How often you look · Market Vidyalaya

Two colleagues put ₹6,00,000 each into the same index fund in the same week, on the same recommendation, for the same reason. One installed the app, put it in the second slot on the home screen and left notifications on; he sees the number most days and twice on bad ones. The other bought through a distributor, gets a folded statement in the post twice a year, and has never installed anything. Six years later one of them still holds the fund and the other moved to a deposit somewhere in the third year and has been meaning to come back since. Nothing about the fund was different. What was different is how many times each of them was shown a number, and what proportion of those numbers were losses.

Think of it like this

The pencil mark on the door frame

A child’s height is marked on the door frame once a year on her birthday. Every mark is above the last one and the growth is unmistakable. Now imagine measuring her with a tape every morning instead. The numbers wobble — a little shorter after a long day on her feet, a little taller after a night’s sleep, and the tape is never held quite the same way twice. A parent doing that would see roughly as many falls as rises and could reasonably conclude that she had stopped growing. She is growing at exactly the same rate in both households. Only the interval between measurements changed.

In the market

Growth accumulates with time. The wobble does not accumulate the same way — it grows roughly with the square root of time, so it is proportionally much bigger over a day than over a year. Look daily and you are shown mostly wobble. Look every five years and you are shown mostly growth. Same fund, same six years, two assets that look nothing like each other.

Why the proportion of red days is a fact about the interval

This is not a psychological claim yet. It is arithmetic about sampling, and it has one moving part. Over a window of n years the expected return accumulates roughly in proportion to n, while the scatter around it grows roughly in proportion to the square root of n. So the ratio between the two — how much of what you are looking at is drift and how much is noise — improves as the window lengthens, and it improves by the square root of the lengthening.

Drift ÷ Scatter, over n years = (μ × n) ÷ (σ × √n) = (μ ÷ σ) × √n

μ: The expected return over a year
σ: The standard deviation of the annual return — the usual measure of volatility
√n: Why a ten-year window is about three times as favourable a place to stand as a one-year window, on an asset that has not changed at all

Example: At μ = 12% and σ = 18%, the ratio is 0.67 over one year and 2.11 over ten. Neither number says anything about the fund. Both are statements about the length of the window you are looking through.

Worked example

The same fund, sampled at five different intervals

Illustrative assumptions: 12% expected a year, 18% standard deviation a year, about 250 trading days, and a normal distribution

One dayThe drift is roughly a twenty-fifth of the noise. A single day carries almost no information about the fund and arrives as a notificationDrift 0.05%, scatter 1.14% — about 48% of days are red

One weekBarely better. Fifty-two observations a year, of which about twenty-four hurtDrift 0.23%, scatter 2.50% — about 46% red

One monthTwelve observations a year, five of them losses. This is the interval a statement arrives at, and it is still mostly noiseDrift 1.00%, scatter 5.20% — about 42% red

One yearOne observation in four is a loss. The ratio of drift to noise is now 0.67 rather than 0.04Drift 12%, scatter 18% — about 25% red

Five yearsRoughly one five-year window in fourteen. The asset has not changed once across any of these five rowsDrift 60%, scatter 40% — about 7% red

What one observation is worth, if a loss is felt about twice as keenly as a gainThe average gain multiplied by the chance of a gain, less twice the average loss multiplied by the chance of a loss. The daily and monthly figures are negative; the annual one is strongly positiveDaily: about −0.4 points. Monthly: about −0.6 points. Yearly: about +9 points

The interval at which the average observation stops hurtingIt lengthens as volatility rises and shortens as the expected return rises. The exact figure is an artefact of the assumptions; that such a threshold exists at all is notSomewhere between one month and one quarter, on these assumptions

Two people holding the identical fund over the identical six years were shown different assets, and the whole of the difference is the sampling interval. That is what myopic loss aversion is: not weakness, and not a failure to understand compounding, but the entirely reasonable response of somebody who has been handed a series in which nearly half the entries are losses. The arithmetic here uses a normal distribution and a constant expected return, and real returns are neither — they are fat-tailed, the worst days cluster together, and any actual six years is a fact rather than a computation. Every one of those objections makes the short interval worse rather than better, and none of them touches the mechanism: the ratio of drift to noise rises with the square root of the window, so the window decides how much of what you see is information.

Interval	Roughly what fraction is a loss	What one observation can actually tell you
A notification, or a glance during the day	About half	Nothing about the holding. Something about the market’s mood, and reliably an urge to act — which is the only output it has
A week	About 46 in 100	Nothing that a month would not tell you better. This is the interval at which most people form their sense of "how it is going"
A month	About 42 in 100	One useful thing, and it is not a price: whether the contribution actually went through. That is a machinery fact and needs no chart
A year	About 1 in 4	Whether the allocation has drifted past its limits, whether a fund still does what it said it would, and whether the plan is on course
Five years	About 1 in 14	Whether the strategy was right. Which is the only question the price series was ever able to answer

Careful

This is not an argument for never looking, and reading it that way produces a different and equally expensive failure. Separate looking at the price from checking the machinery. The arithmetic above is entirely about the price: it says a daily price carries almost no information and a large amount of pain. It says nothing about the mandate that stopped four months ago when a card expired, the nominee never registered, the fund whose mandate changed at a merger, the cover that lapsed, the KYC that froze the folio. Every one of those needs checking on a schedule, none of them requires a price, and other lessons in this track are about what happens when they go unchecked for years. The variable to change is not "look less". It is: put the price on a long interval, and put the machinery on a calendar.

In the Indian market

In an Indian retail account a fresh price exists to be looked at every business day, and nobody in the household chose that. A mutual fund’s net asset value is published daily because the rules require it, which is a genuine protection and also means a number exists to be shown. The app pushes "your portfolio is down 3.2% today". A broking app opens on a profit-and-loss screen rather than on an allocation screen, because that is the screen people open the app for. None of this is a scandal and none of it is aimed at you personally. It simply means that the observation frequency of a household that has installed nothing is roughly six-monthly, and the observation frequency of a household that has installed the ordinary things is roughly hourly — and that gap was settled by a product decision rather than by a plan.

What the interval changes, other than comfort

It changes the allocation you can hold. Somebody shown a red number half the days of their life will end up holding less equity than the plan requires, and will describe the reason as prudence rather than as sampling. The allocation was decided by the interval.
It changes how many decisions you take. A number that arrives is a prompt, and a prompt with no accompanying obligation gets discharged as an action. This is the mechanism behind overtrading, which has its own lesson, and the interval is the upstream cause of it.
It changes what you remember. Vivid recent observations crowd out the distribution. Somebody who watched a 6% fall happen in real time remembers it more strongly than somebody who read the same fall as one line in a half-yearly statement, and both of them own the same fund.
It does not change the return by one paisa — until it changes a decision, at which point it changes it permanently. Which is why this belongs in a psychology module rather than a statistics one.
It runs the other way for a trader. If your holding period is three days, a daily observation is not noise, it is the data, and lengthening the interval would be negligence. The arithmetic above applies to a holding whose horizon is years. The rule is that the observation interval should match the decision interval, and the failure in an ordinary household is that the two are five orders of magnitude apart.

◆ Your call

Six weeks of red notifications

A ₹14,00,000 portfolio, held for a retirement nineteen years away, has fallen about 11% over six weeks. Nothing in the plan has changed, no fund has changed its mandate, the income is secure and the emergency fund is intact. The app has sent something on twenty-eight of the last thirty-one days.

Check yourself

Two people hold the identical index fund over the identical six years. One checks the app most days; the other receives a statement twice a year. Which reading is accurate?

Simple bhasha mein

Darwaze pe pencil ka nishaan

Bachche ki lambai darwaze pe saal mein ek baar nishaan lagate ho — aur har baar khushi hoti hai. Roz naapna shuru kar do, toh aadhe din lagega ki kuch hua hi nahi, aur kuch din lagega ki kam ho gayi. Bachcha wahi badh raha hai; aapne naapne ka interval badal diya. Do saathi, ek hi index fund, ek hi hafte mein khareeda. Ek ke phone pe notification on, doosre ko chhah mahine mein ek statement daak se aata hai. Chhah saal baad fund ek hi hai — par sirf ek ke paas woh ab bhi hai. Wajah fund nahi, red numbers ka hissa hai: roz dekho toh kareeb aadhe din laal, hafte mein dekho toh kam, saal mein dekho toh bahut kam. Aap woh interval chun rahe ho jis pe aapka portfolio kitni baar "nuksaan" jaisa dikhega. Aur dhyaan do — chhah hafte laal notification aane pe bechne ka mann karta hai; wahi chhah hafte ek statement mein ek line hote hain. Interval pehle se tay karo, mood se nahi. SIP chal rahi hai toh dekhne ki zaroorat mahine mein ek baar se zyada nahi hai; review saal mein do baar tareekh pe. Notification band karna kaayarta nahi hai — woh bhi ek faisla hai, aur aksar poore plan ka sabse sasta faisla.

What to remember

Expected return grows with time and the scatter grows with the square root of time, so the observation interval decides how much of what you see is information.
On ordinary assumptions about half of all daily observations are losses and about one in fourteen five-year windows is — on the same asset.
If a loss is felt about twice as keenly as a gain, the average short-interval observation has negative value, and there is a threshold interval above which it turns positive.
Separate the price from the machinery: the price belongs on a long interval, and mandates, nominees and cover belong on a calendar.
The interval should match the decision interval — which is why a three-day trader needs daily data and a nineteen-year holder does not.

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