Chapter 22: What to do with the numbers
One row per metric: the question it answers, the question people wrongly ask it, and the conversation it starts.
By Matt Lang and Bree Lang · About the authors
Where this is on Sifter: Portfolio · Analyze · Risk Flags · Fund
Imagine that the president of the Maple Fund sits down the night before the spring meeting and opens the platform. There is a lot on the screen. Twenty chapters of this book have each added a number or two to it, Risk Flags has turned a few tiles red, and the meeting is at four o'clock. There are two temptations at this point, and every student fund gives in to one or the other at least once a year. The first temptation is to read all of the numbers aloud at the meeting, in the order the tabs happen to list them, so that the committee ends the hour better informed and no closer to a decision. The second is to hunt through the tabs for the one number that says what to do, which is a shorter evening, because that number does not exist.
So what does a fund do with all of this? The answer this chapter offers is a bit less satisfying than a formula and a good deal more useful. Every number the platform computes answers exactly one question, refuses several others that people habitually put to it, and, when it is read correctly, starts a conversation that the committee was going to need to have anyway. This means that the job the night before a meeting is not to find the answer in the numbers but to find the questions, and to bring the numbers that raised them. The table below does the sorting for the whole book, one row per metric, and the rest of the chapter walks the Maple Fund through it. Nobody in this chapter will be told what to decide, because the platform does not know, and neither do we. What we can do is make sure that the right question gets asked and that the right number comes with it.
Every number in the book, and the one question it answers
| Number | Answers | Does not answer | Starts a conversation about |
|---|---|---|---|
| Time-weighted return (Chapter 3) | How did the book do, with the timing of deposits removed? | Whether the fund decided well; a good year and a good decision are different things. | The benchmark. TWR on its own means little until you compare it with the benchmark's return over the same window. |
| Money-weighted return (Chapter 4) | How did the money do, deposits and their timing included? | How the manager did; the timing of donations is not the manager's skill. | Why the two returns disagree, and whether a large inflow landed at a bad moment. |
| Volatility and drawdown (Chapter 5) | How bumpy was the ride, and how deep was the worst fall from a peak? | Whether the bumps were worth it (that is the Sharpe ratio's job) or where they came from. | Whether the fund's members and its advisors can live with a ride like that one. |
| Sharpe and Sortino (Chapter 5) | Did the return earn the bumps, per unit of bumpiness? | Whether the fund beat the market; Sharpe is measured against cash, not the benchmark. | Nothing on its own at a student horizon; over a few years, whether the fund's style is paying. |
| Beta (Chapter 6) | How much of the book's movement was the market's? | Whether the fund is good; a beta of 1.3 is a choice, not a grade. | Whether the fund meant to be that exposed, and whether a policy line says so. |
| Alpha (Chapter 6) | Over this window, what was left after the market's share was removed? | Whether the manager has skill; on a semester of daily data the band around alpha is wider than the number. | Very little until the window is long; the right conversation is about the width, not the sign. |
| Active return (Chapter 6) | Did the book beat the benchmark, and by how much? | Why; that is attribution's job. | The benchmark itself, if the difference is large in either direction for a long time. |
| Tracking error and information ratio (Chapter 7) | How far did the book deviate from the benchmark, and did the deviation pay? | Whether deviating is good; a closet indexer and a concentrated fund both have a TE, and the mandate decides which is right. | Whether the fund is taking the amount of active risk it said it would. |
| CTE and MCTE (Chapter 8) | Which holdings delivered the active return, and which holdings are spending the active risk? | What to sell; a holding spending a lot of risk may be doing exactly what the fund wants. | Sizing: whether each holding's share of the risk matches the conviction the fund holds in it. |
| Brinson effects (Chapter 8) | Was the active return earned by sector weights or by picks within sectors? | Whether either was skill, on one quarter; the split is real and the sample is small. | Whether the fund is the kind of fund it thinks it is (an allocator or a stock picker). |
| Correlation and clusters (Chapter 9) | Which holdings moved together, and how much of the book is one bet? | Why they moved together, or whether they will next year. | Whether the fund is holding a hidden bet on purpose, and whether it wants to. |
| Sleeve drift (Chapter 10) | How far has each sleeve wandered from its target weight? | Whether to rebalance; a drift can be a winner the fund is happy to let run. | Whether the targets still describe the fund the members want to run. |
| Monte Carlo and stress tests (Chapters 12 and 13) | Under an assumed model, how wide is the range of outcomes, and what would a bad day or a past crisis cost? | What will happen; these are models fed by the same history the matrix warns about. | Whether the fund could survive the tail it can see, and who would be asked to explain it. |
| VaR and CVaR (Chapter 13) | On a normal bad day, roughly how much is at risk, and how bad is the average day beyond it? | The worst case; VaR on a short window cannot exceed the worst day it has seen. | Whether the fund has ever said, in advance, what loss it would consider unacceptable. |
| Factor tilts (Chapter 9) | What styles is the book leaning on, compared to the market? | Whether the tilt is a mistake; a value tilt in a value fund is intended. | Whether the tilts the book shows are the tilts the fund meant to hold. |
| A gauge status (Chapter 21) | Is a book-level number inside the line the fund wrote for it? | What to do about a breach; the line was written to start this conversation, not to end it. | The breach itself, in the open, with the line and the value on the table. |
| A stock's status (Chapter 21) | How many of the triggers the fund set for this stock have tripped, and how serious are they? | Whether the thesis is broken; a status is a count of worries, and the analyst owns the thesis. | Whether the fund holds, trims, exits or rebuilds its case, recorded with a reason. |
Read the third column twice, because it is the one that saves a meeting. Most of the ways a number gets misused come from asking it a question from a neighboring row. Sharpe gets asked whether the fund beat the market, alpha gets asked whether the manager is good, and MCTE gets asked what to sell, and in each case the number answers politely and wrongly. The fourth column is the chapter's real content. A number with no conversation attached to it is a number that did not need to be at the meeting.
Take a minute to notice the three kinds of number the table mixes together, because they behave differently at a meeting. The first kind looks backward. Returns, contribution, the Brinson split and the hit rate all describe a period that has finished, and the plain thing to say about a backward-looking number is that it is banked. It can explain, and it can be learned from, but it cannot be changed by anything the committee does at four o'clock. The second kind describes the book as it stands today. Weights, sector exposures, the correlation matrix, the factor tilts and every gauge on Risk Flags are a photograph of the current position, and these are the numbers the committee can actually act on, because a decision made this afternoon changes them by tomorrow. The third kind is a model. The Monte Carlo fan, the stress tests, VaR and the optimizer all begin with an assumption and end with a number that looks as solid as the first two kinds and is not, and the right way to bring one of them to a meeting is with its assumption attached.
Several rows of the table make the same point. Some of the numbers, at the horizon a student fund actually has, are too noisy to carry weight, and the platform does not hide this. Chapter 6 asked for at least thirty daily observations before it would print a beta at all, and even a full year of daily returns gives an alpha whose plausible range is usually wider than the alpha itself. A Brinson split on a single quarter is arithmetic, and it is also one quarter. This does not make the numbers wrong. It means that the range of plausible values around each of them is large, and what a fund does with a number like that is to say so at the meeting rather than to argue about its sign. In other words, the sentence "our alpha this semester was positive, and the band around it includes zero" is a better sentence than "we generated alpha," and it is the sentence the numbers actually support.
A small book: weight and share of tracking error
| Name | Weight | Share of fund TE |
|---|---|---|
| Alder | 8% | 24% |
| Birch | 12% | 18% |
| Cedar | 5% | 12% |
| Dogwood | 20% | 22% |
Four holdings from an imaginary book, with the share of the fund's tracking error each one is spending (the %TE column of the Attribution tab, built from MCTE in Chapter 8). Weight is capital. Share of TE is active risk. The two are different budgets, and the question a committee asks of this table is which holding is drawing on the second budget hardest relative to the first.
Practice
For each holding, divide its share of tracking error by its weight to get its active risk per point of weight. Find the holding that spends the most and enter its ratio (a number such as 1.5).
Solution. Alder 24 / 8 = 3.00, Birch 18 / 12 = 1.50, Cedar 12 / 5 = 2.40, Dogwood 22 / 20 = 1.10. Alder spends 3.0 points of active risk for every point of weight, three times what a holding that matched its capital share would spend, while Dogwood, the largest position, is the most economical of the four. Take a moment to think about what the table can and cannot say from here. It can say that Alder is the fund's most concentrated bet in risk terms, and it cannot say whether that is a problem, because a fund that holds Alder with its highest conviction may be spending its risk exactly where it wants to. The question for the meeting is whether the conviction is really that high, and the number is what puts the question on the table.
Check yourself
The fund's Sharpe ratio for the year is 1.4, well above the benchmark's 0.9. Which of these four questions can that pair of numbers actually answer?
- Did the fund beat the market this year? Sharpe is measured against cash, not against the benchmark, so two Sharpe ratios do not tell you which return was higher. A fund can have the higher Sharpe and the lower return in the same year, and often does. Active return is the number for this question.
- Per unit of volatility, did the fund earn more than the benchmark did over the same window? (correct) Right. That is the whole content of the comparison. The fund was paid better for the bumps it took than the index was for its own. Whether that was skill, style or one lucky quarter is a different question, and a year of data does not settle it.
- Is the manager skilled? A single year of Sharpe is far too short to separate skill from the year the market happened to give the fund's style. Over several years the comparison starts to mean something, and the calibration chapters later in the book are about exactly how much.
- Is the fund riskier than the benchmark? Sharpe divides return by volatility, so a high Sharpe is consistent with a fund that is either much riskier or much calmer than the index. Volatility and beta answer this one directly.
Worked example: Worked example: reading the Maple Fund the night before
Let's read the Maple Fund's numbers from the earlier chapters in the order the table suggests, with one rule: each number becomes the question it raises, never a decision. The period is the two weeks from Chapter 3, which is too short for some of these numbers, and we say so where it matters.
- Return and active return TWR 3.34% against 2.52%, so 0.82pp active (Chapters 3 and 6). Banked. The question is not whether the fund did well but whether the benchmark is the right one, since every number below is measured against it.
- Money-weighted return MWRR 3.43% against a TWR of 3.34% (Chapter 4); the difference is the $1,000 that arrived on day six. The difference is a donation's timing, not a decision. The question is what happens to cash that arrives between meetings.
- Volatility and drawdown Volatility 8.1% annualized from ten days; worst fall from peak -0.50% (Chapter 5). An uncertain number and a small one. Together they ask the members, not the book, what size of fall they would sit through.
- Beta and alpha Beta 1.26 on ten observations; period alpha 0.22pp (Chapter 6). The alpha's plausible range is wider than the alpha itself, so it gets reported as a range rather than a number. The beta is above the example band from Chapter 21, which asks whether the fund meant to be that exposed.
- Tracking error and information ratio TE 3.0% annualized; IR about 6.72 (Chapter 7). Low for a three-stock fund, which means the three mostly moved with the market. Is the fund taking the active risk its mandate describes?
- Attribution Allocation 0.35pp, selection 0.30pp, interaction 0.15pp; largest contribution MPL at 1.62pp (Chapter 8). Both effects helped, on one period. The sharper question is MPL: it delivered most of the active return and is the largest position, so is the fund's conviction as high as its weight?
- The matrix and the cluster MPL and BRC at 0.82, a cluster of 85% of the book at the 0.60 line (Chapter 9). Two bets, not three, and the larger one is most of the book. Does the fund know why the two move together, and is it holding that bet on purpose?
- The sleeves Growth is 5pp over target (Chapter 10). A winner grew its own allocation. Does the target still describe the sleeve the fund wants?
- The policy check Against the example policy from Chapter 21: five breaches (beta, pair, cluster, single position, sector), tracking error OK. Five red tiles, each with its value, its line and the posture the club wrote. None says what to do; all five are now on the table with the numbers attached.
The page the president brings to the meeting
| Question for the committee | Raised by | Where the fund records whatever it decides |
|---|---|---|
| Why is the benchmark the benchmark, and does everyone know? | Active return (Chapter 6) | Manage, if the benchmark changes |
| What happens to cash that arrives between meetings? | The MWRR gap (Chapter 4) | A written policy line, or nothing |
| What size of fall would the members sit through? | Volatility and drawdown (Chapter 5) | A written policy line, or nothing |
| Did the fund mean to carry a beta of 1.26? | Beta against the example band (Chapters 6 and 21) | Risk Flags, as a response to the beta tile if the fund has adopted limits |
| Is the fund taking the active risk its mandate describes? | Tracking error (Chapter 7) | The mandate, if it changes; otherwise a note in the minutes |
| Is the fund's conviction in MPL as high as its weight? | Contribution and weight (Chapter 8) | Pitches, if the answer is to change the position; the ledger, if it acts |
| Why do MPL and BRC move as one, and is the fund holding that bet on purpose? | The matrix and the cluster (Chapter 9) | Risk Flags, as a response to the cluster tile; Pitches, if a holding changes |
| Does the Growth target still describe the sleeve the fund wants? | Sleeve drift (Chapter 10) | Manage › Sleeves, if the target moves; the ledger, if it rebalances |
Eight questions, each with the number that raised it and the place on the platform where the fund would record its answer. Nothing on this page is a decision. Take a moment to notice what a meeting run from this page looks like compared with one run from the tabs in order: the numbers are still all there, but each one arrives attached to the thing the committee has to talk about, and the ones that did not raise a question stayed on the screen where they belong.
Check yourself
A stock in your fund's book goes from Clean to Discuss / trim overnight, because two of its triggers tripped on a new filing. What does the platform do?
- Trims the position toward the cap. The platform never writes to the ledger on its own. A trade is a decision, and every decision belongs to the fund; the append-only ledger from Chapter 2 records what people did, not what a rule did.
- Emails the committee an instruction to sell. It notifies the members of the status change, and the notification lists the triggers that tripped, but it gives no instruction, because the status is a count of worries and not a recommendation.
- Records the status change in the flag log, lists it as unanswered, and waits for a member to record what the fund decided and why. (correct) Right. The log gains one row with the old status, the new status and the triggers, the item goes into the unanswered list, and the next thing that happens is a person recording a response (hold, trim, exit, thesis rebuilt or other) with a sentence. The platform stores the response and does nothing further with it.
- Lowers the fund's standing against other funds on the platform. Nothing on Risk Flags is scored or ranked, on the fund's page or anywhere else. The record exists for the committee and for whoever the committee chooses to show it to.
Notice what we have done in this chapter, because it is the opposite of what the chapter's title might have promised. We did not find the number that says what to do, and we did not write down a method for running a fund. What we did was take every number the book has taught, ask what it can and cannot answer, and turn the Maple Fund's evening into a page of eight questions with the numbers that raised them and the place each answer would be recorded. Whether the fund holds, trims, rebuilds or lets a winner run is the committee's to decide, and the platform's whole design rests on its not pretending otherwise. Everything it does, from the append-only ledger of Chapter 2 to the flag log of Chapter 21, is built to record what people decided and why, so that the reasoning survives the people who did it.
Before we leave the fund, there is one more point to make, and it is about everything the page of questions leaves out. Take a moment to think about how much of the thinking that happens in a fund over a semester never makes it into any record at all. Somebody floats a pitch in the last ten minutes of a meeting, for a good reason, and it never gains traction because the hour ran out. Somebody argues against a position in October, turns out to have been right in March, and the minutes say only that the fund held (and somebody else noticed the cluster on the Diagnostics tab weeks before the committee got around to it). The ledger and the flag log record what the fund decided, which is exactly what a fund ought to record, but a fund's decisions are a small share of the thinking that went into them, and most of the rest has evaporated by the time anyone is in a position to give credit for it. This means that two members can leave the same meeting with the same minutes when one of them saw the whole thing coming and the other did not, and nothing on the platform we have used so far can tell them apart.
That is where the book turns. The rest of it is about a record that belongs to the person rather than to the fund, where a claim gets written down before anyone knows how it turns out, so that the thinking has somewhere to go even when the committee never acts on it, and so that the members who consistently think clearly about these questions end up with something that shows it. Chapter 23 takes it up.
The Analyst's Handbook is Sifter's textbook for student investors, written by Matt Lang and Bree Lang. Sifter is free for students. This chapter as markdown.