# Chapter 21: Risk limits

*The Analyst's Handbook, Sifter's textbook for student investors · By Matt Lang and Bree Lang · Risk and decisions · https://sifter.finance/textbook/ch21-risk-limits*

A policy is a set of lines written down before the quarter. How Risk Flags checks a book and each holding against them, and why a line moves only on the record.

Where this is on Sifter: Portfolio · Risk Flags

Imagine that a student fund's largest position has doubled over the course of a year, and at the spring meeting somebody finally asks whether it has become too large. The analyst who pitched it says that the position is fine. The treasurer says that it feels heavy. A first-year member asks what "too large" means for this fund, and there is a pause, because nobody wrote that number down. What follows is a debate in which every participant already knows how they want it to come out, and the number that gets settled on will be, by a strange coincidence, one that the current weight is just inside of.

This is the problem that a risk policy exists to solve, and the solution is almost embarrassingly simple. A **risk limit** is a line written down before the situation arises, when nobody has a position to defend. The line says, for example, that no single stock will be more than a tenth of the book, and it says it in September so that in March there is nothing to debate except whether to act. The line does not make the decision for the committee (a fund can hold a stock above its cap on purpose, and many do), but it does force the decision to be a decision, taken in the open and written down, rather than a debate that dissolves into "let's keep an eye on it."

Risk Flags, the lens on a fund's Portfolio, is where those lines live on Sifter, and this chapter is about how it applies them. It is not a chapter about which lines to draw. The right beta band for a fund that tracks the S&P 500 is the wrong one for a fund built around fifteen high-conviction stocks, and the right cash band for a fund that receives donations in lumps is the wrong one for a fund that never does. The numbers we will use throughout the chapter belong to one club, whose framework shipped as the platform's starting template, and they appear here because a worked example needs numbers in it, not because they are the right ones for your fund. (If your book is in a personal context rather than a fund, Risk Flags is not there at all, and you can read this chapter as a preview of the day your fund adopts a policy of its own.)

**The 16 book gauges, with one club's example lines**

| Gauge | What it measures | Example line | Severity |
| --- | --- | --- | --- |
| Portfolio beta | How much the book moves for a 1% move in the benchmark. | 0.90 – 1.20 | red line |
| Tracking error | Annualized deviation of returns from the benchmark. | ≤ 10% | red line |
| Stock-specific share of TE | Share of active risk from stock picks rather than sector or style drift. Estimated from the CTE split. | ≥ 70% | minor |
| Highest pairwise correlation | The most correlated pair of holdings over the trailing year. | ≤ 0.70 | minor |
| Largest correlated cluster | Combined weight of the largest group of holdings that move together. | ≤ 25% | red line |
| Largest single position | Largest single stock as a share of the book. Funds exempt. | ≤ 10% | red line |
| Tracking error target | The tracking-error range the committee aims for. Outside it calls for a documented review. | 4% – 6% | minor |
| Top five stocks | The five largest stocks together, as a share of the book. Funds exempt. | review over 35%, ≤ 40% | minor |
| Largest sector tilt | The largest difference between a sector's weight in the book and in the benchmark, in points. | ≤ 5% | minor |
| Invested | Everything but cash, as a share of the book. | ≥ 95% | minor |
| International | Stocks of companies outside the US (ADRs included), as a share of the book. | ≤ 25% | minor |
| Smallest stock position | Smallest single stock as a share of the book. Funds exempt. | ≥ 2% | minor |
| Number of stocks | Stocks held. Funds not counted. | ≤ 30 | minor |
| Largest sector vs cap | Biggest stock sector vs the lesser of 2x its benchmark weight or the absolute cap. Funds exempt. | lesser of 2x benchmark or 30% | red line |
| Cash level | Cash as a share of the book. | 1% – 2% | minor |
| Fund sleeve | ETFs and funds as a share of the book. | no limit | context only |

Every gauge in this table is a number you have already met. Beta is Chapter 6, tracking error (and the target range a committee aims for inside its hard line) is Chapter 7, the share of tracking error that comes from stock picks is the CTE split from Chapter 8 (the tile labels it an estimate, and it is one), and the highest pair and the largest cluster are the matrix from Chapter 9. The largest sector tilt compares each sector's weight in the book with its weight in the benchmark (an index fund counts as holding the benchmark's sectors), and the rest are weights and counts straight off the Holdings page. The example lines are the benchmark-aware template, which the platform offers as one of three starting shapes (the other two are a concentrated stock-picker and an income fund) and which a fund edits line by line before adopting. Nothing in the Example column is in force on any book until a committee ratifies it.

Take a minute to read the Severity column, because the engine treats the two kinds of line differently. A **red line** is a hard limit on the book, and a book outside one is in breach until it comes back. A **minor** line on a book gauge is a caution that the fund has chosen to watch rather than a limit it has promised to keep, and the informational rows (the fund sleeve, with no line at all) are simply printed. Every gauge works the same way regardless of its severity. Inside the line it shows OK, outside the line it shows Breach, and within ten percent of the boundary it shows Review, which means that the number is approaching the line and the committee should look at it before it crosses. (The top-five gauge is the one exception, because its review line is a number of its own, 35% in the example, rather than ten percent short of the limit.) A gauge the engine cannot compute yet (the book's holdings are still being priced, say) shows No data rather than guessing.

The sector cap is not a single number but the lesser of two things, a multiple of the sector's weight in the fund's benchmark (the example uses 2x) and an absolute ceiling (30%). This means that a sector that makes up 5% of the benchmark gets a cap of 10%, a sector that makes up 30% of the benchmark gets a cap of 30% rather than 60%, and the cap for every sector is different. The reason for the two-part rule is that a flat cap would let a fund put 30% of its money into a sector that is 3% of the market, which is not an overweight so much as a different fund. The Sector tab prints every sector's weight next to its own cap, so you never have to compute one, but you should know how the number got there.

![The Portfolio tab of Risk Flags on a fund's book: eight gauge tiles in a grid, each with a value, its limit and an OK or Breach chip, plus an Add tile slot. The highest pairwise correlation tile shows 0.71 against a limit of 0.70, marked Breach and Unanswered, with the posture line beneath it.](https://sifter.finance/textbook/figures/ch21-risk-tiles.png)

*The Portfolio tab of Risk Flags, on a fund's book. Every tile prints the value, the line and a status chip, and a tile in breach adds the posture the club wrote for itself and an Unanswered mark until a member records the fund's response. Here the book is inside every line but one: its two most correlated holdings show 0.71 against a line of 0.70. The stock-specific share tile has its EST. label, the cash tile shows a band a committee has already edited (0 to 2 percent rather than the template's 1 to 2), and the fund sleeve prints with no line at all. Your book's tiles, values and lines will differ.*

### Practice

Under the example policy (2x benchmark weight or 30%, whichever is smaller), what is the cap for a sector that makes up 14% of the fund's benchmark? Answer in percent.

**Solution.** 2 × 14% = 28%, which is below the 30% ceiling, so the cap is 28%. Take a moment to notice that the ceiling did not bind here and would only start to bind once a sector reached 15% of the benchmark, which in the S&P 500 is territory only technology has visited lately.

### Worked example: Worked example: the Maple Fund against the example policy

Let's read the Maple Fund's three-stock book (the 60 / 25 / 15 sector view from Chapter 8) against the example lines, gauge by gauge, using numbers from earlier chapters. This is a bit of a stretch, because a three-stock teaching book was never going to pass a policy written for a fund with forty holdings, but the point of the exercise is to see how each gauge works, not to grade the Maple Fund.

1. **Portfolio beta: 1.26 against 0.90 – 1.20** Value from Chapter 6. Line: 0.90 – 1.20. *Breach. Ten days of returns is a thin basis for a beta (Chapter 6 asked for at least thirty), and the platform would say so, but the arithmetic is the arithmetic, and the number is outside the band.*
2. **Tracking error: 3.0% against ≤ 10%** Value from Chapter 7. Line: ≤ 10%. *OK. The fund deviates from its benchmark by about 3% a year, comfortably inside a line that was written for a fund allowed to stray much further.*
3. **Highest pairwise correlation: 0.82 (MPL · BRC) against ≤ 0.70** Value from Chapter 9. Line: ≤ 0.70. *Breach. The twins from Chapter 9, checked against a line that says two stocks above 0.70 are to be treated partly as one bet.*
4. **Largest correlated cluster: 85% (MPL · BRC) against ≤ 25%** Value from Chapter 9. Line: ≤ 25%. *Breach. The same two stocks as a cluster, and the cluster is most of the book.*
5. **Largest single position: 60% (MPL) against ≤ 10%** Value from Chapter 8. Line: ≤ 10%. *Breach. One holding is six times the cap. On a real book this is the tile the committee sees first.*
6. **Largest sector vs cap: 60% (Technology, cap 30%) against a cap of 30%** Value from Chapter 8. Line: lesser of 2 × 50% benchmark weight (100%) or 30%, so 30%. *Breach. The whole technology weight is against a cap of 30%, which the two-part rule set at the absolute ceiling because technology is half the benchmark.*

So the Maple Fund breaches five of the six gauges the toy book can be read against, and the three it cannot be read against (the stock-specific share of tracking error, the cash band and the fund sleeve) would print No data, because the sector view has no cash and no CTE split. Before you feel too sorry for the Maple Fund, notice what the exercise showed. Every gauge was read against its line by the same rule, every value came from a chapter you have already worked through, and at no point did the policy say what to do. A real committee looking at this page would see five tiles in red, each printing the value, the line and the posture the club wrote for itself when it drew the line, and the meeting would start from there.

That is the book. The other half of Risk Flags is the holdings, and they are checked differently, because a company cannot be measured with one number the way a beta can. On the Equity tab, each stock in the book has a set of **triggers**, and each trigger is a question with a line in it. Some of the lines are the analyst's own, set when the stock was pitched. The example policy asks for a revenue growth line, judged against the company's own run rate, and a returns floor (ROIC, or ROE for a financial), and the fund can add a leverage line, a multiple cap, a price floor or a beta cap for any holding. The rest of the triggers are rules that need no line, such as the operating margin falling two fiscal years running, free cash flow weakening or turning negative, the share price below its 200-day average for two quarters, the multiple stretched more than a quarter above its own five-year average, or a cluster of insider sales. The platform evaluates all of these from the company's filings and prices, continuously, and each one prints CLEAR, MINOR, MAJOR or NO DATA next to the value and the line.

**The per-stock triggers in the shipped library**

| Trigger | Read from | Severity |
| --- | --- | --- |
| Revenue growth below the line | filings and prices, against a line set for this stock | major |
| Returns below the floor | filings and prices, against a line set for this stock | major |
| Operating margin down two years | filings and prices, fixed rule | major |
| FCF weakening or negative | filings and prices, fixed rule | major |
| Working capital outrunning sales | filings and prices, fixed rule | minor |
| Leverage above the line | filings and prices, against a line set for this stock | minor |
| Interest coverage thin | filings and prices, fixed rule | minor |
| Valuation stretched vs history | filings and prices, against a line set for this stock | minor |
| Below the 200-day | filings and prices, fixed rule | minor |
| Multiple above the cap | filings and prices, against a line set for this stock | minor |
| Price below the floor | filings and prices, against a line set for this stock | minor |
| Beta above the cap | filings and prices, against a line set for this stock | minor |
| Insider selling cluster | filings and prices, fixed rule | minor |
| Drawdown from cost | the ledger, against cost | prompts a look, never counted |
| Structural market share loss | marked by an analyst | major |
| Guidance cut two quarters running | marked by an analyst | major |
| Restatement / auditor dispute | marked by an analyst | major |
| Unplanned CEO / CFO exit | marked by an analyst | minor |
| Customer / geography / supplier dependence | marked by an analyst | minor |
| Regulatory / structural remedy risk | marked by an analyst | minor |
| Competitive advantage broken | marked by an analyst | red flag |

The first group is computed. The second group, from "Structural market share loss" down, is **attested**, which means that the platform does not pretend to detect it. A structural loss of market share or a guidance cut is something an analyst has to see and mark, and the mark persists until somebody clears it, with both events logged. The two groups render differently on the page, on purpose, so that nobody mistakes a checkbox for a measurement. A fund can also add a custom mark of its own to any holding (the thing the pitch said would break the thesis, in the analyst's own words).

**A stock's status**

```
red flag → Discuss (hard);  2+ majors → Discuss / trim;  1 major or 3+ minors → On watch;  drawdown trigger only → Check;  else Clean
```

Count the tripped triggers by severity, including any attested marks, and read down the list until a rule fires. The arithmetic is the same for every fund on the platform and is not something a committee configures; what a fund configures is which triggers are on, where the lines are, and how severe each one is. "Competitive advantage broken" is the one red flag in the shipped library, and it goes straight to Discuss (hard) on its own. The drawdown-from-cost trigger (the example line is 10% below the fund's cost) is never counted as a flag; on its own it turns a Clean stock into Check, which is a prompt to look and nothing more.

### Practice

A stock has no majors tripped and no red flag. How many minor triggers have to be tripped before its status moves from Clean to On watch?

**Solution.** Three. One major puts a stock On watch by itself, but minors only add up to the same status at three, which is the engine's way of saying that three small worries are worth the same conversation as one large one. Two minors leave a stock Clean, and the page still shows them, so a committee looking at the Summary can see a stock that is one minor away from a status change.

### Check yourself

A stock in the book has "Revenue growth below the line" (major) and "Returns below the floor" (major) both tripped, plus "Below the 200-day" (minor). Its analyst has also marked "Insider buying cluster", one of the greens. What status does the engine print?

- On watch: the green cancels one of the majors. Greens never net against reds, on the platform or in this chapter. A green appears next to the flag it refers to, as evidence for the conversation, and the status arithmetic does not see it at all.
- Discuss / trim: two majors, and the green is displayed but not counted. **(correct)** Right. Two majors trip the second rule regardless of the minor and regardless of the green. When the committee opens the stock it will see the green listed with the flags, which is where it belongs, but the status is a count of what has gone wrong and not a vote.
- Discuss (hard): three flags in total is the threshold. Discuss (hard) is reserved for the one red flag, the named competitive advantage from the pitch no longer holding. Counts of majors and minors never reach it on their own.
- Clean, until the committee records a response. There is no response ceremony to wait for. Statuses evaluate continuously from the filings and prices the platform already holds, and the first thing a committee sees is the status as it stands today.

Because the statuses evaluate on their own, the next question is what happens when one of them changes. The change is written down and nothing else happens. The **flag log** records every status transition (from what, to what, which triggers tripped, and when), every attested mark set or cleared, every line moved and every limit adopted, in order, with the person attached. It deliberately records change rather than existence. A stock that has been Clean all year does not generate a row every morning, and a stock that goes On watch generates exactly one row on the day it does, which means that the log is a history of what happened to the book rather than a diary. The committee's side of the record is a response. When a status change or a book breach is open, the log lists it as unanswered, and any member can record what the fund decided and why, choosing from the outcomes the page offers (hold, trim, exit, thesis rebuilt, or other) and writing a sentence. The platform stores the choice and the sentence and does nothing with them, because the decision was the committee's, and the platform's job is to keep the record of it. Chapter 22 is about that decision.

Two clocks run in the background of all this. The first is the watch clock. A stock that has stayed non-clean continuously for 180 days since its last transition (two quarters, near enough) gets a "Vote due" mark, which is the engine noticing that a worry has gone unaddressed long enough to need a decision. The second is the drawdown trigger, which asks for a look at a stock that has fallen 10% from the fund's cost in it, whatever its fundamentals say. Both clocks prompt. Neither one changes a status or a position.

Lastly, the lines themselves. Every line on the page can be edited by a manager, and every edit writes a row to the log with the old value, the new value, who moved it, when and a required note. This is the part of the design that matters most and is easiest to overlook. A policy whose lines can move quietly is not a policy, because the March committee can always find a number that the current weight is just inside of, and the meeting from the first paragraph of this chapter happens anyway. A policy whose lines move only on the record can still move (a fund that has grown from ten holdings to forty may well find that a cap written for ten no longer fits), but the reader of the log a year later can see that it moved, when, and for what reason, and can judge the reason. The same logic runs the adoption step. Until a fund's committee ratifies its lines, the page shows "proposed limits · not yet adopted" and computes everything anyway, and the act of adoption writes the whole set to the log as its founding entry, with the archetype the fund started from and the note it wrote.

### Check yourself

A fund is drafting its policy. Which of these four sentences is a line Risk Flags can hold the book to?

- We will keep the book's beta between 0.90 and 1.20. **(correct)** Right. It specifies a gauge, a band and nothing else, which means that on any given day the book is either inside it or not, and the engine can say which. Whether 0.90 to 1.20 is the right band for this fund is a separate question, and one for the committee.
- We will be careful about concentration. Nobody will ever be able to say on which day this sentence was violated, and a sentence that cannot be violated cannot be a limit. The lines that do this work are the single-position cap, the sector cap and the cluster cap, each with a number in it.
- We will not hold too much technology. Closer, because it specifies a sector, but "too much" is the number that the March meeting will settle by looking at the current weight. Write the cap down and the sentence becomes a line.
- We will review every position regularly. A fine habit, and not a limit. It says nothing about any number, so the engine has nothing to hold the book to. The watch clock is the platform's version of this sentence, and even that one has a number of days in it.

> **Computed and attested look different on purpose** Everything the engine measures from filings, prices and the ledger appears as a value next to a line. Everything an analyst has to see for themselves (a market share loss, a guidance cut, a restatement, an executive leaving, a customer dependence, a regulatory action, a broken advantage) renders as a mark that says "marked, until cleared." The page never fakes the second kind as the first, and it never hides the first kind behind a checkbox. When you read a status, the flags underneath it tell you which kind of evidence it rests on, and the page keeps the two kinds apart so that a measured operating margin and a marked guidance cut can be weighed as the different things they are.

> **Try it on Sifter: Read one line and its history** Open Risk Flags on your fund, go to the Portfolio tab, and find the gauge that is closest to its line (a Review tile if there is one, otherwise the OK tile with the least room). Read its value, its line and the posture printed under it. Then open the Flag log tab and find the row that set or last moved that line, and read who set it and why. If the page still says "proposed limits · not yet adopted," note that too, because it means that everything you just read is a proposal and your committee has not yet held its first conversation about it. Do not change anything; this chapter is about reading the record, and writing to it belongs to the committee.

## Checking a trade before it is made

Everything so far has judged the book as it stands, which suits the spring meeting from the first paragraph but comes a little late for the analyst who is about to pitch a new position. Imagine that the committee is weighing a 2% position in a stock the fund does not own, and somebody asks what the trade will do to the fund's tracking error. Somebody else points at the tracking error tile on Risk Flags. The trouble is that the tile measures the past. It was computed from a year of the fund's actual daily returns (the method from Chapter 7), and the stock under discussion was not in any of them, so the tile has nothing to say about the book the fund would hold after the trade.

What the committee wants instead is an estimate of how far the new book will stray from its benchmark over the next year, which is called the **expected tracking error** (practitioners also call it ex ante tracking error, ex ante being Latin for "before the event", and we will leave the Latin there). The idea is to keep the history and swap the weights. Rather than asking how the fund's returns actually behaved, we take the weights the book would have after the trade, look up how each holding and the benchmark moved over the past year, and ask how far a book with those weights would have strayed. The benchmark gets the same treatment, which means that its stocks are also held at the weights they have today (an index drifts over a year as its winners grow, so the index of a year ago is not quite the one a fund would be buying now). In other words, the past year supplies the volatilities and correlations, and the proposal supplies the weights.

There is a catch here, which is that a fund with thirty holdings has 435 pairs of stocks, and a year of daily prices is not a lot of data with which to pin down 435 correlations, which means that some of the estimates will come out too high or too low by chance alone. Sifter handles this the way many risk models do, by pulling each estimate part of the way toward what a simpler model says it should be. The simpler model assumes that two stocks are related only through the market (each has a beta to the benchmark, and that is all they share), and blending the two estimates is called **shrinkage**, after a method published by Ledoit and Wolf.[1] Their paper also shows how to choose how far to pull from the data, and Sifter keeps things simple by pulling every estimate a tenth of the way. The choice of a tenth is arbitrary, and a different fraction would move the estimates a little. The bigger assumption is the one underneath all of it. An expected tracking error assumes that next year's volatilities and correlations will look like last year's, and they will not look exactly like them, so the number is best treated as an estimate with a range around it rather than a promise.

So what happens to tracking error when one position is added? Let's take the simplest version of the trade, in which the new stock is paid for by selling a slice of an index fund that tracks the benchmark. This is a bit of a stretch for most funds, but it makes the arithmetic clean, because selling the benchmark and buying the stock changes the book's active return by exactly the stock's return minus the benchmark's, times the weight. The answer then depends on the size of the position, on how far the stock strays from the benchmark on its own (its **active volatility**), and on whether the stock tends to stray in the same direction as the book's existing bets (the one students most often forget).

**Tracking error after adding a position**

```
TE_new = √( TE² + x²σ² + 2·x·ρ·σ·TE )
```

TE is the book's expected tracking error before the trade, x is the weight of the new position, σₛ is the stock's active volatility (the volatility of its return minus the benchmark's), and ρ is the correlation between the stock's active return and the book's. The first term is the risk the book already has, the second is the stock's own straying, and the third is how the two interact, which can be positive or negative. This is the portfolio-variance formula from Chapter 9 applied to the book's active return, and it assumes the position is paid for out of an index fund that tracks the benchmark.

### Worked example: Worked example: one 2% position, three ways

Let's put numbers on it. Assume that the book's expected tracking error is 4.00%, that the new stock's active volatility is 30% (a round figure for a single stock against a broad index), and that the position is 2% of the book. The only thing we will change is the correlation.

1. **Correlation 0.0 with the book's bets** √(0.04² + 0.02² × 0.30² + 0.000000) = √(0.001600 + 0.000036 + 0.000000) *4.04%, up from 4.00%. The position strays 0.6% a year on its own (2% times 30%), but variances add rather than volatilities, and once that 0.6% is squared it is small next to the 4.00% the book already carries, so the tracking error barely moves.*
2. **Correlation 0.5 with the book's bets** √(0.04² + 0.02² × 0.30² + 0.000240) = √(0.001600 + 0.000036 + 0.000240) *4.33%. This is the same stock at the same size with about 7 times the effect, because the stock now tends to stray in the same direction as the book's existing bets and adds to them.*
3. **Correlation -0.3 with the book's bets** √(0.04² + 0.02² × 0.30² − 0.000144) = √(0.001600 + 0.000036 − 0.000144) *3.86%, which is lower than where the book started. The stock tends to stray the opposite way from the book's bets and partly offsets them, which means that a trade that looks like a fresh bet on paper can bring the book closer to its benchmark in practice.*

### Practice

Keep the same book (expected tracking error 4.00%) and the same stock (active volatility 30%, correlation 0.5 with the book's active return), but make the position 3% instead of 2%. What is the book's expected tracking error? Answer in percent to two decimals.

**Solution.** √(0.001600 + 0.000081 + 0.000360) = √0.002041 = 4.52%. Take a moment to compare this with the 4.33% from the 2% position. Half again as much stock added 0.52 points rather than 0.33, and most of the increase came from the last term, which grows in step with the weight while the stock's own term grows with its square.

Now that we have the arithmetic, we can look at the page that does it for a whole list of trades at once. Simulate, on your Portfolio, opens by asking what you are changing, and the first answer (a few positions) is built from a tool a student fund analyst wrote for their own committee. You type the stocks you would buy, trim or sell, and for each one you pick a conviction stance (Underweight, Neutral, Initial, Core or High). The stance becomes a suggested weight, sized so that the position's weight times its active volatility comes to a set amount for each stance, which means that a volatile stock gets a smaller suggested weight than a quiet one at the same conviction. The book-aware version of the suggestion then uses the correlation from the worked example, sizing down a stock that would add to the book's existing bets and sizing up one that would offset them (within half and twice the plain suggestion). The committee is free to ignore the suggestion and type its own weight.

Each change also says how it is paid for (from cash, from one holding, from an index fund, or spread across trims chosen to keep tracking error low), because where the money comes from changes the answer, as the worked example assumed. The page then shows the expected tracking error, beta and sector tilts after every change in the list, and it checks the result against the same lines this chapter has been reading, which come from the fund's Risk Flags page. Those lines can be changed on the page for a single test (a committee might ask what the trade looks like under a tighter cap), but the change stays with the test and never reaches the fund's policy, because the lines still move only on the record. If you run a full simulation instead, its Compare step shows the same expected-risk numbers for the original and simulated books side by side, without the lines, under the backtest's view of the past.

There is a catch in the book-aware suggestion that is easy to miss, and a student fund analyst was the one who pointed it out to us. Because the suggestion depends on how the stock moves with the book's existing bets, and on how much room is left under the tracking-error ceiling, the same stock at the same stance can get a different suggested weight in a different book. The adjustment is designed to do that, but it means that we have to be careful about which book we size against. Imagine that a fund has voted to move from a book that is half an index fund to a planned portfolio of thirty stocks, and that it is partway through the move. Sizing a new position against today's book asks how the stock would fit a portfolio the fund has already decided to leave, and the answer will change once the move is finished. In other words, a fund in the middle of a transition should size against the portfolio it means to hold. This is why the page lets you choose what to start from (the current portfolio, the book on a past date, your Track Record, a custom portfolio, or a saved simulation such as the planned portfolio), and every suggested weight is sized against whichever one you pick.

> **Try it on Sifter: Test one trade** Open Simulate, choose Plan some trades, press Start, and type a stock your fund does not own. Before you touch anything, write down the expected tracking error at the top of the results. Then move the stance from Initial to High and watch the suggested weight and the tracking error change, and try two or three ways of paying for it. If you have time, look for a stock that lowers the tracking error when it is added, and use the correlation on its card to work out why. Nothing on this page trades, so you can test as many as you like.

Notice what this chapter did not do. It did not tell you where any line belongs, and it did not tell you what to do when a tile turns red or a stock goes On watch, because the platform does not know either, and the design of Risk Flags rests on its not pretending to. What we did do was take every gauge apart into a number you already knew how to compute and a line somebody wrote down in advance, work the status rules until they were arithmetic, follow a status change into the log, where the committee's answer will eventually be recorded, and check a trade against the lines before anyone made it. That leaves the question this whole book has been circling since Chapter 3. You now have twenty chapters of numbers about a book and a page that tells you which of them crossed a line. What does a fund do with all of that? Chapter 22 takes it up, and its answer is a list of questions rather than a list of instructions.

## Sources

1. Ledoit, O., and Wolf, M. (2003). *Improved estimation of the covariance matrix of stock returns with an application to portfolio selection*. Journal of Empirical Finance 10(5), 603-621 https://doi.org/10.1016/S0927-5398(03)00007-0