---
title: "Running a Multi-Strategy Book"
book: "Strategies I: Equities and Futures"
subject: quant
language: en
chapter: 28
exercises: 8
source: https://one-course.com/books/quant/8/en/chapter/28-running-a-multi-strategy-book
---

# Chapter 28 — Running a Multi-Strategy Book

In the first week of August 2007 many quantitative equity funds lost at once. Khandani and Lo, rebuilding the episode from factor and transaction data, found a market-wide deleveraging: two unwinds, on 1 August and from the open of 6 August, beginning with financials, long book-to-market and short earnings momentum, the positions many funds held under different names. A firm that runs many strategies is exposed to the same thing inside its own walls. On this chapter’s synthetic firm of ten [pods](#def-s1-running-a-multi-strategy-book-multi), five share hidden factors that crash together three times in twenty years; detecting the overlap and capping it cuts the firm’s largest drawdown from 43.5% to 35.7% at 10% volatility, and a 5% [drawdown limit](#def-s1-running-a-multi-strategy-book-limit) on each [pod](#def-s1-running-a-multi-strategy-book-multi) stops 91.6% of healthy [pods](#def-s1-running-a-multi-strategy-book-multi) within a year. The build is `firm.multistrat`.

## 28.1 Allocation across strategies

**Definition 28.1 (Multi-strategy book, pod).**

A *multi-strategy book* is a firm’s combined portfolio of several strategies run by separate teams, allocated capital or risk by a central function that nets their trades and controls their combined risk. A *pod* is one such team with its own capital, risk limits and P&L.

**Definition 28.2 (Strategy correlation).**

*Strategy correlation* is the correlation between the P&L streams of two strategies; measured over normal periods it can be low while the strategies share an exposure that dominates in stress, so a firm estimates it both from P&L and from the positions’ factor exposures.

The firm’s first decision is how much risk each [pod](#def-s1-running-a-multi-strategy-book-multi) gets. Book 7, chapter 26’s risk budgeting gives the default: weights inversely proportional to each [pod](#def-s1-running-a-multi-strategy-book-multi)’s trailing volatility, so that each contributes similar risk, rebalanced monthly ([Listing 28.1](#lst-s1-running-a-multi-strategy-book-firm)). The synthetic firm has ten [pods](#def-s1-running-a-multi-strategy-book-multi) at 10% volatility each, with Sharpe ratios from 0.5 to 1.0. [Pods](#def-s1-running-a-multi-strategy-book-multi) 1 to 3 load 0.4 on a shared factor, [pods](#def-s1-running-a-multi-strategy-book-multi) 4 and 5 on another; the factors are as quiet as any other noise except in three ten-day crashes, each a fall of six [pod](#def-s1-running-a-multi-strategy-book-multi) volatilities. [Pod](#def-s1-running-a-multi-strategy-book-multi) 10’s edge dies after ten years.

## 28.2 Netting and shared risk

Measured on twenty years of daily P&L, the three [pods](#def-s1-running-a-multi-strategy-book-multi) on the first factor have an average correlation of 0.22; a [pod](#def-s1-running-a-multi-strategy-book-multi) on neither factor, $-0.004$ with the first. The correlation understates what they share. In each crash the three [pods](#def-s1-running-a-multi-strategy-book-multi) lose 2.4 to 2.6 of their annual volatilities together, 24% to 26% of capital, in ten days. The same trade under different names is invisible in correlations measured over calm years and obvious in the [pods](#def-s1-running-a-multi-strategy-book-multi)’ positions: a risk model (Book 7, chapter 24) maps each [pod](#def-s1-running-a-multi-strategy-book-multi)’s holdings to the factors, and the firm can cap the total exposure to each.

| firm at 10% volatility | no overlap control | factor cap 1.0 | factor cap 0.5 |
| --- | --- | --- | --- |
| Sharpe ratio | 1.45 | 1.52 | 1.70 |
| largest drawdown | 43.5% | 42.8% | 35.7% |
| loss in the three crashes | 31.5, 31.7, 33.6% | 30.1, 30.1, 32.3% | 21.6, 20.7, 22.9% |

The cap limits each shared factor’s total exposure to the equivalent of one (or half) equal-weight [pod](#def-s1-running-a-multi-strategy-book-multi), scaling down the [pods](#def-s1-running-a-multi-strategy-book-multi) that carry it. Capping at half a [pod](#def-s1-running-a-multi-strategy-book-multi) cuts each crash by about a third and raises the firm’s Sharpe ratio from 1.45 to 1.70 ([Figure 28.1](#fig-s1-running-a-multi-strategy-book-paths)), because the crashes were the main cost of the overlapping [pods](#def-s1-running-a-multi-strategy-book-multi). The losses are large because a firm of ten nearly uncorrelated [pods](#def-s1-running-a-multi-strategy-book-multi) must lever them to reach 10% volatility, and leverage multiplies whatever they share.

![The synthetic firm of ten pods, scaled to 10% volatility, with and without a cap on the pods’ shared factor exposures; cumulative sums of daily returns over twenty years, the shaded bands marking the three crashes of the shared factors. Data: s1_multistrat.paths.](https://one-course.com/images/onecourse/chapters/quant-8/s1-running-a-multi-strategy-book/fig-c96fdda79ead.svg)

***Figure 28.1.** The synthetic firm of ten [pods](#def-s1-running-a-multi-strategy-book-multi), scaled to 10% volatility, with and without a cap on the [pods](#def-s1-running-a-multi-strategy-book-multi)’ shared factor exposures; cumulative sums of daily returns over twenty years, the shaded bands marking the three crashes of the shared factors. Data: `s1_multistrat.paths`.*

The same central view saves costs. When [pods](#def-s1-running-a-multi-strategy-book-multi) trade the same instruments, the firm executes only the net: Book 7, chapter 27’s internal crossing. Ten [pods](#def-s1-running-a-multi-strategy-book-multi) trading 200 instruments independently, each trading a fifth of them, have 34.6% of their gross volume cancel inside the firm; if all trade all, 68.5%, close to $1 - 1/\sqrt{10}$.

## 28.3 Turning strategies off

**Definition 28.3 (Drawdown limit).**

A *drawdown limit* stops or cuts a strategy’s risk when its loss from its previous peak exceeds a threshold, a share of its allocated capital; it trades the cost of stopping good strategies in bad luck against the cost of running dead ones too long.

Every stop rule makes two errors. It stops [pods](#def-s1-running-a-multi-strategy-book-multi) whose edge is alive, and it lets dead ones run. [Figure 28.2](#fig-s1-running-a-multi-strategy-book-stops) shows the first: a [pod](#def-s1-running-a-multi-strategy-book-multi) with a Sharpe ratio of 0.7 at 10% volatility hits a 5% drawdown within a year on 91.6% of 20 000 simulated paths, a 10% drawdown on 34.5%, 20% on 2.1%. A limit is measured in the [pod](#def-s1-running-a-multi-strategy-book-multi)’s own volatilities: 5% is half a year’s standard deviation, well inside ordinary noise. In the synthetic firm, where stopped [pods](#def-s1-running-a-multi-strategy-book-multi) restart each year, a 5% limit stops 85.8 live [pods](#def-s1-running-a-multi-strategy-book-multi) for every hundred pod-years; at 20% it still stops 14.7, because the shared crashes push several [pods](#def-s1-running-a-multi-strategy-book-multi) through it together.

![False stops: the share of pods with a live edge that hit a drawdown limit within a year, for a single pod with a Sharpe ratio of 0.7 at 10% volatility (simulated paths) and for the synthetic firm’s pods, whose shared crashes add stops. Data: s1_multistrat.limits.](https://one-course.com/images/onecourse/chapters/quant-8/s1-running-a-multi-strategy-book/fig-f9f19948606e.svg)

***Figure 28.2.** False stops: the share of [pods](#def-s1-running-a-multi-strategy-book-multi) with a live edge that hit a [drawdown limit](#def-s1-running-a-multi-strategy-book-limit) within a year, for a single [pod](#def-s1-running-a-multi-strategy-book-multi) with a Sharpe ratio of 0.7 at 10% volatility (simulated paths) and for the synthetic firm’s [pods](#def-s1-running-a-multi-strategy-book-multi), whose shared crashes add stops. Data: `s1_multistrat.limits`.*

The second error is the dead [pod](#def-s1-running-a-multi-strategy-book-multi). Its Sharpe ratio falls from 0.9 to $-0.3$ after ten years; the 5% limit stops it 98 trading days later, the 10% limit after 307, the 15% limit after 979, and wider limits never, in the ten years left. A tight limit catches the dead [pod](#def-s1-running-a-multi-strategy-book-multi) quickly by catching nearly every [pod](#def-s1-running-a-multi-strategy-book-multi) quickly. The firm’s Sharpe ratio across limits (1.49 at 5%, 1.74 at 10%, 1.61 at 15%, 1.48 at 20%) peaks in the middle, and in a sample this size that peak is not a robust optimum.

## 28.4 Capital, drawdown limits and the pod model

The [drawdown limit](#def-s1-running-a-multi-strategy-book-limit) has a theory. Grossman and Zhou solved the problem of an investor who never wants wealth to fall below a fixed fraction of its running maximum: the optimal risky position is proportional to the distance to that floor. Risk falls as losses approach the floor instead of switching off at it, and it rises again as the surplus is rebuilt. A [pod](#def-s1-running-a-multi-strategy-book-multi) model that halves a [pod](#def-s1-running-a-multi-strategy-book-multi)’s risk at one threshold and stops it at a second is a two-step version of that rule. The central lessons of the chapter follow. Limits belong in units of each [pod](#def-s1-running-a-multi-strategy-book-multi)’s volatility and expected Sharpe ratio, not in round percentages. Shared exposures must be measured from positions, not from P&L correlations. And the firm’s capital is safest when drawdowns are controlled continuously, as Grossman and Zhou’s rule does, rather than by a cliff that stops many good [pods](#def-s1-running-a-multi-strategy-book-multi) to catch a few bad ones.

## 28.5 Strategy files

**Strategy file 28.1 — Multi-strategy allocation with overlap control.**

**Who pays you, and why.** The [pods](#def-s1-running-a-multi-strategy-book-multi)’ combined edges, with diversification when their risks are truly different.

**Instruments and venues.** Whatever the [pods](#def-s1-running-a-multi-strategy-book-multi) trade.

**Signal.** [Pods](#def-s1-running-a-multi-strategy-book-multi)’ trailing volatility and their positions’ factor exposures.

**Sizing and execution.** Risk budgets by inverse volatility; caps on each shared factor; trades netted across [pods](#def-s1-running-a-multi-strategy-book-multi).

**Costs.** Lower through netting; a risk model and a central execution desk.

**How it dies.** Crowded factors shared by many firms, as in August 2007.

**Horizon, capacity, infrastructure.** Continuous; position-level data from every [pod](#def-s1-running-a-multi-strategy-book-multi).

**Backtest honestly.** Exposures from positions at each date; crash episodes in the sample.

**Sources.** Khandani and Lo (2011); this chapter: drawdown 43.5% to 35.7% with a cap of half a [pod](#def-s1-running-a-multi-strategy-book-multi).

**Strategy file 28.2 — Drawdown-controlled exposure.**

**Who pays you, and why.** Nobody: it is a risk rule that trades expected return for a floor on losses.

**Instruments and venues.** Any strategy or the firm.

**Signal.** The distance from the running peak to a floor.

**Sizing and execution.** Risk proportional to the surplus over the floor, or cut in steps.

**Costs.** False stops and the return given up after them.

**How it dies.** Limits set in percentages rather than volatilities; shared crashes that hit many [pods](#def-s1-running-a-multi-strategy-book-multi) together.

**Horizon, capacity, infrastructure.** Continuous; daily P&L.

**Backtest honestly.** Count false stops as well as avoided losses.

**Sources.** Grossman and Zhou (1993); this chapter: 91.6% of healthy [pods](#def-s1-running-a-multi-strategy-book-multi) stopped in a year at a 5% limit.

## 28.6 Tutorial: five at once

**Goal.** Run a firm of ten [pods](#def-s1-running-a-multi-strategy-book-multi) with hidden shared factors, allocate with and without overlap control, apply [drawdown limits](#def-s1-running-a-multi-strategy-book-limit) and measure false stops and the dead [pod](#def-s1-running-a-multi-strategy-book-multi)’s survival, and net trades. **End state:** the tables and the two figures.

1. **Allocation and the firm**: risk budgets, the factor cap, drawdown stops. `def allocate (pnl, load, t: int , window: int = 252 , factor_cap: float | None = None ): vol = pnl[max (0 , t - window):t].std(0 ) w = 1 / np.maximum(vol, 1e-12 ) w /= w.sum() if factor_cap is not None : for k in range (load.shape[1 ]): expo = np.abs(load[:, k] * w * len (w)).sum() # in units of one equal-weight pod if expo > factor_cap: on = load[:, k] != 0 w[on] *= factor_cap / expo w /= w.sum() return w def run_firm (S, rebalance: int = 21 , factor_cap: float | None = None , limit: float | None = None ): pnl, load = S[" pnl " ], S[" load " ] T, P = pnl.shape firm = np.zeros(T) alive = np.ones(P, bool ) peak, eq = np.zeros(P), np.zeros(P) stops = [] w = np.full(P, 1 / P) for t in range (252 , T): if (t - 252 ) % rebalance == 0 : w = allocate(pnl, load, t, 252 , factor_cap) firm[t] = (w * alive * pnl[t]).sum() eq += pnl[t] * alive peak = np.maximum(peak, eq) if limit is not None : hit = alive & (peak - eq > limit) for i in np.flatnonzero(hit): stops.append((i, t)) alive &= ~hit eq[hit] = peak[hit] = 0.0 if (t - 252 ) % 252 == 0 : # stopped pods restart at the start of each year alive[:] = True return firm, stops` **Listing 28.1.** Risk budgets with a factor cap, and the firm with drawdown limits. code/firm/multistrat/firm_multistrat.py
2. **False stops and netting**. `def stop_rate (sr: float , vol: float , limit: float , years: float = 1.0 , n: int = 20_000 , rng=None ): rng = rng or np.random.default_rng(1 ) days = int (252 * years) d = vol / math.sqrt(252 ) x = np.cumsum(sr * d / math.sqrt(252 ) + d * rng.standard_normal((n, days)), axis=1 ) dd = np.maximum.accumulate(np.maximum(x, 0 ), axis=1 ) - x return float ((dd.max(1 ) > limit).mean()) def netting (trades): trades = np.asarray(trades, float ) gross = np.abs(trades).sum() return float (1 - np.abs(trades.sum(0 )).sum() / gross)` **Listing 28.2.** The chance of a false stop, and netting. code/firm/multistrat/firm_multistrat.py
3. **Run** `correlations()` , `overlap(cap)` , `limits(limit)` , `net_savings()` and `fig_multistrat.py` .

**What to change next.** Replace the cliff with Grossman and Zhou’s proportional rule; estimate the shared factors from P&L alone and see how late they are found; plug in the P&L of this book’s own strategies (chapters 2, 5, 19 and 20) as [pods](#def-s1-running-a-multi-strategy-book-multi).

## 28.7 Build: the multi-strategy firm

**Purpose.** Simulated [pods](#def-s1-running-a-multi-strategy-book-multi) with shared factors, risk-budget allocation with overlap control, [drawdown limits](#def-s1-running-a-multi-strategy-book-limit), false-stop rates and netting.

**Interface.** `PodConfig(…)`, `simulate_pods(cfg, rng)`, `allocate(pnl, load, t, window, factor_cap)`, `run_firm(S, rebalance, factor_cap, limit)`, `stop_rate(sr, vol, limit, years, n, rng)`, `netting(trades)`.

**Rules.** Allocations from past data; loadings from positions; stopped [pods](#def-s1-running-a-multi-strategy-book-multi) restart yearly.

**Acceptance tests.** `code/firm/multistrat/tests/`: shared factors correlate [pods](#def-s1-running-a-multi-strategy-book-multi) and crash them together, the cap lowers loaded [pods](#def-s1-running-a-multi-strategy-book-multi)’ weights, netting by hand, false stops falling with the limit.

**Stretch.** Proportional drawdown control; capital reallocation after stops; the book’s own strategies as [pods](#def-s1-running-a-multi-strategy-book-multi).

Sources and further reading

- A. E. Khandani and A. W. Lo, “What happened to the quants in August 2007? Evidence from factors and transactions data”, *Journal of Financial Markets* 14(1), 2011.
- S. J. Grossman and Z. Zhou, “Optimal investment strategies for controlling drawdowns”, *Mathematical Finance* 3(3), 1993.
- L. H. Pedersen, *Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined* , Princeton University Press, 2015.

## 28.8 Exercises

**Exercise 28.1 ★.**

Ten [pods](#def-s1-running-a-multi-strategy-book-multi) trade the same instruments with independent trades of equal size. What share of their gross volume does netting save?

**Solution of Exercise 28.1.**

The net of ten independent equal trades has a standard deviation $\sqrt{10}$ times one, against a gross of ten: netting saves $1 - 1/\sqrt{10} = 68.4\%$ (the simulation measures 68.5%).

**Exercise 28.2 ★.**

A [pod](#def-s1-running-a-multi-strategy-book-multi) loads 0.4 on a factor that falls six [pod](#def-s1-running-a-multi-strategy-book-multi) volatilities in a crash. What does the [pod](#def-s1-running-a-multi-strategy-book-multi) lose, in volatilities and in percent at 10% volatility?

**Solution of Exercise 28.2.**

$0.4 \times 6 = 2.4$ volatilities, 24% of capital at 10% volatility.

**Exercise 28.3 ★.**

Why do three [pods](#def-s1-running-a-multi-strategy-book-multi) with a correlation of 0.22 lose together in a crash?

**Solution of Exercise 28.3.**

Their correlation is measured mostly over calm days, when the shared factor is small noise; in a crash the shared factor dominates and all three move with it. A low average correlation hides a large common exposure in the tail.

**Exercise 28.4 ★★.**

A 5% [drawdown limit](#def-s1-running-a-multi-strategy-book-limit) stops 91.6% of [pods](#def-s1-running-a-multi-strategy-book-multi) at 10% volatility within a year. What share does it stop for [pods](#def-s1-running-a-multi-strategy-book-multi) run at 5% volatility, and why?

**Solution of Exercise 28.4.**

34.5%: at 5% volatility a 5% limit is one annual volatility, the same as a 10% limit at 10% volatility. What matters is the limit in the [pod](#def-s1-running-a-multi-strategy-book-multi)’s own volatilities.

**Exercise 28.5 ★★.**

Why does a tight limit catch the dead [pod](#def-s1-running-a-multi-strategy-book-multi) fastest, and at what cost?

**Solution of Exercise 28.5.**

Any [pod](#def-s1-running-a-multi-strategy-book-multi), dead or alive, hits a tight limit soon; the dead [pod](#def-s1-running-a-multi-strategy-book-multi)’s negative drift makes it sooner (98 days at 5%). The cost is stopping nearly every live [pod](#def-s1-running-a-multi-strategy-book-multi) each year (91.6% on the paths), losing their edge until they restart.

**Exercise 28.6 ★★.**

Explain Grossman and Zhou’s rule and how a two-step [pod](#def-s1-running-a-multi-strategy-book-multi) limit approximates it.

**Solution of Exercise 28.6.**

With wealth kept above a fraction of its running maximum, the optimal risky position is proportional to the surplus above that floor: risk shrinks smoothly as losses approach the floor and grows as the surplus is rebuilt. Halving risk at one drawdown and stopping at a second is a two-step approximation of that line.

**Exercise 28.7 ★★★.**

*Coding.* Run `overlap(0.25)` with a stricter cap. What happens to the crashes and the Sharpe ratio, and what would you worry about in a real firm?

**Solution of Exercise 28.7.**

With a cap of a quarter of a [pod](#def-s1-running-a-multi-strategy-book-multi), the crash losses fall to 12.2%, 11.1% and 13.0%, the largest drawdown to 28.0% and the Sharpe ratio rises to 1.72. In a real firm the factor map is estimated, not known: a strict cap on factors measured with error would cut [pods](#def-s1-running-a-multi-strategy-book-multi) for exposures they do not have, and would push [pods](#def-s1-running-a-multi-strategy-book-multi) toward exposures the risk model does not see.

**Exercise 28.8 ★★★.**

*Find the flaw.* “Our ten [pods](#def-s1-running-a-multi-strategy-book-multi) have an average pairwise correlation of 0.05 over three years, so the firm’s risk is diversified.”

**Solution of Exercise 28.8.**

Three years of mostly calm data measure the correlation of noise, not of the exposures that matter in stress; the synthetic firm’s overlapping [pods](#def-s1-running-a-multi-strategy-book-multi) had 0.22 on average and lost a quarter of their capital together. Measure exposures from positions and test the firm in stress scenarios.

## 28.9 Problem: Five at Once

**Problem 28.1.**

Weekend problem — a firm of pods

The chapter’s synthetic firm and the public record.

**Part I — The firm.**

1. Define a [multi-strategy book](#def-s1-running-a-multi-strategy-book-multi) , a [pod](#def-s1-running-a-multi-strategy-book-multi) and [strategy correlation](#def-s1-running-a-multi-strategy-book-correlation) .
2. Describe the synthetic firm: [pods](#def-s1-running-a-multi-strategy-book-multi) , shared factors, crashes and the dead [pod](#def-s1-running-a-multi-strategy-book-multi) .
3. How does the firm allocate risk?
4. What did Khandani and Lo find about August 2007?

**Part II — Shared risk.**

5. Give the correlations measured over twenty years and the [pods](#def-s1-running-a-multi-strategy-book-multi) ’ crash losses.
6. How does the firm detect the overlap?
7. Give the firm’s Sharpe ratio, largest drawdown and crash losses with and without the cap.
8. How much does netting save?

**Part III — Stops.**

9. Define a [drawdown limit](#def-s1-running-a-multi-strategy-book-limit) and its two errors.
10. Give the false-stop rates on simulated paths and in the firm.
11. How long does the dead [pod](#def-s1-running-a-multi-strategy-book-multi) run under each limit?
12. Why is the firm’s best limit not a robust optimum?

**Part IV — The verdict.**

13. State the *named result* : the firm’s drawdown with and without overlap detection, and the false-stop rate of a 5 per cent [drawdown limit](#def-s1-running-a-multi-strategy-book-limit) .
14. What did Grossman and Zhou show?
15. In what units should limits be set?
16. Why do shared crashes raise false stops at wide limits?
17. What data must every [pod](#def-s1-running-a-multi-strategy-book-multi) report to the centre?
18. How does this chapter relate to Book 7, chapter 28?
19. Which [pods](#def-s1-running-a-multi-strategy-book-multi) would you cut first after a crash, and why not all?
20. In one sentence: what does the centre of a multi-strategy firm add?

**Solution of Problem 28.1.**

1. A firm’s combined portfolio of strategies run by teams; one team with its own capital and limits; the correlation of their P&L, which can hide shared exposures.
2. Ten [pods](#def-s1-running-a-multi-strategy-book-multi) at 10% volatility, Sharpe ratios 0.5 to 1.0; [pods](#def-s1-running-a-multi-strategy-book-multi) 1–3 and 4–5 on two shared factors with three crashes; [pod](#def-s1-running-a-multi-strategy-book-multi) 10 dead after ten years.
3. By inverse trailing volatility, monthly.
4. A market-wide deleveraging in quantitative equity strategies, with unwinds on 1 and 6 August.
5. 0.22 among [pods](#def-s1-running-a-multi-strategy-book-multi) on the same factor, $-0.004$ with others; 2.4 to 2.6 volatilities lost together in each crash.
6. From positions mapped to risk-model factors, capping each factor’s total exposure.
7. 1.45, 43.5% and 31.5–33.6% without; 1.70, 35.7% and 20.7–22.9% with a cap of half a [pod](#def-s1-running-a-multi-strategy-book-multi) .
8. 34.6% when [pods](#def-s1-running-a-multi-strategy-book-multi) trade a fifth of the instruments, 68.5% when all trade all.
9. A stop on a loss from the peak; stopping live [pods](#def-s1-running-a-multi-strategy-book-multi) and running dead ones.
10. 91.6%, 34.5%, 8.9%, 2.1% and 0.0% on paths; 85.8%, 38.9%, 22.1%, 14.7% and 5.8% in the firm, for 5% to 30%.
11. 98, 307 and 979 days at 5%, 10% and 15%; never at 20% and 30%.
12. One sample, five candidates, and differences within the noise.
13. **Named result.** At 10% firm volatility the largest drawdown is 43.5% without overlap detection and 35.7% with the shared factors capped at half a [pod](#def-s1-running-a-multi-strategy-book-multi) ; a 5% [drawdown limit](#def-s1-running-a-multi-strategy-book-limit) stops 91.6% of healthy [pods](#def-s1-running-a-multi-strategy-book-multi) (Sharpe ratio 0.7, 10% volatility) within a year.
14. The optimal risky position is proportional to the surplus over a floor set as a fraction of the running maximum.
15. In the [pod](#def-s1-running-a-multi-strategy-book-multi) ’s own volatilities and expected Sharpe ratio.
16. Several [pods](#def-s1-running-a-multi-strategy-book-multi) lose together, each through its own limit.
17. Positions and their factor exposures, daily P&L, and trades for netting.
18. Book 7 measured crowding across firms; this chapter measures it inside one.
19. The [pods](#def-s1-running-a-multi-strategy-book-multi) most exposed to the factor that crashed, reduced to the cap; the others did not cause the loss.
20. A view of shared risk across [pods](#def-s1-running-a-multi-strategy-book-multi) , netting, and limits set in each [pod](#def-s1-running-a-multi-strategy-book-multi) ’s own units.

## 28.10 Interview questions

**Interview question 28.1 ★ risk.**

How would you set a [drawdown limit](#def-s1-running-a-multi-strategy-book-limit) for a new [pod](#def-s1-running-a-multi-strategy-book-multi)?

**Solution of Interview question 28.1.**

From the [pod](#def-s1-running-a-multi-strategy-book-multi)’s expected volatility and Sharpe ratio: choose the limit so that the chance of stopping a [pod](#def-s1-running-a-multi-strategy-book-multi) with the expected edge within a year is acceptable (a few percent), with a soft step that halves risk first; revise as the [pod](#def-s1-running-a-multi-strategy-book-multi)’s record grows.

**Interview question 28.2 ★★ risk.**

Two [pods](#def-s1-running-a-multi-strategy-book-multi) in different asset classes lost 8% each in the same week. What do you look for?

**Solution of Interview question 28.2.**

A shared exposure: map both books’ positions to common factors (crowded styles, liquidity, a common counterparty or funding source), check whether both hold the same names or trades under different labels, and look at other firms’ known positioning.

**Interview question 28.3 ★★ researcher.**

How would you estimate whether a strategy’s edge has died, and how long would it take?

**Solution of Interview question 28.3.**

Compare recent performance with the distribution implied by the expected Sharpe ratio, look for a mechanism that would have killed it (crowding, costs, regime), and accept that a Sharpe ratio drop from 0.9 to $-0.3$ takes about a year or more to detect with confidence.

**Interview question 28.4 ★★ developer.**

Design the netting of trades across [pods](#def-s1-running-a-multi-strategy-book-multi) trading the same instruments.

**Solution of Interview question 28.4.**

Collect [pods](#def-s1-running-a-multi-strategy-book-multi)’ orders by instrument over a short window, cross opposite orders internally at a fair reference price, send only the net to the market, and allocate fills and costs back to each [pod](#def-s1-running-a-multi-strategy-book-multi) fairly; keep an audit trail.

**Interview question 28.5 ★★ trader.**

Your [pod](#def-s1-running-a-multi-strategy-book-multi) is 4% below its peak and the limit is 5%. What do you do, and what should the firm want you to do?

**Solution of Interview question 28.5.**

Reduce risk before the limit does it for you, keeping the positions with the best edge; the firm should want risk cut smoothly as the drawdown grows, not a [pod](#def-s1-running-a-multi-strategy-book-multi) that gambles to recover or one that dumps everything at the line.

**Interview question 28.6 ★★★ researcher.**

A [pod](#def-s1-running-a-multi-strategy-book-multi)’s cumulative P&L is a Brownian motion with drift $\mu$ and volatility $\sigma$. Using the fact that for $\mu = 0$ the drawdown from the running maximum at time $T$ is distributed as $|W_T|$, give the probability that the drawdown exceeds $L$ at a given time $T$, and explain why the probability that it ever exceeds $L$ within $T$ is larger.

**Solution of Interview question 28.6.**

For $\mu = 0$, $P(D_T > L) = P(|W_T| > L) = 2\big(1 - \Phi(L/(\sigma\sqrt{T}))\big)$; for $L = 0.5\sigma$ and $T = 1$ year it is 0.617. The drawdown can exceed $L$ at some time before $T$ and recover by $T$, so the probability that it ever exceeds $L$ within $T$ is larger; that is what a stop rule triggers on.