# Chapter 27: The Quarter: knowing your own risk

*The Analyst's Handbook, Sifter's textbook for student investors · By Matt Lang and Bree Lang · The record · https://sifter.finance/textbook/ch27-quarter*

Build a book to a brief, say what its risk will be before the quarter runs, and find out whether you knew what you built.

Where this is on Sifter: Training Floor · Exercises · Quarter

## Why a book

The two exercises you have met so far asked you to make claims about stocks. The Quarter asks you to make a claim about yourself. You choose one of three standard briefs, you build a small book of four to eight stocks to fit it, and then, before the quarter runs, you say what the book's risk is going to be. Ninety days later the platform measures what the risk actually was, and your score is the distance between what you said and what happened.

That is harder than it sounds. Chief financial officers were asked to put 80 percent confidence intervals on the market's return, more than thirteen thousand times over ten years, and the realized return landed inside their intervals 36 percent of the time.[1] An interval built at 80 percent should catch the outcome four times in five, and seasoned professionals caught it closer to one time in three. Knowing the risk of a book you built is a scarce skill. It is also the daily work of a portfolio manager.

There is a chance element here too, and it is different from the Sprint's. Your return over the quarter is mostly luck and is not scored at all. Your tracking error and beta are what the resolver measures, and even those are measured on only 63 trading days, so even a careful call misses by a little. The Quarter counts a call as close when the tracking error lands within 30 percent of what you said and the beta within 0.20 of it. The standard is to land close on book after book, which is slow, because you run one book per brief per quarter. A recruiter sees the count of your books and how many of them showed that the risk was understood.

## The page

The page opens with its question, "Can you build a portfolio that hits a risk target?", and the first thing on it is a sentence with a three-way switch inside it, "A Defensive, Core or Aggressive book, held for three months." Pick one, and a line beneath describes the brief, its beta range, and the tracking error that kind of book usually runs (a suggestion, not a limit). A small clock marks a brief that already has a live book, because you run one at a time per brief.

Second comes the book. You search for a stock, add it, and type its weight, until you have four to eight stocks whose weights add to 100 percent. Funds are not allowed (the page says so if you try to add an ETF), because a book that simply bought the S&P could hit any tracking-error call it liked and would show nothing about how you build a portfolio. An "even split" button does the arithmetic if you want equal weights, and the page will not take a ninth stock.

Third comes the call, one more sentence with two blanks in it, written in the first person because it is your claim: "Over the next 3 months, I expect this portfolio to have a beta of __ and a tracking error of __ against the S&P 500." You type both numbers. Under the sentence the page prints what this book has actually done at these weights, its tracking error over the past year, the range it landed in for two thirds of past quarters, and its beta, as a reference you are free to use or ignore.

A beta outside the brief's range closes the lock door and says so ("Beta is outside the Core range"), because a book outside its beta range belongs to a different brief. Tracking error has no limit, because the number you call is your own active-risk budget, and the Quarter's job is to check whether you kept to it. Under the sentence are two required lines, "Why this book?" and "What is the biggest risk in it?", which are the Quarter's version of the two boxes you know, and an optional predicted worst drawdown. Then the two doors, "See the evidence," which does not open until the book has at least two stocks with weights, because there is nothing to read until then, and "Lock in your call" with the settlement date under it. Nothing on the page fills in either number for you.

![The Quarter page with a live Core book: the sentence "A Defensive | Core | Aggressive book, held for three months." with Core selected, the brief's line "Beat the S&P 500 without drifting far from it. Market-like exposure, with a real but contained active bet. Beta 0.85 to 1.15. Tracking error has no limit; this kind of book usually runs 3 to 7%." with a Live pill and "settles 2026-12-14", the book as six cards, AAPL 20%, JPM 15%, LLY 15%, CAT 15%, HD 15% and GOOGL 20%, the record strip "9 books, 8 resolved, risk understood on 3", and the frozen bar: "Your risk call, frozen, Core book vs the S&P 500 by Dec 14, tracking error 10.0%, beta 0.95x, Aimed in the Core brief (0.85 to 1.15)", "Why this book: Core exposure across six sectors with a tilt toward healthcare and industrials", "Your biggest risk: LLY is 15% of the book and reports in late October", and a live standing "Behind, Book +0.3%, SPY +1.2%, 0.9 pp behind, 39% of window, 56d left".](https://sifter.finance/textbook/figures/ch23-quarter.png)

*The page, with a Core book five weeks in. Training Floor › Exercises › The Quarter, signed in on the example record of Future Banker, whose Core brief has a live book. With a brief live, the page shows the frozen book and the risk call as they were locked, with the live standing next to them. On a brief with no live book, the same places hold the search box, the weight inputs and the call sentence with its two blanks. The record strip counts books, resolved books and how many were close on both numbers.*

The table below lists the three briefs.

**The three briefs**

| Brief | What it asks | Beta range | Tracking error it usually runs (not a limit) | The seat it rehearses |
| --- | --- | --- | --- | --- |
| Defensive | Protect capital. Move less than the market and hold up better when it falls. | 0.50 to 0.85 | often 6 to 12% | a capital-preservation seat |
| Core | Beat the S&P 500 without drifting far from it: market-like exposure, a real but contained active bet. | 0.85 to 1.15 | roughly 3 to 7% | a core long-only PM seat |
| Aggressive | Swing for alpha. Concentrated, high-conviction, comfortable being very different from the index. | 1.15 and up | 8% and up | a high-conviction seat |

A book on its own is hard to judge, but a book built to a stated brief can be graded against that brief, and that is how a recruiter judges it. The brief fixes how much market risk you take, and you set your own tracking-error budget by calling it. The beta ranges line up end to end without overlapping, so every book has exactly one natural home.

You may be wondering why a Defensive book usually runs such a high tracking error, since a careful defensive book sounds like one that should stay close to the market. It turns out that a low beta and a low tracking error against the S&P cannot happen together. A book with a beta of 0.75 moves about three quarters as much as the S&P, which means that on a day the S&P moves 2 percent the book moves about 1.5 percent, and that half-point difference counts as tracking error before we have even looked at which stocks are in the book. With the S&P running at about 15 percent a year, the beta difference alone puts the tracking error near 3.8 percent, and the stocks themselves add more on top. Consumer staples have run about 11 percent against the S&P over the last fifteen years, and even a professionally built low-volatility fund runs about 7 percent. In other words, the defensive part of a Defensive book is its beta, and the high tracking error is the price of it. An earlier version of this brief asked for a tracking error under 5 percent, which almost no low-beta book can manage. This is why none of the briefs limits tracking error now. The brief fixes the beta, and the tracking error you call is your own budget, which the Quarter then checks.

## The simplest book

Let's build the simplest book there is and see how far arithmetic alone gets us. Take five stocks at the weights below, and start with beta, because beta is the easy half. A book's beta is the weighted average of its stocks' betas, so you can compute it by hand before the page confirms it.

### Practice

A five-stock book, weights and betas: 30% at β 1.30, 25% at β 1.10, 20% at β 0.95, 15% at β 0.80, 10% at β 0.60. What is the book's beta, and (for yourself) which brief is its natural home?

**Solution.** Multiply each weight by its beta and add the five products, which gives 0.30 × 1.30 + 0.25 × 1.10 + 0.20 × 0.95 + 0.15 × 0.80 + 0.10 × 0.60 = 1.035. A beta of 1.03 is inside the Core range (0.85 to 1.15) and a touch above the market, so the natural home for this book is Core. This took no judgment at all, because the weighted average gave us the answer. The tracking-error half takes judgment.

Tracking error does not work that way, for the same reason the hedge block in the Spread chapter had to subtract a covariance term. Stocks that move together overlap, which means that a book of eight semiconductor stocks has the tracking error of roughly one big bet rather than eight small ones, and you cannot know how much your five stocks overlap without the data. So the uninformed tracking error is the brief's guide. Core says roughly 3 to 7 percent, and a student with nothing else to go on should type 5.

That gives us the simplest call, a beta of about 1.03 and a tracking error of 5, and here the Quarter differs from the Sprint. You cannot make this call ten times a semester to find out whether your 5 is really a 7, because a book runs a quarter and you run one per brief. So on this page, more than anywhere else on the Floor, look before you type, which is what the evidence door is for.

## Look before you type

Press "See the evidence" and three lines open under the call. The first one does most of the work. It says something like, "Over 15 years at these weights, this book ran a beta of 0.94 and a tracking error of 6.8%, and beat the S&P in 53% of quarters." In other words, the page took the book you just built and read it against fifteen years of history for those stocks at your weights, every overlapping 63-session window, in the resolver's own arithmetic, so the number history shows you, the number you are asked to type, and the number that will eventually score you are the same quantity measured at three different moments.

Open the line and you get the rest, the beta over the last 60 days next to the fifteen-year figure, the book's volatility against the S&P's, the worst fall on record with its dates, the worst and best quarters, how the book did in the quarters the S&P fell, and whether the history falls inside or outside the brief you chose.

The second line looks inside the book. "MSFT carries 38% of the risk. Technology is 25% of the book." Most students have never asked that of a portfolio they built five minutes earlier, and it is the question the tracking error mostly turns on, because a book whose risk is in one stock behaves like that stock.

The third line is the calendar, how many of your stocks report inside the quarter and what the S&P did last quarter. A book of four stocks that all report in the same week will do most of its moving in that week, and a quarter that follows a big index move is not a quarter that follows a quiet one.

Two cautions go with the first line. The first is that history is not a forecast, and the quarter ahead is neither the last 60 days nor the last fifteen years. The second is that the 60-day beta and the fifteen-year beta often disagree, which means the book has drifted, and the right prediction usually lies between them, with a reason.

### Worked example: Worked example: from the weighted average to two numbers

Start where arithmetic and the brief left you, and move only where a line gives you a reason. The figures are the five-stock Core book above, with invented history.

1. **Start with the weighted average and the guide** Beta 1.03 from the weighted average; tracking error 5 from the middle of the Core guide *These are the numbers a stranger with a calculator and the briefs table would type.*
2. **Line one: the book's history** Fifteen years at these weights: beta 0.94 (last 60 days 1.05), tracking error 6.8%, beat the S&P in 53% of quarters *Beta stays near 1.0, between the long history and the recent one. Tracking error moves up, because 6.8 is the resolver's own arithmetic on this book and 5 was a guess from a table. Call it 6.5.*
3. **Line two: what is inside** The 30% stock holds 41% of the risk; two stocks are in the same sector *No change to the numbers, but the reason for the 6.5 is now written down. A book this concentrated runs hotter than a spread-out book of the same stocks.*
4. **Line three: the calendar** All five stocks report inside the quarter, three of them in the same week *No change to the numbers. The reports do not raise the quarter's tracking error so much as bunch it, and that goes in the biggest-risk line.*
5. **Your call** Beta 0.98, tracking error 6.5, inside Core *Two numbers with a sentence behind each, and a book you can now explain to someone who asks why.*

## When the evidence disagrees

Now imagine that the lines had come back differently, because the page is really about what you do when the history and the recent past disagree, or when the numbers and the brief do.

### Worked example: Worked example: when the evidence disagrees

The same five stocks with different evidence. Take the lines one at a time.

1. **Line one: the book's history** Fifteen-year beta 0.96, but the last 60 days say 1.18; tracking error 3.9% *The book has drifted toward Aggressive lately. You can trim the high-beta stock and stay Core, or move to the Aggressive brief, or predict 1.05 and say in the first box that you expect the drift to fade. You have to choose between those, and predicting 0.96 from the long history alone, while the recent number is in front of you, ignores the evidence.*
2. **Line two: what is inside** One stock holds 40% of the risk *Up on tracking error. A 3.9% history is near the bottom of the Core guide, and a book with two fifths of its risk in one stock will not stay there if that stock has a quarter. Predict 5 rather than 3.9, and say why.*
3. **Line three: the calendar** Two stocks report in the same week, the 40% stock among them *No change to the numbers. The biggest-risk line follows from this.*
4. **Your call** Beta 1.05, tracking error 5, inside Core *Both numbers are away from the long history for reasons a reader can check in the lines above them.*

Both numbers moved away from the history, and both moves have a line behind them. The two boxes are where those lines go, and for a book they have a shape of their own, which the table below shows and the next section explains.

**The two boxes for that book**

| Box | What you would type |
| --- | --- |
| Why this book? | Core exposure with one active bet: the 30% stock is a cash-flow compounder the market prices as a cyclical, and the other four are there to keep the beta near one. |
| What is the biggest risk in it? | Two fifths of the risk is in one stock that reports in week seven; a miss there takes the tracking error past the Core guide on its own. |

One line each. The first box says what the book is for. The second states the thing that would make your tracking-error number wrong, which is the Quarter's version of what would change your mind.

## What is the biggest risk in it

The second box is the Quarter's falsifier, and it asks a slightly different question from the Sprint's. A Sprint falsifier states the observation that would show your reasoning about a stock was wrong. The Quarter's biggest-risk line states the thing that would make your risk numbers wrong, which is nearly always one of three things, a stock that holds too much of the risk, a cluster of stocks that are really one bet, or an event inside the quarter that will move several of them at once.

The three tests still apply. The line should be observable, dated inside the quarter, and decisive, so that when the tracking error comes in hot you can read the line and know whether it came in hot for the reason you gave. And the line's strength follows the numbers, as it did in the Sprint. A tracking error typed at the middle of the guide needs only a plain reason. A tracking error typed well above or below the history is a claim, and the second box is where you say what would have to be true for it to hold.

## Lock the book

When you press "Lock in your call", the brief, the book at its weights, the two numbers and the two lines freeze together, and the page keeps a frozen copy of the evidence as it looked on the day, so the replay later shows the lines you had, not the lines a later day would give. The book is priced from daily closes, starting with the close of the day you lock it, or the next session's close if you lock after 3:50 in the afternoon New York time, and the line under the door gives the date. Ninety days later the resolver measures what the book actually did on the 63 trading days: its tracking error against the S&P and its beta, in the same arithmetic the first line used. Your return is printed as context and is never scored. The score is built the way the formula below says, and the worked example runs it on one of the Maple Fund's analysts.

A book can have a write-up too. The row under "Your books" offers "+ Attach a deep-dive write-up" for 24 hours after the lock, a linked Workspace document or an uploaded PDF, and once it is attached the row and the frozen bar show a link to it. The two lines are the claim, and the write-up is the work behind them.

**How a settled Quarter book is read**

```
ratio = actual TE / called TE;  close on TE if |ratio − 1| ≤ 0.30;  close on beta if |actual β − called β| ≤ 0.20
```

A book that is close on both counts as "risk understood" and scores 1, a book that is close on one counts as "partly aware" and scores 0.5, and a book that is close on neither counts as "risk misjudged" and scores 0. Your card adds the scores up and calls the total on target, so three books might show 1.5 of 3 on target. The ratio itself is the headline on your card, where 1.00× means you knew exactly how much active risk you were running, above 1 means more than you said, and below 1 means less. The two windows come from fifteen years of history. A call anchored on the book's own past year lands within 30 percent on tracking error in roughly three quarters of all quarters, and within 0.20 on beta in about half to nine tenths of them, depending on how concentrated the book is.

The rules are short, but two things in them are easy to miss. The 30 percent window is symmetric, so calling far more risk than you take misses just as surely as calling far less. And the two checks are kept separate rather than averaged, because an average would let a good beta call hide a tracking error that came in at four times the call, which is the miss a portfolio manager most needs to know about. Let's read one settled book by hand so both rules are concrete.

### Worked example: Worked example: reading a settled Quarter by hand

Nell Ashworth ran a Core book. She called a tracking error of 4.5% and a beta of 1.05. Over the 63 trading days the book actually ran a tracking error of 6.1% and a beta of 0.99.

1. **The tracking-error ratio** 6.1 / 4.5 = 1.36 *The book ran 36 percent more active risk than she called, which is just outside the 30 percent window. Ashworth took more risk than she knew.*
2. **The beta difference** 0.99 − 1.05 = -0.06 *A difference of 0.06 is well inside 0.20, which fits, because beta was the half she could compute from the weights.*
3. **The read** Close on beta, not close on tracking error *Partly aware, and 1.36× goes into her record as the headline. Whether the book made money never entered the arithmetic.*

Every student who reads those rules has the same idea within about a minute, and it is a good idea to have, because working out why it fails teaches more about the read than the rules do.

### Check yourself

A classmate running an Aggressive book proposes gaming the read: "call a huge tracking error, like 30%, and you can never be caught taking more risk than you claimed." Does it work?

- Yes. Nobody gets marked down for taking less risk than they said. The 30 percent window is symmetric. A book that is called at 30 percent and runs at 15 percent has a ratio of 0.50, which is far outside the window, so it is not close, and the card prints 0.50× for anyone to read. Overstating your risk is as visible as understating it.
- No. An overstated call misses the 30% window just as an understated one does, and the ratio on the card shows it. **(correct)** Right. Because a miss counts in either direction, the best strategy available is to call the tracking error you actually expect. The book's own history is printed under the call for exactly this reason, so an honest call has something to anchor on.
- No, because the page rejects a tracking-error call that is too high for the brief. No brief limits tracking error, so a call of 30 percent is allowed. The page only checks the beta against the brief. What catches this plan is the ratio after the quarter.

## After a book settles

On the right of the page, under "Your books," each book shows its brief, its stocks, and once it settles, your risk call frozen next to what was realized, with the tracking-error ratio and the sizing effect. The strip above the page keeps three counts, books, resolved, and "risk understood on," which is how many settled books were close on both numbers.

The words the page uses are coarse on purpose. Understood means both numbers landed close, partly aware means one did, and misjudged means neither did. The ratio is kept as a number, because "1.36×" tells a reader more than any word could.

So the question after a settled book is the same question as after a settled call, asked of the numbers rather than the side. If the tracking error ran hot, what was inside the book that the second line warned you about and you discounted, the one stock, the cluster, the week of reports? If the beta drifted, was the 60-day number telling you something the fifteen-year number was not? The answer goes into the next book, and the next book is a quarter away. That is why the evidence door on this page needs more of your time than on any other.

The page asks you to write that answer down while it is fresh. A settled book gets the same post-mortem a settled call does, reached from the settle notification, from the waiting list on the Exercises page, or from the Post-mortem button on the book's row under "Your books." The prompts are the Quarter's own. A book that was understood asks, "Where did the risk actually come from, and was that where you said it would?" A book that did not asks, "Where did the risk come from that you did not size, and what would you build differently?" The three labels are the same, the note freezes after ten minutes, later thoughts are addenda, and the card prints it under the book's risk line.

!["Your books, 9 of 9" with the filters All, Open, Resolved and a brief picker, then nine rows, newest first, each a date, the brief, the tickers, the called beta and tracking error, and a pill: Core 09-15, 0.95x and 10.0%, Open; Aggressive 07-01, 1.90x and 22.0%, Partly aware; Defensive 06-01, 0.65x and 10.0%, Risk misjudged; Core 03-02, 1.00x and 7.5%, Risk understood; Aggressive 01-05, 1.40x and 20.0%, Risk understood; Core 09-02, 0.95x and 8.5%, Risk understood; Aggressive 06-02, 1.90x and 30.0%, Partly aware; Defensive 04-01, 0.60x and 11.0%, Partly aware; Core 03-03, 1.10x and 8.0%, Partly aware.](https://sifter.finance/textbook/figures/ch23-quarter-history.png)

*Your books. The panel on the right of the page. Each row is one book, with its brief, its stocks, the risk call as two numbers, and once it settles, how it read. This record has one live book and eight settled ones, three understood (both numbers close), four partly aware (one close) and one misjudged (neither). Read from the bottom up, the early books got one number right and the later Core and Aggressive books got both.*

## What reaches your card

The Quarter arrives on your Sifter Card as a tile that asks, "Does the risk taken match the risk called?" Its headline is your typical ratio of actual to called tracking error, which is the middle of your settled books (so one strange quarter cannot swing it), and next to it are the number of quarters settled and how many of them were on target, where a book counts 1 when both numbers landed close, half when one did, and nothing when neither did. Open the tile and a recruiter sees every settled book plotted as called against actual, with a different shape for each brief, and under each book the two lines you wrote, why this book and its biggest risk, with your post-mortem under them once the book has settled. Nothing about the return appears as a score.

Each settled book also shows a sizing effect, which is the book's return at your weights minus the same stocks held in equal amounts. A positive number means your biggest positions did better than your smallest, and a negative one means your sizing cost you. The firms that evaluate professional portfolio managers measure exactly this, separately from stock picking, because knowing which of your ideas deserves the most money is its own skill. One quarter of it says very little, so the card treats it as context and lets it build across books.

The Quarter answers one question, whether you knew the risk of the thing you built. The next chapter is the exercise that asks the other one, whether you can run it.

![The Quarter page on a Sifter Card: the label Risk awareness, the title The Quarter, the line "Does the risk taken match the risk called?", a sentence explaining the exercise, three stats, "1.14x actual over called TE, typical", "8 quarters settled" and "5 of 8 on target", then "Called vs actual" as two plots, tracking error and beta, each with a dashed line, a shaded band and eight numbered shapes (circles for Defensive, squares for Core, triangles for Aggressive), most of them inside the band, the caption "Shaded means close (tracking error within 30%, beta within 0.20). Above the line means more risk than called.", then "The books" with the live Core book, AAPL 20%, JPM 15%, LLY 15%, CAT 15%, HD 15% and GOOGL 20%, "Core, TE 10%, beta 0.95, settles Dec 14, 2026", and its Why and Biggest risk lines.](https://sifter.finance/textbook/figures/ch23-card-quarter.png)

*The Quarter on the card. The exercise page on this analyst's card. Each settled book is a shape on two plots, called across and actual up, and the shaded area is close enough. The two Defensive circles (books 2 and 7) sit above the band on tracking error, because both ran far more active risk than called, and one of them also missed on beta. Three books landed on both numbers, four on one and one on neither, which adds up to 5 of 8 on target. Under the plots come the books, each with its risk call and the two lines the analyst wrote.*

The box below lists three things the Quarter does not measure.

> **What the Quarter does not measure** Keep a few boundaries straight when you read a Quarter score.
>
> It is not a returns contest. The realized return appears on the page as context and has zero weight in the score.
>
> It is not unlimited. Each student runs one live book per brief and at most three at once, so nobody can spray a dozen books and quietly keep the lucky one, and abandoned or re-run books stay visible on the record.
>
> It is not a verdict on the quality of the book. A well-understood aggressive book and a well-understood defensive book score identically. What the Quarter measures is whether you knew what you built.

The lab runs the exercise in its real order, prediction first and evidence second.

> **Try it on Sifter: Predict before you look** Open the Quarter and pick the brief that matches the book you would genuinely run. Build your four to eight stocks, type the tracking error and beta you expect, and only then press "See the evidence." The first line will tell you what the book actually did over fifteen years at those weights. The difference between your two numbers and that line is a free and unscored preview of the skill the real quarter is going to grade, and the page keeps both numbers either way.

## Sources

1. Ben-David, I., Graham, J. R., and Harvey, C. R. (2013). *Managerial miscalibration*. Quarterly Journal of Economics, 128(4), 1547-1584 https://people.duke.edu/~charvey/Research/Published_Papers/P110_Managerial_miscalibration.pdf