Test ID: 7442155
The Fundamental Law of Active Management
Question #1 of 15
Question ID: 464589ᅞ A) ᅚ B) ᅞ C)
Question #2 of 15
Question ID: 464584ᅚ A) ᅞ B) ᅞ C)
Question #3 of 15
Question ID: 464591Harmesh Zumaisanactivemanager wholast year achievedaninformationcoefficientof 0.06 andmade52forecastsover
the year. Acomparablemanager hadaninformationcoefficientof 0.03andmade160 forecastsfor the year. Assuminga constantlevelof risk aversenessfor bothmanagers, Zuma'svalueaddedattheoptimallevelof risk is most likely:
equal to the comparable manager higher than the comparable manager lower than the comparable manager
Explanation
Zuma VA = (0.06 × 52) / 4λ = 0.187 / 4λ
Comparable = (0.03 × 160) / 4λ = 0.144 / 4λ
An active manager currently covers 40 stocks and makes a forecast for each of them every quarter. Next year he intendsto
cover the same stocks butonly once every 6 months. Assuming the manager'sskill, measured in termsof the correlation of each forecast with actual returns doesn't change, which of the following statements is most accurate?
The information ratio will fall by approximately 30% The information ratio will fall by approximately 50% The information coefficient will fall by approximately 50%
Explanation
Information ratio (IR) = IC ×
Hence a reduction in the breadth from 160 (40 × 4) to 80 (40 × 2) will cause an approximate 30% drop in the IR Withquarterly predictions IR = IC × 160 = 12.65 (IC)
Withsemi-annualforecasts IR = IC × 80 = 8.94 (IC)
8.94IC / 12.65IC = 0.701
Hence the Information Ratio will fall by approximately 30%. Note that full calculation is not required. Given that IR changes with
the square rootof breadth, a 50% drop in breadth must cause a lessthan 50% drop in IR.
An active manager has an information coefficientof 0.12 and follows 100 stocks. The manager makes a forecaston each 2
2
½
ᅚ A)
ᅞ B)
ᅞ C)
Question #4 of 15
QuestionID:464592ᅚ A) ᅞ B) ᅞ C)
Question #5 of 15
QuestionID:464594stock every quarter. If the manager has a risk aversion of 0.10, which of the following statements is least accurate?
If the manager decided to make forecasts every six months and the information coefficient and risk aversion level remained constant, the optimal level of residual risk would be half of the original.
If the manager keptthe number of forecasts and information coefficient constant, but
doubled his level of risk aversion, the optimal level of residual risk would fall be half. If the manager increased the information coefficientto 0.24 while keeping the number of forecasts and risk aversion constant, the optimal level of residual risk would double.
Explanation
The optimal level of residual risk is a function of the square root of breadth, so the optimal level would not be half its original value if the number of forecasts was cut by half.
Jon Gamlin is comparing a markettiming strategy with a stock selection strategy. He drawsthe following two conclusions: Conclusion 1
To achieve the same information ratio, a markettimer making weekly forecasts on the movement of the market needsto have a higher skill level than a stock selector following 25 stocks and updating the forecastsemi-annually
Conclusion 2
A specialist following only 4 stocks who revises his forecast 100 times per year will achieve the same information ratio as a
stock selector with the same skill level who follows 50 stocks and updates his assessmentssemi-annually Regarding Gamlin's conclusions:
Neither conclusion is correct.
Only conclusion 2 is correct. Only conclusion 1 is correct.
Explanation
In conclusion 1, the markettimer has a breadth of 52 and the stock selector 50. In order to achieve the same information ratio,
the stock selector would need to make up for the lower breadth with a higher information coefficient.
In conclusion 2, the specialist has a breadth of 400 and the selector 100. If they have the same skill level, the specialist with
the larger breadth will have a higher information ratio
ᅞ A)
ᅞ B)
ᅚ C)
Question #
6
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Question ID: 464597ᅚ A)
ᅞ B)
ᅞ C)
Question #7 of 15
Question ID: 464585As Fortina's strategy has a much larger breadth, she must have a larger information coefficient than Grenkin.
As both managers have the same information ratio, they must also have the same information coefficient.
As Grenkin makes fewer bets per year, he requires a higher information coefficient on each betthan Fortina to achieve the same information ratio.
Explanation
As a stock selector, Fortina makes many more bets per period and has a much larger breadth. She therefore requires a lower information coefficientthan Grenkin to achieve the same information ratio. Grenkin requires a higher coefficient.
Grenkin 0.75 = IC × 4 IC = 0.75/2 = 0.375
Fontina 0.75 = IC × 200 IC = 0.75/14.14 = 0.053
(Note: Calculations are not required)
Toby Intark is an active manager who employs a markettiming strategy. He has historically used a single independentsource of information to make his predictions and has consistently achieved an information coefficient of 0.09. Intark is considering
subscribing to an internetservice which will give him a new source of information to assist him with his forecasts. Which of the following statements regarding the information coefficient of the combined forecasts is least accurate?
If the new information source has no correlation with the existing information source, the combined information coefficient will be 0.18.
Asthe correlation between the two sources increases, the value of the second source decreases.
If the new information source is perfectly correlated with the existing information
source, the combined information coefficient will remain at 0.09.
Explanation
When there is no correlation, r = 0. IC = IC(2) . IC = (2) × 0.09 = 0.127.
When there is perfect correlation, r = 1. IC = IC = 0.09.
An active manager expects his information coefficientto drop from 0.08 to 0.02 in the coming period due to extremely volatile and unpredictable markets. As a response he intendsto increase his breadth by a factor of 4. Which of the following
½
½
(combined) ½
(combined) ½
ᅚ A) ᅞ B) ᅞ C)
Question #
8
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Question ID: 464600ᅞ A) ᅚ B) ᅞ C)
Question #
9
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Question ID: 464599ᅚ A) ᅞ B) ᅞ C)
Question #1
0
of 15
Question ID: 464595statements is most accuratelydescribesthe impactonthe information ratio?
The information ratio will decrease
The information ratiowill remain constant
The information ratiowill increase
Explanation
Information ratio (IR) = IC ×
If breadthisincreased by a factor of4, thiswouldincrease the information ratio by a factor of2. Asthe information coefficient
isdecreasing by a factor of4, the information ratiowill decrease.
There are three main assumptions underlyingthe fundamental lawof active management. Whichofthe followingstatements
regardingthose assumptionsisleast accurate?
The information coefficient for each bet is constant. Managers use the same setofinformationtomake each bet.
Managers are aware oftheir owninformation coefficient andinvest appropriately.
Explanation
The assumptionstatesthatthe sourcesofinformation are independenti.e. the manager doesnot betonthe same information
twice.
An active manager is considering adding an additional data source toimprove hisforecasts. The manager's current
information coefficientis 0.02. Ifthe seconddata source has a correlation coefficientof1.0 withthe firstsource, whichofthe
followingis closesttothe manager's combinedinformation coefficient?
0.020
0.028 0.040
Explanation
Asource ofdata thatis perfectly correlatedwith another source will notincrease the information coefficient.
An active manager currently makesquarterly betson100 stocks. Hisinformation coefficientfor these forecastsis 0.02. He is
ᅚ A) ᅞ B) ᅞ C)
Question #11 of 15
QuestionID:464588ᅞ A) ᅞ B) ᅚ C)
Question #12 of 15
QuestionID:464586unrelatedinformationsource, he anticipates aninformation coefficientofonly 0.01for the newforecasts. Whichofthe
followingstatementsis closesttothe impactonthe information ratio?
The information ratio will increase by approximately 12.5%
The information ratiowill remainthe same
The information ratiowill increase by approximately 25%
Explanation
Information ratio (IR) = IC ×
CurrentIR = 0.02 x 400 = 0.40
CombinedIR = (IC × BR) + (IC × BR
CombinedIR = (0.02 x 400) + (0.01 x 400) CombinedIR = 0.20
CombinedIR = 0.45
Increase = 0.45/0.40 − 1 = 12.5%
Whichofthe followingstatements regardingthe optimal level of residual risk is mostaccurate? Optimal level of residual risk:
is independent of the accuracy of the manager's forecasts
will decrease asthe breadthincreases
will increase proportionately withthe skill ofthe manager
Explanation
The optimal level of residual risk that a manager shouldtake ω* is:
The ICmeasuresthe skill level ofthe manager (i.e. the accuracy offorecasts). The optimal level will therefore increase directly
withthe skill level.
Roger Tankartis reviewing a piece of analysis performed by a junior member ofstaffwithinhisinvestmentfirm. The analysis
coversthe performance of active managers, andthe appendix containsthe followingtwostatements:
Statement One:The information coefficientismultiplied by the breadthof a strategy togetthe information ratio. StatementTwo:The information coefficientisthe correlationof eachforecastwiththe actual outcome.
Howmany ofthe statements are CORRECT?
½
2
12 1 22 2
2 2 2
ᅞ A)
The law requires that a manger's information coefficient increases with the number of forecasts made
Question #15 of 15
QuestionID:464596ᅚ A) ᅞ B) ᅞ C)
The markettimer hasa lower breadth. Inorder toachieve the same information ratiohe musthave ahigher information coefficient. Note calculationsnot required.
Aclientiscurrently consideringthree active managerstomanage his portfolio. The three active managershave the following
information ratios:
Manager Information Ratio
A 0.45
B 0.50
C 0.70
Assumingthe managershave independentactive risks, whichofthe followingisclosesttothe highestinformation ratiothe
clientcouldachieve acrossall three managers?
0.97 0.70 0.55
Explanation
Usingthe principle ofadditivity:
OverallIR = IR + IR + IR
= 0.45 + 0.50 + 0.70
= 0.9425
IR = 0.97
2
A2 B2 C2
