Answers - Reading 40 Analysis of Active Portfolio Management

Question #1 of 40 Question ID: 1474068 Charles Griffith makes quarterly bets between stocks of industrial and utility sectors. The historical correlation between the returns of the two sectors is -0.20 and Griffith's bets have been correct 55% of the time. Further information is as below: Benchmark Sector Industrial Utility E (R) σ Weight 12.00% 13.0% 80% 5.2% 2.5% 20% The expected annualized active return of Griffith's sector rotation strategy is closest to: A) 13.72% B) 10.64% C) 5.48% Explanation IC = 2(0.55) – 1 = 0.10 Combined active risk = σC = [σI2 -2σIσUrIU+ σU2]1/2 = [0.132 + 0.0252 – 2 (0.13)(0.025)(-0.20)]1/2 = 0.1372 or 13.72% Annualized active risk = 0.1372 x (4)1/2 = 0.2744 or 24.44% Annualized active return = IC x √BR x σA = 0.10 x (4)1/2 x 0.2744 = 0.0548 or 5.48% Alternatively, Active return from this strategy using a probability weighted average (given Griffith makes correct calls 55% of time) of combined risk is: (0.55)(0.1372) + (0.45)(-0.1372) = 0.0137 or 1.37% per quarter. Annual active return = 1.37% x 4 = 5.48%. (Module 40.4, LOS 40.e) Question #2 of 40 Question ID: 1474066 Charles Griffith makes quarterly bets between stocks of industrial and utility sectors. The historical correlation between the returns of the two sectors is -0.20.Further information is as below: Benchmark Sector Industrial Utility E (R) σ Weight 12.00% 13.0% 80% 5.2% 2.5% 20% The annualized active risk of Griffith's strategy is closest to: A) 13.72% B) 10.90% C) 27.44% Explanation Combined active risk = σC = [σI2 -2σIσUrIU+ σU2]1/2 = [0.132 + 0.0252 – 2 (0.13)(0.025)(-0.20)]1/2 = 0.1372 or 13.72% Annualized active risk = 0.1372 x (4)1/2 = 0.2744 or 27.44% (Module 40.4, LOS 40.e) Question #3 of 40 Question ID: 1474052 Which of the following is correct for a constrained active portfolio? A) TC=1 B) TC<1 C) TC>1 Explanation When we impose constraints on portfolios, the actual active weights (Δwi) will differ from optimal active weights (Δwi*) and TC<1. (Module 40.3, LOS 40.c) Radina Radichkova, CFA, is considering investing in one of three actively managed funds whose benchmark is the FTSE 100. The Sharpe ratio and standard deviation of the benchmark are 0.50 and 15%, respectively. Alpha Bankso Crystal Active return 3.2% 2.8% 12.5% Active risk 3.6% 15.5% 4.1% Radichkova is also analyzing an actively managed portfolio consisting of financials and pharmaceuticals. The following table shows the weights and returns of the benchmark and portfolio: Sector Financials WB WP RB RP 50% 70% 9.2% 17.8% Pharmaceuticals 50% 30% 8.1% 6.3% Radichkova makes the following comments about the two-sector portfolio: Comment 1: The value added is 5.7%. Comment 2: The asset allocation decision only accounts for 0.22% of the value added. Radichkova is writing a summary of the fundamental law of active management. In that section of the report, she states that the transfer coefficient can be viewed as the correlation between: 1. ex-ante active returns and actual active weights 2. risk-weighted optimal active weights and risk-weighted actual active weights 3. ex-ante active returns and realized active returns Question #4 - 7 of 40 Question ID: 1474059 In relation to funds Alpha, Bankso, and Crystal, the highest achievable Sharpe ratio is closest to: A) 0.85. B) 0.90. C) 0.95. Explanation First, find out which fund has the highest information ratio (IR) as IR = active return / active risk. This would be Crystal with an IR of 0.806. Then apply the following formula to discover the combined Sharpe ratio (SR): SR2P = SR2B + IR2 SRP2 = 0.52 + 0.8062 = 0.8996, SRP = 0.9485 (Module 40.2, LOS 40.b) Question #5 - 7 of 40 Question ID: 1474060 If the FTSE 100 and Crystal fund are combined in an optimal portfolio, what proportion should be invested in Crystal? A) 136%. B) 146%. C) 156%. Explanation We first compute the optimal level of risk: IR σA = SRB σB , therefore, σ 0.806 A = 0.5 0.15 = 0.242 This implies a weight in Crystal of 0.242 / 0.155 = 156%. (Module 40.2, LOS 40.b) Question #6 - 7 of 40 Question ID: 1474061 How many of Radichkova's comments are correct in relation to the two-sector portfolio? A) One. B) Both. C) None. Explanation Both comments are correct. The return of the portfolio is 70% × 17.8 + 30% × 6.3% = 14.35%. The return of the benchmark is 50% × 9.2% + 50% × 8.1% = 8.65%. Value added = 14.35 – 8.65 = 5.7%. Return from asset allocation is (70% – 50%) × 9.2% + (30% – 50%) × 8.1% = 0.22% (i.e., active weights times benchmark returns). This implies that return from stock selection is 5.7 – 0.22 = 5.48%. Let us check that: 70% × (17.8% – 9.2%) + 30% × (6.3% – 8.1%) = 5.48% (i.e., portfolio weights times active returns). (Module 40.1, LOS 40.a) Question #7 - 7 of 40 Question ID: 1474062 Which are the correct definitions of the transfer coefficient included in Radichkova's report? A) 1 and 2. B) 2 and 3. C) 1 and 3. Explanation The first two are correct definitions whereas number 3 is the definition of the information coefficient. (Module 40.3, LOS 40.c) Question #8 of 40 Question ID: 1474055 An active manager currently covers 40 stocks and makes a forecast for each of them every quarter. Next year he intends to cover the same stocks but only once every 6 months. Assuming the manager's skill, measured in terms of the correlation of each forecast with actual returns doesn't change, which of the following statements is most accurate? A) The information ratio will fall by approximately 30% B) The information ratio will fall by approximately 50% C) The information coefficient will fall by approximately 50% Explanation Information ratio (IR) = IC × √BR Hence a reduction in the breadth from 160 (40 × 4) to 80 (40 × 2) will cause an approximate 30% drop in the IR With quarterly predictions IR = IC × 160½ = 12.65 (IC) With semi-annual forecasts IR = IC × 80½ = 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 root of breadth, a 50% drop in breadth must cause a less than 50% drop in IR. Note that it does not matter if the portfolio is constrained or unconstrained. (Module 40.3, LOS 40.c) Question #9 of 40 Question ID: 1474034 Helen Wilde is trying to estimate the active return of Optimal fund. A comparison of Optimal's holdings and that of the benchmark are shown below: Asset Class (i) Benchmark Optimal Benchmark Optimal Weight (wPi) Weight (wBi) Return E(RPi) Return E(RBi) Industrials 30% 40% 11% 12% Financials 50% 30% 6% 5% Utilities 20% 30% 14% 12% The expected active return due to asset allocation for Optimal is closest to: A) – 1.40% B) – 0.86% C) -0.44% Explanation Asset Class (i) Portfolio Weight (wPi) Benchmark Benchmark Return Weight (wBi) Active Return Weight (Δwi) E(RBi) (Δwi) (E(RBi)) Industrials 30% 40% 12% -10% -1.20% Financials 50% 30% 5% 20% 1.00% Utilities 20% 30% 12% -10% -1.20% (Module 40.1, LOS 40.a) Question #10 of 40 Question ID: 1474040 Which of the following statements is least accurate? A) A closet index fund has a low Sharpe ratio. B) C) The Sharpe ratio of a portfolio is unaffected by addition of cash or leverage in the portfolio. Investors can take active risk that is suitable for them by investing in a combination of actively managed portfolio and benchmark portfolio. Explanation A closet index fund will have Sharpe ratio close to the benchmark's Sharpe ratio. The Sharpe ratio is for a portfolio is indeed unaffected by addition of cash or leverage to the portfolio. However, information ratio does change as we add cash or leverage to the actively managed portfolio. Investors can combine benchmark portfolio and active portfolio to obtain optimal level of active risk for them. (Module 40.2, LOS 40.b) Question #11 of 40 Question ID: 1474054 An active manager expects his information coefficient to drop from 0.08 to 0.02 in the coming period due to extremely volatile and unpredictable markets. As a response he intends to increase his breadth by a factor of 4. Which of the following statements is most accurately describes the impact on the information ratio? A) The information ratio will increase B) The information ratio will decrease C) The information ratio will remain constant Explanation Information ratio (IR) = IC × √BR If breadth is increased by a factor of 4, this would increase the information ratio by a factor of 2. As the information coefficient is decreasing by a factor of 4, the information ratio will decrease. (Module 40.3, LOS 40.c) Question #12 of 40 Question ID: 1474064 Jon Gamlin is comparing a market timing strategy with a stock selection strategy. He draws the following two conclusions for unconstrained active managers: Conclusion 1 To achieve the same information ratio, a market timer making weekly forecasts on the movement of the market needs to have a higher skill level than a stock selector following 25 stocks and updating the forecast semi-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 assessments semi-annually Regarding Gamlin's conclusions: A) Only conclusion 2 is correct. B) Only conclusion 1 is correct. C) Neither conclusion is correct. Explanation In conclusion 1, the market timer 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 (Module 40.4, LOS 40.e) Question #13 of 40 Question ID: 1474038 Zeta fund has active return and active risk of 1.6% and 8% respectively. Benchmark portfolio has a Sharpe ratio of 0.35 and standard deviation of benchmark returns is 10.5%. What is the level of active risk that an investor would need to take to maximize the Sharpe ratio of a portfolio consisting of Zeta fund and the benchmark portfolio? A) 8% B) 7% C) 6% Explanation Information ratio (IR) = 1.6% /8% = 0.2 Optimal level of active risk = σ IR ∗ A = SRB 0.2 σB = 0.35 (10.5) = 6% Active risk of Zeta fund = 8% Weight of Zeta fund = 6% / 8% = 0.75 Weight of benchmark = 0.25 (Module 40.2, LOS 40.b) Question #14 of 40 Question ID: 1474074 An active manager makes quarterly bets on the stocks in the Russell 2000 index and uses the index as the benchmark. The manager claims a modest IC of 0.02 using a stock screening model. Sam Fox, CFA makes the following two statements: I. The bets on the 2000 stocks in the index is not independent as the screens by definition introduce dependency in the decision process. II. The quarterly bets are likely to be independent. How many of Fox's statements are correct: A) Both statements are correct. B) Neither statement is correct. C) Only one statement is correct. Explanation Fox is correct that screens (e.g., minimum dividend yield) would pass stocks with similar attributes and hence would introduce dependency in the decision making process. Fox is incorrect that the decisions over time are independent. Those stocks that pass the screen in one quarter are probably more likely to pass the same screen in the next quarter and hence the decisions are not truly independent. (Module 40.4, LOS 40.f) Question #15 of 40 Question ID: 1474035 Helen Wilde is trying to estimate the active return of Optimal fund. A comparison of Optimal's holdings and that of the benchmark are shown below: Asset Class (i) Benchmark Optimal Benchmark Optimal Weight (wPi) Weight (wBi) Return E(RPi) Return E(RBi) Industrials 30% 40% 11% 12% Financials 50% 30% 6% 5% Utilities 20% 30% 14% 12% The expected active return for Optimal is closest to: A) -0.44% B) – 0.80% C) – 1.40% Explanation Portfolio return = RP = ∑(wPi) x E(RPi) = 9.10% Benchmark return = RB = ∑(wBi) x E(RBi) = 9.90% Active return = RP - RB = 9.10% – 9.90% = -0.80% (Module 40.1, LOS 40.a) Question #16 of 40 Question ID: 1474057 Alisa Darent is evaluating several active portfolio managers with the same style and benchmark portfolio. Manager Active return Active risk Alfred 3.00% 12.00% Brad 2.20% 11.00% Charles 2.00% 10.50% Benchmark return is expected to be 11%. What will be the maximum expected return for Darent's portfolio assuming that she wants to limit her active risk to 11%? A) 13.75% B) 2.75% C) 2.20% Explanation Darent will select the manager with the highest information ratio – or Alfred. IR (Alfred) = 3/12 = 0.25 IR(Brad) = 2.2/11 = 0.20 IR(Charles) = 2.0/10.50 = 0.19 Expected active return = E(RA) = IR x σA =0.25 x 11 = 2.75%. Expected return = E(RB) + E(RA) = 11% + 2.75% = 13.75% (Module 40.3, LOS 40.d) Question #17 of 40 Question ID: 1474037 Zeta fund has active return and active risk of 1.6% and 8% respectively. Benchmark portfolio has a Sharpe ratio of 0.35 and standard deviation of benchmark returns is 10.5%. The maximum possible Sharpe ratio of a portfolio consisting of Zeta fund and the benchmark portfolio is closest to: A) 0.55 B) 0.4 C) 0.5 Explanation SRP = [SRB2 + IR2]1/2 = [0.352 + 0.202]1/2 = 0.4031 (Module 40.2, LOS 40.b) Ufton Wealth Management's Ranger fund has proved popular with clients. An extract from the prospectus of the Ranger fund is shown in Exhibit 1. Exhibit 1: Ranger Fund Asset U.S. equities U.S. corporate bonds International equities U.S. real estate Portfolio Benchmark Expected portfolio Expected weight weight return benchmark return 15% 20% 11% 9% 35% 35% 8% 7% 8% 40% 14% 10% 42% 5% 7% 7% Ufton awards its best performing fund manager with a large cash bonus each year. Details of the performance of three funds is shown in Exhibit 2. Risk-free rate is 2%. Exhibit 2: Selected Fund Performance Fund Portfolio Benchmark Portfolio Benchmark standard standard deviation deviation return return Saltire 8.46% 5.80% 6.13% Dragon 13.01% 11.56% Rose 11.39% 11.37% Question #18 - 21 of 40 Sharpe Tracking ratio error 4.50% 1.05 1.58% 7.64% 5.15% 1.44 2.12% 11.01% 11.14% 0.85 0.21% Question ID: 1474042 The expected level of active return expected to be achieved by the Ranger fund is closest to: A) –9.00%. B) –0.09%. C) +3.49%. Explanation The expected active return achieved by a portfolio are calculated as the difference between the expected return on the portfolio and the expected return on the benchmark: E(RA)=∑wPi × E(RPi) − ∑wBi × E(RBi) = E(RP) – E(RB) Exhibit 1: Ranger Fund Portfolio weight Benchmark weight Expected portfolio return Expected benchmark return U.S. equities 15% 20% 11% 9% U.S. corporate bonds 35% 35% 8% 7% International equities 8% 40% 14% 10% U.S. real estate 42% 5% 7% 7% Asset E(RP) = (0.15 × 11%) + (0.35 × 8%) + (0.08 × 14%) + (0.42 × 7%) = 8.51% E(RB) = (0.20 × 9%) + (0.35 × 7%) + (0.40 × 10%) + (0.05 × 7%) = 8.60% E(RA) = –0.09% (Module 40.1, LOS 40.a) Question #19 - 21 of 40 Question ID: 1474043 The largest positive contribution to the active return achieved by the Ranger fund is expected to come from: A) security selection. B) asset allocation. C) Cannot tell from the information available. Explanation The active return on a portfolio can be deconstructed to assess how much of the active return comes from active weighting, and how much comes from security selection. The active return from active weighting is calculated by taking the sum of the active weights of each asset class multiplied by the benchmark return of the asset class: RA(from active weighs) = ∑ΔwiRBi For the Ranger fund: RA (from active weighs) = (–0.05 × 9%) + (0 × 7%) + (–0.32 × 10%) + (0.37 × 7%) = –1.06% The active return from security selection is calculated by taking the sum of the weight each asset class in the portfolio multiplied by the difference in portfolio return on the asset class and the benchmark return on the asset class: RA (from security selection) = ∑wi(RPi – RBi) For the Ranger fund: RA (from security selection) = (0.15 × 2%) + (0.35 × 1%) + (0.08 × 4%) + (0.42 × 0%) = 0.97% Of the total active return of –0.09%, active weighting has a negative contribution (1.06%), whereas security selection has a positive impact of 1.06%. (Module 40.1, LOS 40.a) Question #20 - 21 of 40 Question ID: 1474044 Of the three funds described in Exhibit 2, the fund with the highest information ratio is: A) Saltire. B) Dragon. C) Rose. Explanation The information ratio measures the active return (RP – RB) per unit of active risk (tracking error). The information ratio for each fund is calculated as follows: Saltire: (8.46% – 5.80%) / 1.58% = 1.68 Dragon: (13.01 – 11.56%) / 2.12% = 0.68 Rose: (11.39% – 11.37%) / 0.21% = 0.10 (Module 40.2, LOS 40.b) Question #21 - 21 of 40 Question ID: 1474045 Of the three funds described in Exhibit 2, the most likely to be a closet index fund is: A) Saltire. B) Dragon. C) Rose. Explanation A closet index fund is a fund, which is presented as being actively managed but covertly tracks the underlying benchmark index. It will achieve little active return and be exposed to little active risk, will have a low information ratio, and will have a Sharpe ratio close to the Sharpe ratio of the underlying benchmark. The Sharpe ratio is calculated as excess return over the risk-free asset per unit of portfolio risk: (RP – RF) / σP. Sharpe ratios for each fund's benchmark are calculated below (RB – RF) / σB: Saltire: (5.80% – 2%) / (4.50%) = 0.84 Dragon: (11.56% – 2%) / (5.15%) = 1.86 Rose: (11.37% – 2%) / (11.14%) = 0.84 The Rose fund has the lowest information ratio of the three funds, and its Sharpe ratio (0.85) is very close to that of its benchmark (0.84). It is therefore most likely to be a closet index fund. (Module 40.2, LOS 40.b) Question #22 of 40 Question ID: 1474046 Which of the following terms is the cross-sectional correlation between forecasted active returns and actual active weights adjusted for risk? A) Transfer Coefficient B) Breadth C) Information Coefficient Explanation Transfer coefficient = TC = CORR (μi/σi, Δ wiσi) (Module 40.3, LOS 40.c) Question #23 of 40 Question ID: 1474036 Zeta fund has active return and active risk of 1.6% and 8% respectively. Benchmark portfolio has a Sharpe ratio of 0.35 and standard deviation of benchmark returns is 10.5%. What is the weight of benchmark portfolio in a portfolio consisting of Zeta fund and the benchmark portfolio assuming that the portfolio is constructed to have optimal active risk? A) 0.1667 B) 0.2 C) 0.25 Explanation Information Ratio = active return / active risk = 1.6% / 8% = 0.2 Optimal level of active risk = σ IR ∗ A 0.2 = SRB σB = 0.35 (10.5) = 6% Active risk of Zeta fund = 8% Weight of Zeta fund = 6% / 8% = 0.75 Weight of benchmark = 0.25 (Module 40.2, LOS 40.b) Question #24 of 40 Question ID: 1474033 Susan Thomas is evaluating the holdings of Primus fund. Based on the information below, the estimated active return is closest to: Portfolio Security (i) Benchmark ReturnE Weight (wPi) Weight (wBi) (Ri) X 30% 40% 11.20% y 15% 25% 4.25% z 55% 35% 14.00% Total 100% 100% A) 0.44% B) 1.77% C) 1.26% Explanation Portfolio return = RP = ∑(wPi) x E(Ri) = 11.70% Benchmark return = RB = ∑(wBi) x E(Ri) = 10.44% Active return = RP - RB = 11.70% – 10.44% = 1.26 (Module 40.1, LOS 40.a) Question #25 of 40 Question ID: 1474056 When choosing an active manager, an investor with a high level of risk aversion: A) will choose the manager with the highest information ratio. B) will choose the manager with the highest active return. C) will choose a manager with the lowest active risk. Explanation Value added is independent of the level of risk aversion. All investors will choose the manager with the highest information ratio. Those with higher levels of risk aversion will implement the strategy less aggressively (i.e., invest a larger proportion in the benchmark portfolio). (Module 40.3, LOS 40.d) Question #26 of 40 Question ID: 1474049 Which of the following terms is the number of independent bets per year made by an active manager? A) Breadth B) Transfer Coefficient C) Information Coefficient Explanation Breadth is the number of independent bets (based on unique information) made per year by the active manager. (Module 40.3, LOS 40.c) Question #27 of 40 Question ID: 1474075 Pamela Grieve claims that her information coefficient is 0.20 on monthly bets on 10 stocks in the healthcare industry. Assuming unconstrained optimization, the reduction in her information ratio if her bets have a correlation coefficient of 0.45 as opposed to being truly independent is closest to: A) 45% B) 22% C) 86% Explanation Grieve's breadth assuming independent bets = 10 × 12 = 120 Information ratio assuming independent bets = IC√BR = 0.20 × √120 = 2.19 If the bets are correlated, BR = N 1+(N−1)r 120 = 1+(120−1)0.45 = 2.20 New information ratio assuming correlated bets IC√BR = 0.20 × √2.20 = 0.30 % reduction = 1 − 0.30/2.19 = 86.4% (Module 40.4, LOS 40.f) Question #28 of 40 Question ID: 1474039 Which of the following statements is least accurate? A) B) Unlike Sharpe ratio, information ratio is affected due to addition of cash or leverage. The information ratio of a constrained active portfolio is unaffected by aggressiveness of the active weights. Sharpe ratio of a portfolio consisting of a combination of benchmark and C) actively managed portfolio with positive active return will be higher than the Sharpe ratio of the benchmark. Explanation Information ratio of an unconstrained active portfolio is unaffected by aggressiveness of the active weights. Sharpe ratio is unaffected by addition of cash or leverage but information ratio would be. A portfolio consisting of a combination of benchmark and an actively managed portfolio is calculated as: SRP2 = SRB2 + IR2 If the active return is positive, IR>0 and SRP>SRB. (Module 40.2, LOS 40.b) Question #29 of 40 Question ID: 1474047 Which of the following terms is the ex-ante risk weighted correlation between forecasted active returns and actual active returns? A) Breadth B) Information Coefficient C) Transfer Coefficient Explanation Information coefficient is the ex-ante correlation between forecasted active returns and actual active returns. It captures the skill of the manager. (Module 40.3, LOS 40.c) Question #30 of 40 Question ID: 1474050 An active manager has an information coefficient of 0.08, transfer coefficient of 0.50, and makes 100 independent bets per year. What is the expected active return for an active risk constraint of 5%? A) 1.8% B) 2.0% C) 2.4% Explanation E (RA ) = (TC) IC√BRσA = (0.50) (0.08) √100 (0.05) = 0.02 or 2% (Module 40.3, LOS 40.c) Question #31 of 40 Question ID: 1474063 Charles Griffith makes quarterly bets between stocks of industrial and utility sectors. Griffith's strategy has an annualized active risk of 18%. Based on the information below, If Griffith wants to limit his active risk to 6%, what is the allocation to Utility sector when Griffith is bullish about Industrial stocks? Benchmark Sector Weight Industrial 80% Utility 20% A) -13% B) 5% C) 14% Explanation If active risk is limited to 6%, the deviation from the benchmark weights of 80% and 20% is limited to 6%/18% or 33%. Hence when Griffith is bullish about industrials, the weight to that sector will be 80% + 33% or 113% and the weight to utility sector will be 20% - 33% or -13%. (Module 40.4, LOS 40.e) Question #32 of 40 Which of the following is correct for an unconstrained active portfolio? A) TC<1 B) TC=1 C) TC>1 Question ID: 1474048 Explanation TC=1 if the active portfolio has no constraints. (Module 40.3, LOS 40.c) Sundar Mithai, CFA, is a fund manager for Pearl Investments and makes a monthly report to the firm's partners. Mithai mentions two active managers in his report, Galab and Phasar. Exhibit 1 provides additional information on the two managers: Exhibit 1: Selected Information on Galab and Phasar Galab Phasar Information coefficient 0.22 0.37 Transfer coefficient 0.8 0.73 Active risk 5.6% 6.6% Active return 10.8% 9.2% Mithai makes the following comments regarding the two active managers: Comment The investment mandate of Phasar appears to be less constrained relative to 1: Galab. Comment Galab appears to have better skill at predicting returns. 2: Comment 1: The investment mandate of Phasar appears to be less constrained relative to Galab. Comment 2: Galab appears to have better skill at predicting returns. Mithai recently decided to give all the analysts at the firm a refresher on the fundamental law of active portfolio management. Details of a hypothetical unconstrained fund is shown in Exhibit 2. Exhibit 2: Hypothetical Fund Information coefficient 0.14 Monthly active bets 5 Active risk 4.32% Question #33 - 36 of 40 Question ID: 1474070 According to the fundamental law of active management, how many forecasts is Galab making per month? A) 3. B) 10. C) 36. Explanation The extended law states that: active return = TC × IC × √(BR) × active risk 10.8% = 0.8 × 0.22 × √(BR) × 5.6% BR = 120 (annual), Galab is making 10 bets per month. (Module 40.4, LOS 40.e) Question #34 - 36 of 40 Question ID: 1474071 How many of Mithai's comments are correct in relation to the comparison between Galab and Phasar? A) One. B) Both. C) None. Explanation Both comments are incorrect. Phasar has higher information coefficient, which indicates better skill at predicting results. Phasar has also a lower transfer coefficient, which indicates that it is a more restrained fund. (Module 40.3, LOS 40.c) Question #35 - 36 of 40 Question ID: 1474072 The expected active return generated by the hypothetical fund described in Exhibit 2 is: A) 3.12%. B) 4.68%. C) 8.20%. Explanation The expected level of active return achieved by a portfolio is calculated as follows: E(RA) = TC(IC) √(BR) σA where: TC = transfer co-efficient IC = information co-efficient BR = number of independent active bets taken per year σA = active risk In an unconstrained portfolio, the transfer co-efficient is equal to 1. Therefore the active return generated by the fund will be: E(RA) = 1 × 0.14 × √60 × 4.32% = 4.68% (Module 40.3, LOS 40.c) Question #36 - 36 of 40 Question ID: 1474073 If the hypothetical fund described in Exhibit 3 was subject to investment constraints, its expected active return would be expected to: A) rise. B) fall. C) remain unchanged. Explanation If an actively managed portfolio is not subject to investment constraints, its transfer coefficient will be equal to 1, reflecting the manager's ability to achieve optimal active weight in the portfolio. If constraints are imposed, the transfer co-efficient will be between 0 and 1. Given active return is positively related to the transfer co-efficient, the imposition of constraints must lead to a reduction in expected active return. (Module 40.3, LOS 40.c) Question #37 of 40 Question ID: 1474065 Which of the following statements regarding the information ratio of an unconstrained portfolio is most likely correct? A market timer who uses independent information to make predictions about A) market movements on a monthly basis and has an information ratio of 0.20 must have an information coefficient higher than a stock selector with the same information ratio who follows 10 stocks and revises his forecast quarterly A market timer who uses independent information to make predictions about B) market movements on a monthly basis and has an information ratio of 0.20 must have an information coefficient lower than a stock selector with the same information ratio who follows 10 stocks and revises his forecast quarterly A market timer who uses independent information to make predictions about C) market movements on a monthly basis and has an information ratio of 0.20 must have an information coefficient equal to a stock selector with the same information ratio who follows 10 stocks and revises his forecast quarterly Explanation Unconstrained Information ratio (IR) = IC × √BR Market timer: 0.20 = IC × 12½ IC = 0.20 / 3.464 IC = 0.058 Selector: 0.20 = IC × 40½ IC = 0.20 / 6.325 IC = 0.032 The market timer has a lower breadth. In order to achieve the same information ratio he must have a higher information coefficient. Note calculations not required. (Module 40.4, LOS 40.e) Question #38 of 40 Question ID: 1474067 Tom Grenkin is a market timer with an information ratio of 0.75. He makes a prediction of the movement in the market each quarter. Jane Fortina is a stock selector who follows 50 companies and revises her assessment each quarter. She also has an information ratio of 0.75. Assuming both managers have unconstrained portfolios, which of the following statements regarding the two managers is most accurate? A) B) C) As Grenkin makes fewer bets per year, he requires a higher information coefficient on each bet than Fortina to achieve the same information ratio. As both managers have the same information ratio, they must also have the same information coefficient. As Fortina’s strategy has a much larger breadth, she must have a larger information coefficient than Grenkin. Explanation (IR) = IC × √BR As a stock selector, Fortina makes many more bets per period and has a much larger breadth. She therefore requires a lower information coefficient than Grenkin to achieve the same information ratio. Grenkin requires a higher coefficient. Grenkin 0.75 = IC × 4½ IC = 0.75/2 = 0.375 Fontina 0.75 = IC × 200½ IC = 0.75/14.14 = 0.053 (Note: Calculations are not required) (Module 40.4, LOS 40.e) Question #39 of 40 Question ID: 1474051 An active manager has an information coefficient of 0.05 and makes 36 independent bets per year. What is the manager's information ratio given a transfer coefficient of 0.75? A) 0.45 B) 0.23 C) 1.35 Explanation Information ratio = IR = (TC) IC√BR = (0.75) (0.05) √36 = 0.225 (Module 40.3, LOS 40.c) Question #40 of 40 Question ID: 1474053 An active manager has an information coefficient of 0.07, transfer coefficient of 0.90, and makes 49 independent bets per year. Benchmark portfolio has a Sharpe ratio of 0.40 and standard deviation of benchmark returns is 12%. The optimal amount of active risk is closest to: A) 8% B) 6% C) 14% Explanation IR = ( TC ) IC √BR = ( 0.90 ) ( 0.07 ) √49 = 0.441 For a constrained portfolio, the optimal level of residual risk can be computed as: σ*A =(IR / SBB)σB = (0.441 / 0.40)(0.12) = 13.23% (Module 40.3, LOS 40.c)