the Concert Master of the All-State Wind Ensemble (Chapter 6, page 73) and played my way into the New Jersey Governor's School for the Arts in 1988 (Chapter 9, page 110). Nobody had to be coming up the driveway. And years later, on a sabbatical in Santa Fe, I wrote that "music was its own reward. Performing, even merely practicing on my clarinet, brought balance and joy to my frenetic entrepreneur's life" (Chapter 9, page 110).
So I have known both kinds of practice: the kind you do for the person who can see you, and the kind you do because it makes you feel alive. The piano taught me the first. The clarinet taught me the second. And this year, at fifty-five, with a baby down the hall, I caught myself doing the first kind again, with fatherhood as the instrument.
There is a long tradition of distrust toward performances of this kind. "Be careful not to perform your righteous acts before men to be seen by them," Jesus told the crowd on the mountain (Matthew 6:1, Berean Standard Bible), and he promised a reward from "your Father, who sees what is done in secret" (Matthew 6:4). I don't think the Sermon on the Mount was written about piano practice. But it does say plainly what the mathematics below says with symbols: an act done for the watcher is a different act from the same act done for its own sake, and only one of them is any evidence of the heart.
Here is the problem as a model. Suppose I spend a share p of my day with Solomon and the rest at the laptop. My wife comes home at various times and looks. What fraction of her looks find me in the nursery?
If she arrives at random and I have no warning, the answer is p, on average. This is one of the most useful results in the theory of queues, proved in general by Ronald Wolff in 1982 and known by the cheerful acronym PASTA: Poisson Arrivals See Time Averages. An observer who arrives at moments that carry no information about the system sees the system as it is on average. A random inspector of a factory sees its true share of idle machines; a random caller to a busy help line hears the true share of busy signals; a random wife sees the true share of fatherhood.
Now add the warning. Suppose a fraction q of her arrivals give me notice, the sound of the garage door, and that on those arrivals I always make it to the nursery before she does. Then the share of looks that find me there is:
observed share = q + (1 - q) x p
where p is the true share of time and q is the share of arrivals that come with a warning. Take my illustrative 30%. With no warning, q = 0, she sees 30%. With warning half the time, she sees 0.5 + 0.5 x 0.3 = 65%. With warning every time, q = 1, she sees 100%, whatever p is. The line goes flat. Flat lines are bad news. A flat line is the mathematical picture of a measurement that has stopped measuring: every truth, from a doting father to an absent one, produces the same 100%.
Two consequences follow, and both are cheerful. The first is that a partly warned observer can still learn the truth, if she knows how often she warns. Rearranged, p = (observed - q) / (1 - q). Seeing 65% with warning half the time, she can infer (0.65 - 0.5) / 0.5 = 30%, exactly. My wife, if she wanted to, could defeat my entire strategy by coming home quietly a few times and doing a little algebra. The second is that it does not take many surprise visits to learn a great deal. A random observer's estimate of p after n looks has a standard error of the square root of p x (1 - p) / n. For p = 30%, that is about 23 points after four looks, 13 points after twelve, and 6 points after a year of weekly visits. A warned observer learns nothing, no matter how many times she looks.
George Orwell understood the other end of this line in 1949. In Nineteen Eighty-Four, the telescreen can watch you at any moment, and "there was of course no way of knowing whether you were being watched at any given moment" (Part One, Chapter One). That is q driven to zero by design: if the watcher's arrivals are invisible, the only safe strategy is to behave as if watched all the time. Jeremy Bentham had proposed the same machine in brick in 1791, a prison he called the Panopticon, in which the inmates could never tell whether the inspector in the central tower was looking. Orwell turned it into a nightmare. Bentham, for his part, had his own body preserved and displayed in a glass case at University College London, and in July 2013 it was wheeled into a meeting of the college council and recorded in the minutes as present but not voting. The man who designed the perfect watchtower became the most watched figure on campus. My household had turned his idea inside out: our version of the telescreen announces itself with the sound of a garage door.
Why would anyone, me included, keep sprinting? Because of what the sprint is paid. Suppose the praise I receive, or the criticism I avoid, depends on what my wife sees. Then the payoff for raising p, actually spending more time with my son, is the slope of the line above:
d(observed share) / dp = 1 - q
With no warning, every extra point of real fatherhood is fully rewarded. With warning half the time, half of it is. With warning every time, the reward for more real fatherhood is exactly zero, and the whole reward goes to the sprint. That is Steven Kerr's classic paper of 1975, "On the Folly of Rewarding A, While Hoping for B," in one line of calculus, and it is the heart of the multitask model of Bengt Holmström and Paul Milgrom (1991), which is the entry our Library calls "The plan rewards what it measures": when a person does several things and only some of them can be seen, effort flows to the ones that are seen.
Offices are full of pianos. In 1994 I was a twenty-two-year-old management consultant at Price Waterhouse, working for our client Sony Music (I had asked the partner to put me on that engagement, as I wrote in The Scholars' Treasure, Chapter 3, page 33). We always, always left our suit jackets on the backs of our chairs, when we went out to lunch and even when we went home. A jacket on a chair is a consultant at his desk, as far as anyone walking past can tell. One of my colleagues went further. He programmed an emergency button on his laptop that brought up a spreadsheet instantly, even in the middle of a game of Tetris. One day the boss walked in. The button was pressed. A long business conversation took place. The boss started to walk out, then turned around and said, "By the way, how's the spreadsheet looking?" He knew perfectly well we weren't working on any spreadsheet.
That boss had done my wife's algebra. He knew that his visits came with a warning, he discounted what he saw accordingly, and with one question he let us know that the sprint had fooled nobody. It may be the gentlest performance review in the history of consulting.
Researchers have since measured the jacket on the chair. Kimberly Elsbach, Daniel Cable and Jeffrey Sherman (2010) found that managers judge employees they simply see at their desks, especially early and late, as more dependable and committed, for nothing more than being seen. In June 2024 Wells Fargo disclosed, in filings with the brokerage industry's regulator, that it had fired more than a dozen employees after reviewing allegations of the "simulation of keyboard activity creating impression of active work," the work of gadgets that wiggle a mouse so a laptop looks busy. Paul Oyer (1998) showed that sales across American industry bunch at the end of fiscal years because of how salespeople's quotas are paid, and Ian Larkin (2014) caught enterprise software salespeople timing deals to their quota periods, at a cost to their employer in discounts. Each is the same equation. When the watcher arrives on a schedule, people practice on the schedule.
The leader's version of my wife's algebra is the oldest management advice there is: go and look, unannounced, on an ordinary day. Toyota calls it genchi genbutsu, go and see for yourself, and its managers walk the floor where the work is done, the gemba. Hewlett-Packard called it management by walking around (Peters and Waterman made it famous in 1982). The point of both is q: an inspection announced a week ahead gets you a Potemkin village, the painted village facades that Grigory Potemkin is said to have built to impress Catherine the Great on her tour of Crimea in 1787. Historians now think the story was largely an exaggeration spread by his rivals, which only makes it a better parable. The story lasted two centuries because everyone who has ever been inspected knew it was true even if it wasn't.
The deeper question is why the reflex outlived the piano by so many years. The answer came from psychology in 1947, when O. H. Mowrer proposed what became the two-factor theory of avoidance. First, a fear is learned by association: a sound (the garage door) comes to predict something unpleasant (criticism). Second, an escape from the feared situation is rewarded by relief, and so it is repeated. The trap is that the escape prevents the test. If I always sprint, I never find out whether my wife would actually have criticized me for working. The fear is never disconfirmed, and so it never fades. It just waits.
The simplest mathematics of learning makes this exact. In the model of Robert Rescorla and Allan Wagner (1972), the strength of an association V changes only on a trial, by a fraction alpha of the surprise:
V(next) = V(now) + alpha x (lambda - V(now))
where lambda is what actually happens (1 if the criticism comes, 0 if it does not) and alpha is how fast one learns. If I sprint every time, there is no trial, and V stays exactly where my childhood left it. If I stay at the laptop when the door opens, and nobody criticizes me, then lambda = 0 on every trial and the fear shrinks geometrically: V(n) = V(0) x (1 - alpha)^n. With alpha = 0.2, an illustration rather than a measurement, the fear falls to 80% after one homecoming, below half after four, and to about a tenth after eleven.
As I wrote in The Scholars' Treasure, at a fireside chat at Northwestern in 1991, Professor Bond, our Resident Master and a professor of the History and Literature of Religions, told us that "your intellect, the knowing parent, must govern the mind which, like a child, always has negative and distracting thoughts," and asked, "What does FEAR stand for? False Emotions Appearing Real!" (Chapter 1, pages 4 to 5). In the nursery I am now, quite literally, the knowing parent, and the child with the negative and distracting thoughts is still, apparently, me.
So the prescription from the model is wonderfully unglamorous. Let her catch me working. Say hello from the laptop. Run the trial. And the prescription from the first model is the same one from the other side: tell her about the piano, so that she knows q and can do the algebra, and agree on time with Solomon that we choose together, which carries a signal no sprint can fake.
That last point has its own branch of biology. Amotz Zahavi proposed in 1975 that a signal is believed only if it is costly to fake, which is why a peacock's enormous tail impresses a peahen: a weak bird could not carry it. A sprint to the nursery costs me nothing and so tells my wife nothing. An afternoon with him that we planned together costs me an afternoon of writing, and so it means something. Our Library calls this "What they said versus what it cost them."
Once I saw the pattern, I found it everywhere, and the best examples are funnier than mine.
At Newcastle University in 2006, Melissa Bateson, Daniel Nettle and Gilbert Roberts taped a picture above the honesty box where staff paid for their coffee and tea, alternating each week between a pair of eyes and a picture of flowers. In the weeks with the eyes, people paid 2.76 times as much for their milk. A photocopied pair of eyes nearly tripled the takings.
Six years later the same group put up signs with staring eyes and the words "Cycle thieves, we are watching you" over the bicycle racks on campus. Over the following year, thefts at those racks fell by 62%, and rose by 65% at racks without signs. The thieves were not reformed. They moved around the corner, which is a lesson every regulator should keep by the bed.
In Botswana, lions and leopards like to ambush cattle from behind. A team led by Cameron Radford worked with farmers to paint eyes on the rumps of a third of the cattle in fourteen herds, crosses on another third, and nothing on the rest, 2,061 animals in all. After four years, reported in 2020, predators had killed fifteen of the plain cattle and four of the crossed ones. Not one of the cattle with eyes on their backsides had been killed. In the Sundarbans of India and Bangladesh, where tigers also attack from behind, forest workers took to wearing face masks on the backs of their heads in the 1980s, as The New York Times reported in 1989. For a while the tigers seem to have been fooled. Then, by later accounts, they caught on, which is the other half of the lesson: a performance works only as long as the watcher believes it.
The ocean has sprinters too. The cleaner wrasse is a small fish that eats parasites off larger fish, but it would rather bite off a mouthful of its client's nourishing mucus, which the client does not enjoy. Redouan Bshary and Alexandra Grutter showed in Nature in 2006 that cleaners cheat less when other potential clients are watching. The fish has a reputation to keep. And Nathan Emery and Nicola Clayton found that western scrub-jays who were watched while hiding food will come back and hide it again somewhere else, but only if they have stolen food themselves. It takes a thief to know one, and evidently it takes a sprinter to know that the watcher's view can be managed.
Medicine has the best name for my condition. Joyce Cramer and her colleagues gave patients pill bottles whose caps recorded every opening, and reported in 1990, in a paper titled "Compliance declines between clinic visits," that patients took their medicine most faithfully around their appointments and less faithfully in between. Doctors call it white-coat compliance. It is the sprint to the piano, measured in pills. Blood pressure has the same problem in both directions: white-coat hypertension is high only in the doctor's office, and masked hypertension is normal in the office and high at home. The cure was a cuff that takes readings around the clock, an observer that never gives warning. Sport learned the same lesson the hard way. When athletes could predict drug tests, they timed their doping around them. Sports bodies began random testing out of competition around 1990, and the anti-doping agencies that came later made no-notice testing the rule, with athletes required to say in advance where they can be found.
The open road has its version. Drivers brake hard just before a fixed speed camera and speed back up just after it, so that speeds along the road trace a V with the camera at its point. Traffic engineers call it the kangaroo effect, and their answer is enforcement that cannot be anticipated: cameras that move, or that measure the average speed over a whole stretch of road. Even the air has a version. Many of America's particle-pollution monitors sampled only one day in six, on a published schedule, and Eric Zou (2021) found that the air was measurably cleaner on the days the monitors were running. Physics has the most beautiful version of all. Under a strobe light, a spinning wheel can seem to stand still or even turn backward, because the light flashes in step with the spokes. If you look in step with a cycle, you see a false steady picture. Engineers call it aliasing, and the cure, once again, is to sample at times the system cannot anticipate.
Even mythology anticipated the problem. Hera set the giant Argus, who had a hundred eyes, to watch over Io. Hermes lulled him to sleep with music and stories until every eye closed, then killed him, and Hera set the hundred eyes in the tail of the peacock (Ovid tells it in the first book of the Metamorphoses). So the most famous honest signal in biology carries the eyes of the most famous watchman who fell asleep on the job.
There is a gentler version on every dollar bill. Since 1935 the back of the $1 bill has carried the Eye of Providence above an unfinished pyramid. Every dollar you have ever spent has been watching you spend it. And most of us met our first warned observer before we could read. A popular song of 1934, "Santa Claus Is Comin' to Town," told children that Santa keeps a list and checks it, and in 2005 the book The Elf on the Shelf gave him a field agent who reports every night from the bookshelf. In 2014 two Canadian education scholars, Laura Pinto and Selena Nemorin, asked in all seriousness whether the elf was preparing a generation of children to accept surveillance. Children have window-dressed every December since.
Not every famous case survived checking, and I want to be honest about one. The Hawthorne effect, the claim that workers at Western Electric's Hawthorne plant in the 1920s worked harder simply because they were being studied, became a fixture of management books. When Steven Levitt and John List went back to the original data in 2011, they found the evidence much weaker than the legend. And the watching-eyes studies are mixed when pooled: a 2017 set of meta-analyses found that pictures of eyes do not make people more generous in laboratory games, while a 2019 review by Keith Dear, Kevin Dutton and Elaine Fox, pooling fifteen experiments, found that eyes cut the risk of littering, theft and other antisocial behavior by about 35%. Being watched changes behavior. It does not always change it for the better, and it often only moves it somewhere else.
The lessons from the nursery and the fish tank are the same lessons a chief executive needs, and I find them easier to remember with the story attached.
The first is to look on ordinary days, at times nobody can predict. A board that sees the business only at scheduled reviews sees the sprint. A random sample of Tuesdays, a walk through the plant without an itinerary, a customer call picked from the log at random, each restores the observed share to the true one. PASTA is the theorem behind the gemba walk.
The second is that the fear produces the performance, so lowering the fear raises the truth. Amy Edmondson, studying eight hospital units in the 1990s, found that the units with the best leadership and working relationships had higher rates of detected drug errors, not lower. The better units were not making more mistakes. Their nurses were not afraid to say so. In units where people fear criticism, the leader sees the stage and never the back room.
The third is to reward what you want, and say so. Kerr's folly is cured by measuring the real output, and where it cannot be measured, by agreeing openly on what counts.
The fourth is to value the costly signal. A slide deck is a sprint. A commitment that would be expensive to break is evidence.
And the fifth, which I am still learning, is to tell people about your own pianos. Once the watcher knows her q, she can do the algebra; once I stop sprinting, I can run the trial; and the nursery goes back to being the place I go because I want to be there.
Now to money, which has its own piano and its own parents. Mutual funds report their holdings to their investors and to the Securities and Exchange Commission on a schedule, and for two decades that schedule has been the end of the quarter. The investor who reads the report sees which stocks the fund owned on that day, and only that day.
Finance found the sprint long ago. Josef Lakonishok, Andrei Shleifer, Richard Thaler and Robert Vishny reported in 1991 that pension fund managers sold their losing stocks before the end of the year, so that the holdings their clients saw looked smarter than the year had been. They called it window dressing. Mark Carhart, Ron Kaniel, David Musto and Adam Reed found something cheekier in 2002: fund managers buying their own holdings on the last day of the quarter, pushing up the closing prices that set the fund's reported return, with the gains reversing the next morning. Their paper is called "Leaning for the Tape." Vikas Agarwal, Gerald Gay and Leng Ling (2014) found that the funds that dress their windows tend to be the unskilled ones with poor past returns, and that they do worse afterward, so the performance costs their investors money.
We asked whether the market's sprint is still visible today, with the simplest tools. We compared small companies with large ones, the iShares Russell 2000 fund (IWM) against the S&P 500 fund (SPY), on the last trading day of March, June and September, and on the other month-ends of the year, leaving out December, when tax selling muddies everything. If managers lean on small, thinly traded stocks to dress their quarters, small caps should look better on quarter-ends than on ordinary month-ends, and give it back the next day.
From 2003 to 2016, at the level of these index funds, they did not. On quarter-ends small caps did 9 basis points worse, relative to the S&P 500, than on other month-ends, which is noise. From 2017 to 2026 the picture changed. On the last day of March, June and September, small caps did about 6 basis points better than the S&P 500; on other month-ends they did about 24 points worse. The quarter-end lift was about 30 basis points (t-statistic 2.4; a bootstrap 95% range of roughly 6 to 54 points), and the next day small caps gave back about 32 points more after a quarter-end than after an ordinary month-end. The smallest companies (IWC) and the S&P 600 (IJR) show the same shape.
We would be poor scientists, and poor sons, if we stopped there. The recent lift leans heavily on two years. Without 2020, it is about 17 points; without 2020 and 2024, about 11, and no longer distinguishable from zero. The medians are smaller than the means. What is steady is the direction: the lift was positive in 10 of the 12 years since 2014, and in 3 of the 10 years before. The honest reading is a small, real-looking habit with a loud spring in it.
There is also an innocent suspect, and the interview search found it for us. Index providers rebalance on calendars of their own. The Russell indexes, the benchmark for small companies, are rebuilt once a year at the close on the last Friday of June, and in 2013, 2019 and 2024 that Friday was the last trading day of the quarter. Russell moved its updates of share counts from monthly to quarterly in 2017, close to when our measure turned. And MSCI's quarterly index reviews take effect at the ends of February, May, August and November, which are exactly the ordinary month-ends we compare against. Leaving June out altogether, the lift from 2017 to 2026 is still about 34 points (t-statistic 2.4), so the Russell rebuild is not the whole story. But part of what we measured may be the index providers' calendar rather than the fund managers' vanity. That is exactly the kind of finding that needs a fresh test rather than a longer argument.
I will confess the real reason for this inquiry. A small family drama is not, by itself, a reason to publish research for investors. But the market is about to run the experiment that my wife could run in our kitchen.
Mutual funds and most exchange-traded funds report their holdings to the Securities and Exchange Commission on Form N-PORT. Under the rules in force today, funds report every month's holdings, but only the last month of each fiscal quarter is made public, sixty days later. For many funds the fiscal quarter is the calendar quarter, though not for all. In August 2024 the Commission amended the form so that every month's report would be filed within thirty days and made public sixty days after the month ended. In April 2025 it pushed the start back two years, to November 17, 2027 for the largest fund families, those with $1 billion or more, and to May 18, 2028 for the rest. Then, on February 18, 2026, it proposed to keep publication quarterly after all, and to give funds more time to file. The comment period closed on April 24, 2026. As far as we can find, the Commission has not decided.
The parents, in other words, announced that they would start coming home every month, postponed it, and are now thinking about not coming home at all. If I had tried that schedule on my piano teacher, my parents would have had something to say.
The model makes a clear prediction. Today the warned observer arrives four times a year, and the sprint, if it exists, is timed to those four arrivals. When the observer arrives twelve times a year, a manager who wants to look good must look good at every month-end, or not bother. Either way the quarter-end loses its special status. The gap we measured between quarter-ends and ordinary month-ends should shrink toward zero, either because quarter-ends calm down or because ordinary month-ends start to dress up.
The difficulty is noise. The day-to-day spread between small and large companies is large, and the standard error of the quarter-end lift measured over three years of data is about 22 basis points, over five years about 17. So we set the test down with its uncertainty in plain view, and with a third outcome, which is that we will not be able to tell. We would rather say that now than discover it later.
Almost every piece of this story has been studied, and studied well. The watching-eyes experiments number in the hundreds. PASTA is a textbook theorem. Window dressing has been documented since 1991, and the effect of how often funds disclose their holdings has been studied at least since 2004, when the Securities and Exchange Commission moved funds from reporting twice a year to four times a year (Vikas Agarwal, Kevin Mullally, Yuehua Tang and Baozhong Yang used that change in 2015 to study what more frequent disclosure does to the stocks funds hold and to the funds' own returns).
We are not the first to guess what monthly publication would do. Two days after the rule was adopted in 2024, the team at Real Investment Advice predicted that it "will reduce some volatility and odd trading at quarter ends and distribute it to month ends." David Musto showed in 1999 that money market funds dress their portfolios for the dates on which they are disclosed. Our prediction agrees with both in direction.
What we add is the reason, in the language of queues: a watcher who arrives on a known schedule sees a performance, and the reward for the real thing is one minus the share of visits that come with a warning. We add a measurement of how large, and how fragile, the quarter-end lift is today, a dated test with a third outcome for "we could not tell," and the twist that the regulator may cancel the experiment before it starts. If someone has set down this test before us, we will credit them gladly and add our numbers to theirs.
For anyone judging a manager, a company or a team, the lesson is that a scheduled snapshot is a performance. Read the monthly holdings when they become public, look at the week after the quarter as closely as the quarter, and treat any number that is best on the day it is measured with a little affection and a little suspicion. A fund whose returns jump on the last day of the quarter and fall the next morning is telling you how it spends the other days.
For the funds themselves, more frequent disclosure has a cost the literature has measured: others can trade against your positions sooner. Monthly disclosure would help investors see the truth and would cost some managers their privacy. Both sides of that argument are in the Commission's record, and both are real.
For anyone managing people, including a new father managing himself, the investment idea is cheaper: surprise visits, honest rewards, low fear and costly signals produce better information than any number of scheduled inspections.
The questions above are best answered by people who have done the work, and finding and asking them is what Vista is really about. We would most like to hear from these.
In general, did anyone talk about the closing prices of the fund's own holdings on that day, and what would public monthly holdings change about how a desk thinks about month-ends?
The answer that would change the view"Nobody touched the close; what you are measuring is index and pension rebalancing, and it will not care how often holdings are published."
What patterns did quarter-end surveillance look for, how often did it find them, and did anything change when holdings began to be published four times a year instead of twice?
The answer that would change the view"Marking the close was rare and caught quickly; the dressing that matters happens in which stocks are held, not in their prices."
In general, how much of the flow on the last trading day of a month or quarter came from rebalancing rules, and has its timing changed since 2014?
The answer that would change the view"Quarter-ends became special for us after 2014 because our rules changed, which would explain your lift without any window dressing."
When observation in medicine, sport or the workplace moved from scheduled to continuous, how fast did the performance around the old dates fade, and did it move to the new ones?
The answer that would change the view"It took years, not quarters, and most of it moved to the new dates instead of disappearing."
And, informally, any parent who has ever run to a piano.
We will score this inquiry on January 31, 2031, with daily closes through December 31, 2030, and publish the result whether it flatters us or not. The tests apply only if monthly publication of fund holdings begins for the largest fund families by the end of 2027, as now scheduled. If the Commission keeps quarterly publication, the tests are void, and we will report the same numbers anyway, as a reading of the habit when the warning schedule does not change. The window runs from January 2028 to December 2030: six quarter-ends (March and September; June is left out because the Russell rebuild can fall on it) and twenty-four ordinary month-ends. With about 26 basis points of noise in a three-year measure, the bands below are wide on purpose.
Two or three passes and the model gains ground; one, too early to say; none, and the quarter-end lift never had much to do with who was watching.
The bet. A watcher who gives warning sees a performance and learns nothing; a watcher who arrives at random sees the truth. That is true of parents, spouses, bosses, doctors, regulators and the investors who read a fund's quarterly report.
The payoff. In a family, the payoff of knowing this is a conversation and a few honest afternoons. In a market, it is a test: when funds' holdings become public every month, the quarter-end should lose its special shine.
Our read. The sprint is real, ancient and widespread, it is cheaper to fix than to perform, and in markets it is small and measurable.
What settles it, and when. First, whether the Commission adopts its 2026 proposal or lets monthly publication begin on November 17, 2027. Then three years of month-ends, scored on January 31, 2031. In the nursery, it will be settled sooner: at the next homecoming.
The model's advice for the next time I hear the door is simple. Stay where I am, say hello, and tell my wife about the piano. Then go and see my son, because I want to.
Because the reward follows what is seen. If a fraction q of an observer's arrivals come with a warning, the share of looks that find the performance is q + (1 - q) p, where p is the true share of time spent on the real thing, and the reward for one more point of the real thing is 1 - q. With a warning every time, the observer sees the performance whatever the truth, and the reward for the real thing is zero.
It is a result in the theory of queues, proved in general by Ronald Wolff in 1982 (PASTA). An observer who arrives at random moments, carrying no information about the system, sees the system's true long-run average. A random inspector sees the true share of idle machines; a random visitor sees the true share of time spent practicing. Warned arrivals break the result.
Because avoidance prevents the test. In O. H. Mowrer's two-factor theory, fear is learned by association and the escape is rewarded by relief. In the learning model of Rescorla and Wagner, an association changes only on a trial: if a person always escapes, the fear is never disconfirmed and stays where it started; if the feared moment comes and nothing bad happens, the fear falls by a fixed fraction each time.
Arranging a portfolio, or its closing prices, to look good on the date it is reported. Lakonishok, Shleifer, Thaler and Vishny (1991) found pension managers selling losers before year-end; Carhart, Kaniel, Musto and Reed (2002) found fund managers pushing up their own holdings' closing prices on the last day of the quarter, with the gains reversing the next day; Agarwal, Gay and Ling (2014) found that window dressers tend to be less skilled and do worse afterward.
The observer model says it should: if holdings become public every month, the quarter-end loses its special status, and small caps' quarter-end lift over the S&P 500, about 30 basis points relative to ordinary month-ends from 2017 to 2026, should shrink. The SEC's 2024 rule would start monthly publication for the largest fund families on November 17, 2027, but in February 2026 the SEC proposed to keep publication quarterly. This inquiry sets down the test and scores it on January 31, 2031, if monthly publication begins.
The observer model, the reward slope, the learning curve and the standard errors are computed in model.py from the formulas stated in the text, with illustrative inputs (a true share of 30%; a learning rate of 0.2) that are labeled as illustrations wherever they appear. The market figures use daily closing prices of IWM, IWC, IJR and SPY from a licensed data feed, adjusted for dividends and splits, from September 2003 (August 2005 for IWC) to October 6, 2026. For each month-end, the spread is the small-company fund's daily return minus SPY's, in basis points. Quarter-ends are the last trading days of March, June and September; ordinary month-ends are the last trading days of the other non-December months; December is excluded. The lift is the difference in mean spreads, with a Welch t-statistic and a bootstrap of 4,000 resamples (fixed seed); the next-day figures use the first trading day after each month-end. Only these aggregates are published; the prices themselves are not. Every quotation from The Scholars' Treasure is checked against the book, with chapter and page.
| Input | Value | Source |
|---|---|---|
| Illustrative true share of time (p) | 30% | An illustration; stated as such in the text |
| Learning rate in the fear model (alpha) | 0.2 | An illustration (Rescorla and Wagner leave it to the case) |
| Funds compared | iShares Russell 2000 (IWM), iShares Micro-Cap (IWC), iShares Core S&P Small-Cap (IJR), SPDR S&P 500 (SPY) | Daily closes adjusted for dividends and splits, licensed feed; only aggregates published |
| Sample | September 2003 (August 2005 for IWC) to October 6, 2026 | Same |
| Quarter-ends | Last trading day of March, June and September; December excluded (tax selling) | Our definition |
| Ordinary month-ends | Last trading day of the other non-December months | Our definition |
| Statistics | Difference in means, Welch t-statistic, bootstrap of 4,000 resamples with a fixed seed | model.py |
The model (model.py), its output and the facts files behind each input are kept with the inquiry's working files; the arithmetic in the text was checked against them.
This inquiry is research, not investment advice. It states what the data and models show under labeled assumptions; nothing here is a recommendation to buy, sell or hold any security, and the decision belongs to the reader. As of October 4, 2026, Russ W. Rosenzweig, Vista's founder, owns shares of the SPDR S&P 500 fund (SPY) and the iShares Russell 2000 fund (IWM), both measured in this inquiry, and holds options on SPY; he owns no shares of Wells Fargo, Toyota or HP, named in the stories, nor of the iShares Micro-Cap (IWC) or Core S&P Small-Cap (IJR) funds. Holdings through mutual funds and exchange-traded funds are not counted. Several passages were clarified on October 8, 2026, the day of publication, after the search for interview candidates turned up new sources: the index providers' rebalancing calendars that fall on some of the days we measure, with the checkpoint's quarter-end tests moved to March and September only (from March, June and September, with thresholds of 34 and 40 basis points in place of 30 and 32) before any of the test data exist; fund holdings made public by fiscal rather than calendar quarter; random drug testing begun by sports bodies before the anti-doping agencies; and Edmondson's measure, detected rather than merely reported errors. How this inquiry was made: written by Russ W. Rosenzweig with Vista's AI research desk. It began with a story I told my AI research assistant on October 7, 2026, about a piano and a nursery; the models were built and every figure computed in code, each public source was checked against its original, and the draft was fact-checked before I read it. I read it and listened to it before it was published. Why I write with AI.