Benchmark Risk and Active Risk Budgets

Question 1

A $100m fund holds 42% industry A, 28% B, and 30% C. Its benchmark holds 35%, 35%, and 30% respectively. Ignore cash and price changes. What is the active weight in A?

Accepted Answer

+7 points

Question 2

A $100m fund holds 42% industry A, 28% B, and 30% C. Its benchmark holds 35%, 35%, and 30% respectively. Ignore cash and price changes. What is active weight in B?

Accepted Answer

−7 points

Question 3

A $100m fund holds 42% industry A, 28% B, and 30% C. Its benchmark holds 35%, 35%, and 30% respectively. Ignore cash and price changes. What is active weight in C?

Accepted Answer

Zero.

Question 4

A $100m fund holds 42% industry A, 28% B, and 30% C. Its benchmark holds 35%, 35%, and 30% respectively. Ignore cash and price changes. What trade neutralizes both nonzero active weights?

Accepted Answer

Sell $7m A and buy $7m B.

Question 5

A $100m fund holds 42% industry A, 28% B, and 30% C. Its benchmark holds 35%, 35%, and 30% respectively. Ignore cash and price changes. If A beats B by 4 percentage points, what active contribution follows from these static weights?

Accepted Answer

+28 bp

Question 6

A $100m fund holds 42% industry A, 28% B, and 30% C. Its benchmark holds 35%, 35%, and 30% respectively. Ignore cash and price changes. If the benchmark increases A by 2 points funded from B, what is A's active weight now?

Accepted Answer

+5 points

Question 7

A $100m fund holds 42% industry A, 28% B, and 30% C. Its benchmark holds 35%, 35%, and 30% respectively. Ignore cash and price changes. What happens to B's active weight after that benchmark change?

Accepted Answer

−5 points

Question 8

A $100m fund holds 42% industry A, 28% B, and 30% C. Its benchmark holds 35%, 35%, and 30% respectively. Ignore cash and price changes. Why model active and absolute risk separately?

Accepted Answer

A benchmark weight can be large despite zero active weight.

Question 9

A $100m fund holds 42% industry A, 28% B, and 30% C. Its benchmark holds 35%, 35%, and 30% respectively. Ignore cash and price changes. What makes the benchmark comparison meaningful?

Accepted Answer

A benchmark consistent with the mandate.

Question 10

A $100m fund holds 42% industry A, 28% B, and 30% C. Its benchmark holds 35%, 35%, and 30% respectively. Ignore cash and price changes. Which update matters even if the PM makes no trades?

Accepted Answer

Benchmark constituent or weight changes.

Question 11

Two active themes have standalone annual volatilities of 3% and 4%. Their correlation is zero at first. The tracking-error cap is 6%. Use variance = a² + b² + 2ρab. What is portfolio tracking error at zero correlation?

Accepted Answer

5%

Question 12

Two active themes have standalone annual volatilities of 3% and 4%. Their correlation is zero at first. The tracking-error cap is 6%. Use variance = a² + b² + 2ρab. How much headroom does the initial forecast show?

Accepted Answer

1 point

Question 13

Two active themes have standalone annual volatilities of 3% and 4%. Their correlation is zero at first. The tracking-error cap is 6%. Use variance = a² + b² + 2ρab. What if correlation rises to 0.5?

Accepted Answer

About 6.08%

Question 14

Two active themes have standalone annual volatilities of 3% and 4%. Their correlation is zero at first. The tracking-error cap is 6%. Use variance = a² + b² + 2ρab. Does the 0.5 case meet the cap?

Accepted Answer

No, it exceeds 6%.

Question 15

Two active themes have standalone annual volatilities of 3% and 4%. Their correlation is zero at first. The tracking-error cap is 6%. Use variance = a² + b² + 2ρab. What is tracking error at perfect positive correlation?

Accepted Answer

7%

Question 16

Two active themes have standalone annual volatilities of 3% and 4%. Their correlation is zero at first. The tracking-error cap is 6%. Use variance = a² + b² + 2ρab. What is tracking error at perfect negative correlation?

Accepted Answer

1%

Question 17

Two active themes have standalone annual volatilities of 3% and 4%. Their correlation is zero at first. The tracking-error cap is 6%. Use variance = a² + b² + 2ρab. Which assumption makes an apparent budget surplus fragile?

Accepted Answer

Low correlation that fails under stress.

Question 18

Two active themes have standalone annual volatilities of 3% and 4%. Their correlation is zero at first. The tracking-error cap is 6%. Use variance = a² + b² + 2ρab. What reduction should be compared before trimming either theme?

Accepted Answer

Change in portfolio tracking error.

Question 19

Two active themes have standalone annual volatilities of 3% and 4%. Their correlation is zero at first. The tracking-error cap is 6%. Use variance = a² + b² + 2ρab. Why test a separate stressed risk cap or scenario?

Accepted Answer

Normal tracking error can understate joint losses.

Question 20

Two active themes have standalone annual volatilities of 3% and 4%. Their correlation is zero at first. The tracking-error cap is 6%. Use variance = a² + b² + 2ρab. What should follow an actual trim?

Accepted Answer

Recalculate with confirmed exposures.

Question 21

A software tilt contributes +0.30 active growth-factor beta and a retail tilt +0.25. A utility tilt contributes −0.10. The approved maximum net growth beta is +0.35. Treat betas as additive. What net factor beta is held?

Accepted Answer

+0.45

Question 22

A software tilt contributes +0.30 active growth-factor beta and a retail tilt +0.25. A utility tilt contributes −0.10. The approved maximum net growth beta is +0.35. Treat betas as additive. How far above the cap is the book?

Accepted Answer

0.10

Question 23

A software tilt contributes +0.30 active growth-factor beta and a retail tilt +0.25. A utility tilt contributes −0.10. The approved maximum net growth beta is +0.35. Treat betas as additive. If software alone is trimmed, what beta should it contribute at the boundary?

Accepted Answer

+0.20

Question 24

A software tilt contributes +0.30 active growth-factor beta and a retail tilt +0.25. A utility tilt contributes −0.10. The approved maximum net growth beta is +0.35. Treat betas as additive. What net beta follows closing the utility tilt instead?

Accepted Answer

+0.55

Question 25

A software tilt contributes +0.30 active growth-factor beta and a retail tilt +0.25. A utility tilt contributes −0.10. The approved maximum net growth beta is +0.35. Treat betas as additive. If growth factor falls 8%, what first-order active return follows before trades?

Accepted Answer

−3.6%

Question 26

A software tilt contributes +0.30 active growth-factor beta and a retail tilt +0.25. A utility tilt contributes −0.10. The approved maximum net growth beta is +0.35. Treat betas as additive. At the cap, what modeled active return follows that shock?

Accepted Answer

−2.8%

Question 27

A software tilt contributes +0.30 active growth-factor beta and a retail tilt +0.25. A utility tilt contributes −0.10. The approved maximum net growth beta is +0.35. Treat betas as additive. What does the sector breakdown obscure?

Accepted Answer

Both tilts use the same factor budget.

Question 28

A software tilt contributes +0.30 active growth-factor beta and a retail tilt +0.25. A utility tilt contributes −0.10. The approved maximum net growth beta is +0.35. Treat betas as additive. Which evidence supports keeping a specific tilt?

Accepted Answer

Expected alpha relative to its marginal risk and cost.

Question 29

A software tilt contributes +0.30 active growth-factor beta and a retail tilt +0.25. A utility tilt contributes −0.10. The approved maximum net growth beta is +0.35. Treat betas as additive. What if the factor hedge also offsets an intentional value exposure?

Accepted Answer

Measure the new residual risks.

Question 30

A software tilt contributes +0.30 active growth-factor beta and a retail tilt +0.25. A utility tilt contributes −0.10. The approved maximum net growth beta is +0.35. Treat betas as additive. What should be monitored after a benchmark rebalance?

Accepted Answer

Updated active betas and limit headroom.

Question 31

A risk model reports $4m total active volatility. Euler component contributions are $2.5m for A, $2m for B, and −$0.5m for an offsetting sleeve C. The active volatility cap is $4.5m. What share of total risk comes from A on this attribution?

Accepted Answer

62.5%

Question 32

A risk model reports $4m total active volatility. Euler component contributions are $2.5m for A, $2m for B, and −$0.5m for an offsetting sleeve C. The active volatility cap is $4.5m. What is the combined contribution from A and B?

Accepted Answer

$4.5m

Question 33

A risk model reports $4m total active volatility. Euler component contributions are $2.5m for A, $2m for B, and −$0.5m for an offsetting sleeve C. The active volatility cap is $4.5m. What headroom does the current book have?

Accepted Answer

$0.5m

Question 34

A risk model reports $4m total active volatility. Euler component contributions are $2.5m for A, $2m for B, and −$0.5m for an offsetting sleeve C. The active volatility cap is $4.5m. What does the negative contribution suggest locally?

Accepted Answer

C offsets some current risk.

Question 35

A risk model reports $4m total active volatility. Euler component contributions are $2.5m for A, $2m for B, and −$0.5m for an offsetting sleeve C. The active volatility cap is $4.5m. Can the exact tracking error without C be read from its contribution alone?

Accepted Answer

No, rerun the model.

Question 36

A risk model reports $4m total active volatility. Euler component contributions are $2.5m for A, $2m for B, and −$0.5m for an offsetting sleeve C. The active volatility cap is $4.5m. Which comparison helps rank two possible cuts?

Accepted Answer

Recomputed risk and alpha forgone for each.

Question 37

A risk model reports $4m total active volatility. Euler component contributions are $2.5m for A, $2m for B, and −$0.5m for an offsetting sleeve C. The active volatility cap is $4.5m. What if C loses its offset in a stress?

Accepted Answer

Reassess the budget and stress protection.

Question 38

A risk model reports $4m total active volatility. Euler component contributions are $2.5m for A, $2m for B, and −$0.5m for an offsetting sleeve C. The active volatility cap is $4.5m. Why reconcile total and component figures?

Accepted Answer

They must use the same model and weights.

Question 39

A risk model reports $4m total active volatility. Euler component contributions are $2.5m for A, $2m for B, and −$0.5m for an offsetting sleeve C. The active volatility cap is $4.5m. What if A owns two internally offsetting views?

Accepted Answer

Look through to the drivers and risks.

Question 40

A risk model reports $4m total active volatility. Euler component contributions are $2.5m for A, $2m for B, and −$0.5m for an offsetting sleeve C. The active volatility cap is $4.5m. What committee language is defensible?

Accepted Answer

A is the largest current modeled contributor.

Question 41

A PM must cut at least 40 bp of forecast tracking error. Candidate A cuts 45 bp and gives up 18 bp of expected alpha at 4 bp cost. Candidate B cuts 50 bp and gives up 12 bp alpha at 7 bp cost. Candidate C cuts 30 bp and gives up 6 bp at 2 bp cost. Assumed impacts are on a common horizon and additive for the cost screen. What is A's total modeled economic cost?

Accepted Answer

22 bp

Question 42

A PM must cut at least 40 bp of forecast tracking error. Candidate A cuts 45 bp and gives up 18 bp of expected alpha at 4 bp cost. Candidate B cuts 50 bp and gives up 12 bp alpha at 7 bp cost. Candidate C cuts 30 bp and gives up 6 bp at 2 bp cost. Assumed impacts are on a common horizon and additive for the cost screen. What is B's total cost?

Accepted Answer

19 bp

Question 43

A PM must cut at least 40 bp of forecast tracking error. Candidate A cuts 45 bp and gives up 18 bp of expected alpha at 4 bp cost. Candidate B cuts 50 bp and gives up 12 bp alpha at 7 bp cost. Candidate C cuts 30 bp and gives up 6 bp at 2 bp cost. Assumed impacts are on a common horizon and additive for the cost screen. What is C's total cost?

Accepted Answer

8 bp

Question 44

A PM must cut at least 40 bp of forecast tracking error. Candidate A cuts 45 bp and gives up 18 bp of expected alpha at 4 bp cost. Candidate B cuts 50 bp and gives up 12 bp alpha at 7 bp cost. Candidate C cuts 30 bp and gives up 6 bp at 2 bp cost. Assumed impacts are on a common horizon and additive for the cost screen. Which single action is cheapest among those meeting the requirement?

Accepted Answer

B.

Question 45

A PM must cut at least 40 bp of forecast tracking error. Candidate A cuts 45 bp and gives up 18 bp of expected alpha at 4 bp cost. Candidate B cuts 50 bp and gives up 12 bp alpha at 7 bp cost. Candidate C cuts 30 bp and gives up 6 bp at 2 bp cost. Assumed impacts are on a common horizon and additive for the cost screen. How much more than required does B cut?

Accepted Answer

10 bp

Question 46

A PM must cut at least 40 bp of forecast tracking error. Candidate A cuts 45 bp and gives up 18 bp of expected alpha at 4 bp cost. Candidate B cuts 50 bp and gives up 12 bp alpha at 7 bp cost. Candidate C cuts 30 bp and gives up 6 bp at 2 bp cost. Assumed impacts are on a common horizon and additive for the cost screen. If B's trading cost doubles, what is the cheapest compliant single action?

Accepted Answer

A.

Question 47

A PM must cut at least 40 bp of forecast tracking error. Candidate A cuts 45 bp and gives up 18 bp of expected alpha at 4 bp cost. Candidate B cuts 50 bp and gives up 12 bp alpha at 7 bp cost. Candidate C cuts 30 bp and gives up 6 bp at 2 bp cost. Assumed impacts are on a common horizon and additive for the cost screen. Why avoid summing risk reductions for two actions blindly?

Accepted Answer

Portfolio covariance can make reductions interact.

Question 48

A PM must cut at least 40 bp of forecast tracking error. Candidate A cuts 45 bp and gives up 18 bp of expected alpha at 4 bp cost. Candidate B cuts 50 bp and gives up 12 bp alpha at 7 bp cost. Candidate C cuts 30 bp and gives up 6 bp at 2 bp cost. Assumed impacts are on a common horizon and additive for the cost screen. What could disqualify the cheapest plan operationally?

Accepted Answer

Insufficient executable depth or timing.

Question 49

A PM must cut at least 40 bp of forecast tracking error. Candidate A cuts 45 bp and gives up 18 bp of expected alpha at 4 bp cost. Candidate B cuts 50 bp and gives up 12 bp alpha at 7 bp cost. Candidate C cuts 30 bp and gives up 6 bp at 2 bp cost. Assumed impacts are on a common horizon and additive for the cost screen. What other concentration check matters after the cut?

Accepted Answer

Whether residual risk shifts into one weaker view.

Question 50

A PM must cut at least 40 bp of forecast tracking error. Candidate A cuts 45 bp and gives up 18 bp of expected alpha at 4 bp cost. Candidate B cuts 50 bp and gives up 12 bp alpha at 7 bp cost. Candidate C cuts 30 bp and gives up 6 bp at 2 bp cost. Assumed impacts are on a common horizon and additive for the cost screen. What should the recommendation include?

Accepted Answer

Trade, expected risk reduction, cost, and review trigger.

Question 51

An index will add a stock at 3% next week, funding it by reducing other weights proportionally. A $200m fund holds none and can stage trades. An interim policy allows at most a 2% active overweight before the effective date. What stock notional matches the future weight at unchanged NAV?

Accepted Answer

$6m

Question 52

An index will add a stock at 3% next week, funding it by reducing other weights proportionally. A $200m fund holds none and can stage trades. An interim policy allows at most a 2% active overweight before the effective date. What is the maximum permissible pre-effective holding?

Accepted Answer

$4m

Question 53

An index will add a stock at 3% next week, funding it by reducing other weights proportionally. A $200m fund holds none and can stage trades. An interim policy allows at most a 2% active overweight before the effective date. What residual remains if the fund builds the maximum early?

Accepted Answer

$2m

Question 54

An index will add a stock at 3% next week, funding it by reducing other weights proportionally. A $200m fund holds none and can stage trades. An interim policy allows at most a 2% active overweight before the effective date. If the price rises 5% with no other changes, what must be checked on the early holding?

Accepted Answer

Whether the interim weight breaches the cap.

Question 55

An index will add a stock at 3% next week, funding it by reducing other weights proportionally. A $200m fund holds none and can stage trades. An interim policy allows at most a 2% active overweight before the effective date. What is active weight after effectiveness if the fund still holds exactly 2%, ignoring that price rise?

Accepted Answer

−1 point

Question 56

An index will add a stock at 3% next week, funding it by reducing other weights proportionally. A $200m fund holds none and can stage trades. An interim policy allows at most a 2% active overweight before the effective date. What could justify staging?

Accepted Answer

Spread market impact across windows within interim limits.

Question 57

An index will add a stock at 3% next week, funding it by reducing other weights proportionally. A $200m fund holds none and can stage trades. An interim policy allows at most a 2% active overweight before the effective date. Why track the effective timestamp?

Accepted Answer

It changes when the benchmark exposure applies.

Question 58

An index will add a stock at 3% next week, funding it by reducing other weights proportionally. A $200m fund holds none and can stage trades. An interim policy allows at most a 2% active overweight before the effective date. What if the index delays the addition?

Accepted Answer

Reassess early active risk and exit costs.

Question 59

An index will add a stock at 3% next week, funding it by reducing other weights proportionally. A $200m fund holds none and can stage trades. An interim policy allows at most a 2% active overweight before the effective date. What could reduce last-minute exposure?

Accepted Answer

A permitted transition plan and realistic closing liquidity estimates.

Question 60

An index will add a stock at 3% next week, funding it by reducing other weights proportionally. A $200m fund holds none and can stage trades. An interim policy allows at most a 2% active overweight before the effective date. What performance split helps afterward?

Accepted Answer

Transition costs versus active return while early or late.

Question 61

A $100m equity fund has $10m cash, $90m in unit-beta benchmark-like stocks, and no overlay. Benchmark beta is one. A futures contract supplies $250k of beta notional. What is the fund's current beta?

Accepted Answer

0.90

Question 62

A $100m equity fund has $10m cash, $90m in unit-beta benchmark-like stocks, and no overlay. Benchmark beta is one. A futures contract supplies $250k of beta notional. What is active beta?

Accepted Answer

−0.10

Question 63

A $100m equity fund has $10m cash, $90m in unit-beta benchmark-like stocks, and no overlay. Benchmark beta is one. A futures contract supplies $250k of beta notional. What hedge notional closes the active beta gap?

Accepted Answer

$10m long

Question 64

A $100m equity fund has $10m cash, $90m in unit-beta benchmark-like stocks, and no overlay. Benchmark beta is one. A futures contract supplies $250k of beta notional. How many contracts accomplish that?

Accepted Answer

40 long

Benchmark Risk and Active Risk Budgets

Active weights

Tracking error budget

A common growth factor

Risk contribution

Deciding what to trim

Benchmark transition

Cash and benchmark beta

Time horizon

Deliberate versus incidental risk

Committee allocation