2019 CFA level 3 qbank reading 19 principles of asset allocation answers

Question #1 of 37 Billy Kramer is deciding whether or not to add an emerging markets fund to his current 401k which is broadly diversi ed among a mix of bond and equity funds His current portfolio has an expected return of 9% with a standard deviation of 10% The emerging markets fund has an expected return of 16%, a standard deviation of 21%, and a correlation of 74 with Kramer's current portfolio Assume the risk free rate is 3% Given this information, should Kramer add the emerging markets fund to his current portfolio? A) No, since the emerging markets fund is adding signi cant risk and we don’t know in how much risk Kramer can tolerate en tre B) No, since the correlation between the emerging markets fund and the current portfolio is too high C) Yes, since adding the emerging markets fund to his current portfolio will result in a bo ok c higher Sharpe ratio of the newly formed portfolio Explanation If SharpeEM > SharpeP × ρEM,P then add the emerging market funds to the portfolio Sharpe ratio = (ER − Rf) / Std m Sharpe ratio of current portfolio = (9 − 3) / 10 = 0.6 o Sharpe ratio of emerging markets fund = (16 − 3) / 21 = 0.62 w w 0.62 > 0.6 × 0.74, therefore add the emerging markets fund to the portfolio w It's true we don't know Kramer's level of risk aversion but based on the Sharpe ratio alone we can see that by adding the emerging markets fund that his portfolio becomes more e cient by earning a higher return for the same level of risk (Study Session 9, Module 19.3, LOS 19.b) Related Material SchweserNotes - Book Question #2 of 37 A bank is most likely to use which of the following approaches to liability-relative asset allocation? A) Integrated asset-liability approach B) Two-portfolio approach C) Surplus e cient frontier approach Explanation Banks (along with insurance companies and hedge funds with short positions) make decisions about the composition of their liabilities jointly with their asset allocation decisions, which makes the integrated approach most appropriate Surplus optimization and the two-portfolio approach are distinct in that the composition of the liabilities is already in place when the asset allocations decisions are made, so the two decisions are made independently .in (Study Session 9, Module 19.6, LOS 19.l) en tre Related Material Question #3 of 37 bo ok c SchweserNotes - Book Melissa Brown, an analyst with Mollette Capital Advisors, is reviewing the client pro le of Karrie Jones Mollette manages all of Jones' investment assets; however, since Brown is new to the m rm, she has never met Jones She does know, however, that Jones' asset allocation is shown below: o appropriate given her age and investment policy statement The allocation of Jones' portfolio is Allocation (%) w w Asset Class 5% High quality corporate bonds 5% U.S equities 60% International equities 30% Cash w Intermediate-term Treasury bonds 0% Given Jones' asset allocation, which of the following conclusions about Jones is most accurate? A) Jones’ human capital makes up the bulk of her portfolio B) Jones has a low risk tolerance C) Jones has a large amount of nancial capital Explanation With only 10% in xed assets and the rest in equities, Jones has a very aggressive portfolio At a young age, an aggressive portfolio like this makes sense as the individual will have a high allocation to human capital (future stream of income from working) At this stage, the allocation to human capital will be much larger than the allocation to nancial capital (investment portfolio), therefore, the investment portfolio should be invested in riskier, high return assets Note that Jones likely has a high risk tolerance given the aggressive portfolio (Study Session 9, Module 19.4, LOS 19.c) Related Material in SchweserNotes - Book en tre Question #4 of 37 Which of the following asset classes is least likely to require a liquidity return premium? bo ok c A) Infrastructure B) Commodities C) Direct real estate Explanation o m Commodities are not generally thought of as a less liquid asset class requiring a liquidity return premium to compensate the investor for the additional liquidity risk On the other hand, asset classes such as direct real estate and infrastructure would be considered less liquid and would require a liquidity return premium w w (Study Session 9, Module 19.4, LOS 19.d) Related Material w SchweserNotes - Book Question #5 of 37 The following information is available regarding corner portfolios from an e cient frontier Asset Class Weights Corner Portfolio Expected Return Exp Std Dev 6.90% 4.60% 0.00% 12.00% 88.00% 0.00% 10.00% 8.64% 0.00% 15.00% 45.00% 40.00% 13.00% 12.50% 55.00% 0.00% 45.00% 0.00% A foundation has a spending rate of 8% If in ation is expected to be 3.50% annually and the cost of earning investment returns is 0.5%, which of the following represents the correct weight in of one of the asset classes that will at a minimum satisfy the investor's goals of capital A) Asset class with weight of 50.00% B) Asset class with a weight of 42.90% bo ok c C) Asset class with weight of 39.00% en tre preservation in real terms to an investor with a risk aversion value of 4? Explanation Foundations normally use the multiplicative approach and include the expense rate in the return calculation m r = (1+s)(1+i)(1+c) – = (1.08)(1.035)(1.005) – = 12.34%  o This portfolio would lie between corner portfolios and Let w denote the weight of corner portfolio 2, we solve for w in the following equation:  w w 12.34 = (10.0)(w) + (13.00)(1-w) w = 0.22 w With respect to the asset classes, the weights are then derived as follows:  Weight of asset class = (0.22)(0%) + (0.78)(55%) = 42.90% Weight of asset class = (0.22)(15%) + (0.78)(0%) = 3.30% Weight of asset class = (0.22)(45%) + (0.78)(45%) = 45.00% Weight of asset class = (0.22)(40%) + (0.78)(0%) = 8.80% (Study Session 9, Module 19.3, LOS 19.b) Related Material SchweserNotes - Book Question #6 of 37 Based on the following information, compute the weight of US bonds in an e cient portfolio with an expected return of 12.50%? The following are the long-term capital market expectations: Correlations Asset Class Expected Return Exp Std Dev 1 US Equity 12.00% 16.00% 1.00 US Bonds 8.25% 6.50% 0.32 1.00 Intl Equities 14.00% 18.00% 0.46 0.22 1.00 Intl Bonds 9.25% 12.25% 0.23 0.56 0.32 1.00 11.50% 21.00% 0.25 0.11 0.08 0.06 1.00 in en tre Alt Inv bo ok c The details of each corner portfolio are given below Exp Std Dev Sharpe Ratio 18.00% 0.639 0.00% 0.00% 100.00% 0.00% Asset Class Weights 14.00% 13.66% 16.03% 0.696 0.00% 0.00% 86.36% 0.00% 14.00% 13.02% 13.58% 0.775 21.69% 0.00% 56.56% 0.00% 21.76% A) 6.25% B) 5.75% C) 6.67% Explanation 0.00% 12.79% 13.00% 0.792 21.48% 0.00% 52.01% 5.24% 21.27% 10.54% 8.14% 0.988 9.40% 51.30% 26.55% 0.00% 12.76% 6.32% 0.981 0.00% 89.65% 4.67% 0.00% w w w o m Corner Expected Portfolio Return 8.70% 5.68% The expected return of 12.50% lies between corner portfolios and with expected returns of 12.79% and 10.54% We solve for w in the following equation: 12.50 = w(12.79) + (1-w)(10.54)  w = 0.87 In other words, the e cient portfolio with an expected return of 12.50% has 87% weight of corner portfolio and 13% weight of corner portfolio With respect to the US bonds asset class, the weight is then derived as follows: Weight of US bonds = (0.87)(0%) + (0.13)(51.30) = 6.67% (Study Session 9, Module 19.3, LOS 19.b) Related Material Question #7 of 37 bo ok c Any mean-variance e cient portfolio has the: en tre in SchweserNotes - Book A) lowest standard deviation for a given level of expected return B) highest return among all other portfolios m C) lowest standard deviation and the highest expected return .o Explanation w w A mean-variance e cient portfolio has the lowest standard deviation for a given level of expected return Note that the lowest standard deviation portfolio and the highest return portfolio are just two of the in nite number of e cient portfolios w (Study Session 9, Module 19.1, LOS 19.a) Related Material SchweserNotes - Book Question #8 of 37 In context of portfolio rebalancing, if the correlation of the asset class with the rest of the portfolio is lower, then the optimal corridor of the asset class will be: A) unchanged B) narrower C) wider Explanation The lower the correlation of the asset class with the rest of the portfolio, the narrower the corridor, because the portfolio will not "move" as closely with the asset class so the allocations are more likely to diverge from the target allocation Therefore, the corridor needs to be narrowed in order to control the risk (Study Session 9, Module 19.8, LOS 19.o) Related Material en tre in SchweserNotes - Book Question #9 of 37 Aaron Manning wishes to minimize the risk of his portfolio returns as measured by standard bo ok c deviation while meeting a minimum expected return objective The risk-free rate is 2% The following asset allocations are available: Expected return Standard deviation of returns Allocation 7% w w o Allocation 11% 12% m Allocation 10% 10% 15% Based on the information provided, which of the following allocations should Manning choose? w A) Allocation B) Allocation C) Allocation Explanation Calculate the Sharpe ratio for each allocation: Allocation 1: (10% - 2%) / 12% = 0.67 Allocation 2: (7% - 2%) / 10% = 0.50 Allocation 3: (11% - 2%) / 15% = 0.60 Allocation has the highest Sharpe ratio, therefore it is the optimal risk allocation that Manning should choose (Study Session 9, Module 19.3, LOS 19.i) Related Material en tre in SchweserNotes - Book Question #10 of 37 Dan Laske is evaluating three portfolios for investment of his retirement funds Laske has a risk bo ok c aversion value of Which portfolio would be best for him? Portfolio Return Std Dev 15.0% 17.0% B 10.6% 10.0% C 8.8% 8.0% o w C) C w w A) A B) B m A Explanation RZ =5 UA = E(RA) – 0.5(RZ)(σ2A) = 0.15 – 0.5(5)(0.17)2 = 0.078 UB = E(RC) – 0.5(RZ)( σ2C) = 0.106 – 0.5(5)(0.10)2 = 0.081 UC = E(RD) – 0.5(RZ)( σ2D) = 0.088 – 0.5(5)(0.08)2 = 0.072 Portfolio B has the highest utility.  (Study Session 9, Module 19.1, LOS 19.a) Related Material SchweserNotes - Book Question #11 of 37 Which of the following methods is the most appropriate way of incorporating client risk preferences into asset allocations? A) Specify a risk tolerance factor B) Specify a diversi cation objective en tre Explanation in C) Specify additional constraints One way to incorporate investor risk preferences into an asset allocation decision is to specify additional constraints, such as setting limits on allocations to risky asset classes or setting a ceiling on portfolio risk bo ok c Specifying a risk aversion factor (not risk tolerance factor) is another way to incorporate investor risk preferences into an asset allocation decision There is no such thing as a "diversi cation objective" per se in the reading (Study Session 9, Module 19.5, LOS 19.f) w w o SchweserNotes - Book m Related Material w Question #12 of 37 Shad Reed is on the Board of Trustees for the Wesley Ridge World Hunger Organization The primary role of the organization is to oversee a large endowment fund that was originally established in 1995 as the Wesley Ridge U.S Hunger Fund to provide food to low income children in the United States Recently, the original donor for the endowment has died and provided the fund another $200 million in his will and broadened the scope of the fund to provide food for hungry children all over the world With the new addition, the endowment's assets are currently valued at $600 million When the fund was originally established, the spending rate was 5%; however, with the broader scope, the payout has increased to 6% Also, since funds are going to be distributed to other countries, the board has determined that approximately 25% of the foundation's annual payout will be in the foreign currencies of other in countries The fund's investment policy statement which has been revised by the board is en tre shown below: Accounting for in ation of 2.5% and the new spending Return Objective rate of 6%, the return requirement for the plan is 8.5% A total return approach is appropriate Above average, although risk tolerance has declined due to higher spending needs Liquidity The endowment has minimal operating expenditures – liquidity requirements are low Time Horizon Long-term m Legal/Regulatory N/A bo ok c Risk Tolerance Taxes N/A w w Unique Considerations o N/A w The board has consulted with an investment advisor to discuss changes to the endowment's current asset allocation which is shown below: Allocation (%) Expected Return Expected Standard Deviation Cash 2% 3.0% 2% Intermediate-term U.S Treasury bonds 28% 5.5% 7% Foreign Government Bonds 8% 6.5% 10% U.S equities 50% 9.5% 18% Asset Class Cecil Boller is the portfolio manager for a $500 million de ned bene t pension fund Boller has been conducting a great deal of analysis to select the appropriate allocation for the fund He has come up with the following long-term expectations for various asset classes Asset Class Expected Return Expected Standard Deviation Correlations U.S equity 12.00% 16.00% 1.00 U.S corporate bonds 8.25% 6.50% 0.32 1.00 Int'l equities 14.00% 18.00% 0.46 0.22 1.00 Int'l bonds 9.25% 12.25% 0.23 0.56 0.32 1.00 Alternative Investments 11.50% 21.00% en tre in 0.25 0.11 0.08 0.06 1.00 Based on these expectations, Boller identi es an e cient frontier with four corner portfolios bo ok c with the characteristics shown below The risk-free rate is assumed to be equal to the T-bill rate of 3.0% 0.611 0% 0% 100% 0% 0% 16.03% 0.665 0% 0% 86.36% 0% 13.64% 12.79% 13.00% 0.753 21.48% 0.00% 52.01% 5.24% 21.27% 10.54% 8.14% 0.926 9.40% 51.30% 26.55% 14.00% 13.66% w w 0% w 18.00% o Asset Class Weights m Expected Corner Expected Sharpe Standard Portfolio Return Ratio Deviation Boller has determined that the fund has a spending rate of 7.5% In ation is expected to be 2.5% per year, and the cost of managing the fund is expected to be 0.50% The expected return on the portfolio is therefore (1.075)(1.025)(1.005) – = 10.74% Boller has also stated that he does not want the standard deviation of the pension portfolio to exceed 9.0% and there is a constraint against short selling Conclusion 1: The weight given to U.S equity in the pension portfolio should be greater than 11.0% Conclusion 2: The weight given to corporate bonds in the portfolio should be exactly 30.78% 12.76% Conclusion 3: The weight given to alternative investments in the portfolio should be greater than 13.0% Given this information, which of the following conclusions drawn by Boller are CORRECT? A) Conclusion only B) Conclusions and only C) Conclusions and only Explanation The required rate of return of 10.74% lies between corner portfolios and 4, which have expected returns of 12.79% and 10.54% respectively We can solve for w3 in the following w3 = 0.089, so w4 = 0.911 en tre 0.1074 = w3(0.1279) + (1 - w3)(0.1054) in equation: This means that weighting of each asset class should be 8.9% of the weighting in Portfolio 3, and 91.1% of the weighting in Portfolio bo ok c Using this information, we can test Boller's conclusions: U.S equity weight = (0.089)(21.48%) + (0.911)(9.40%) = 10.48%, so Conclusion is incorrect Corporate bond weight = (0.089)(0.00%) + (0.911)(51.30%) = 46.73%, so Conclusion is incorrect .o m Alternative investment weight = (0.089)(21.27%) + (0.911)(12.76%) = 13.52%, so Conclusion is correct w w (Study Session 9, Module 19.3, LOS 19.b) Related Material w SchweserNotes - Book Question #26 of 37 Which of the following heuristic and other approaches to asset allocation is most closely associated with the assumption of a lack of informationally e cient markets? A) 60/40 stock/bond heuristic B) Norway model C) Endowment model Explanation The endowment model has large allocations to alternative assets as well as support for active management The endowment model also seeks to earn illiquidity premiums Those three factors suggest that there is the assumption of a lack of informationally e cient markets The Norway model's asset allocation emphasizes publicly traded securities, which re ects a belief in the market's informational e ciency (Study Session 9, Module 19.7, LOS 19.n) Related Material Question #27 of 37 en tre in SchweserNotes - Book Following information is a partial list of corner portfolios: 12.00% 16.50% 18.00% 23.00% 10.50% 65.00% 0.00% 35.00% 14.00% 15.00% 20.00% 50.00% 20.00% 30.00% 20.00% 25.00% m Asset class weights bo ok c Portfolio Exp Return Std Dev 15.00% 20.00% 55.00% o 24.00% w w Which asset class is the most signi cant for an e cient portfolio with an expected return of 15% and the approximate standard deviation of this e cient portfolio? w A) Asset class 2, 12.85% B) Asset class 1, 15.00% C) Asset class 3, 12.85% Explanation The expected return of 15% lies between corner portfolios and with expected returns of 12% and 16.50% We solve for w in the following equation: 15 = w(12) + (1-w)(16.50)  w = 0.33 In other words, the e cient portfolio with an expected return of 15% has 33% weight of corner portfolio and 67% weight of corner portfolio With respect to the asset classes, the weights are then derived as follows: Weight of asset class = (0.33)(65%) + (0.67)(15%) = 31.50% Weight of asset class = (0.33)(0%) + (0.67)(20%) = 13.4% Asset class has the highest weight and is the most signi cant .in Weight of asset class = (0.33)(35%) + (0.67)(50%) = 45.05% (Study Session 9, Module 19.3, LOS 19.b) Related Material Question #28 of 37 bo ok c SchweserNotes - Book en tre Approximate standard deviation = (0.33)(10.50) + (0.67)(14) = 12.85% m Which of the functions is least likely to be addressed with Monte Carlo simulation? o A) Assisting individual investors in identifying risk tolerance levels w w B) Rebalancing and taxes of a portfolio in a multi-period framework C) Transforming a data set with a non-normal distribution to a normal distribution w Explanation Transforming data sets from non-normal distributions to normal distributions is not addressed by Monte Carlo simulation Multi-period analysis of rebalancing and taxes within a portfolio is di cult to analyze mathematically but relatively straightforward using Monte Carlo simulation Monte Carlo simulation can be useful in illustrating the range and likelihood of possible outcomes given various assumptions of how much risk to take on That provides the investor with more information to decide on a risk tolerance level with which they are comfortable (Study Session 9, Module 19.4, LOS 19.g) Related Material SchweserNotes - Book Question #29 of 37 David Jalbert is considering three potential asset allocations He wishes to earn a nominal return no less than 2% as he has a low risk tolerance with a lamda of The following asset allocations are available: 0.0100 Allocation 7% 0.0143 Allocation 9% 0.0200 en tre Allocation 5% in Expected return Variance Based on the information provided, which of the following allocations should Jalbert choose? A) Allocation bo ok c B) Allocation C) Allocation Explanation Step 1: Calculate the certainty-equivalent return m Allocation 1: 0.05 – (0.5 × × 0.01) = 0.01500 o Allocation 2: 0.07 – (0.5 × × 0.0143) = 0.01995  w w Allocation 3: 0.09 – (0.5 × × 0.02) = 0.02000 Jalbert would probably be indi erent between allocations and based on the certainty equivalent return and prefers them both to allocation w Step 2: Calculate the Roy's safety- rst criterion Allocation 1: (0.05 – 0.02) / (0.0100)1/2 = 0.300 Allocation 2: (0.07 – 0.02) / (0.0143)1/2 = 0.418 Allocation 3: (0.09 – 0.02) / (0.0200)1/2 = 0.495 Allocation has a higher probability of exceeding the threshold return than allocation 2, so Jalbert should choose allocation (Study Session 9, Module 19.3, LOS 19.b) Related Material SchweserNotes - Book Question #30 of 37 Je Graefe has a risk-aversion value of He is evaluating three competing investments with the following characteristics Which investment would have the least utility for Graefe? Portfolio Return Std Dev 18.0% 24.0% B 13.5% 10.0% C 9.5% 6.0% in A en tre A) A B) B C) C bo ok c Explanation RZ = UA = E(RA) – 0.5(RZ)(σ2A) = 0.18 – 0.5(6)(0.24)2 = 0.007 UB = E(RC) – 0.5(RZ)( σ2C) = 0.135 – 0.5(6)(0.10)2 = 0.105 m UC = E(RD) – 0.5(RZ)( σ2D) = 0.095 – 0.5(6)(0.06)2 = 0.084 o Investment A has the least utility of 0.007 w w (Study Session 9, Module 19.1, LOS 19.a) Related Material w SchweserNotes - Book Question #31 of 37 Frances Bonner, a retired nurse, is a potential new client for Fullen Capital Management Bonner has told Fullen that in order to pay the living expenses not covered by her pension and social security, she must generate $10,000 annually on her $500,000 investment portfolio She does not want to use principal to meet her living expenses Fullen has four model portfolios that Bonner could use for her portfolio A 4.5% 6% B 5.5% 8% C 6.5% 10% en tre Based on Roy's Safety-First Measure, Bonner should select: in Portfolio Expected Return Standard Deviation A) Portfolio B B) Portfolio A bo ok c C) Portfolio C Explanation Bonner states that she requires $10,000 annually on a $500,000, which implies a minimum return of $10,000/$500,000 = 0.02 = 2% Roy's Safety First Measure is calculated as: SF = (RP – RMIN)/σP m SFA = (4.5 – 2)/6 = 0.4167 o SFB = (5.5 – 2)/8 = 0.4375 w w SFC = (6.5 – 2)/10 = 0.4500 Since Portfolio C has the highest Roy's Safety First measure, Bonner should select Portfolio C w (Study Session 9, Module 19.3, LOS 19.i) Related Material SchweserNotes - Book Question #32 of 37 Which of the following statements regarding liabilities in the context of the asset allocation decision is correct? A) The pension liability associated with a de ned pension plan is an example of a xed liability B) A university endowment contribution is an example of a legal liability C) A small pension liability in relation to the size of the sponsoring organization should be ignored Explanation A small liability in relation to the size of the sponsoring organization can usually be ignored as its e ect on the optimal asset allocation is minimal .in The pension liability associated with a de ned pension plan is an example of a contingent liability because the cash ows depend on uncertain future events (Study Session 9, Module 19.6, LOS 19.j) SchweserNotes - Book m Question #33 of 37 bo ok c Related Material en tre University endowment contributions are an example of quasi-legal liabilities, which are not legal obligations, but are cash out ows expected to occur in the future and are essential to the mission of the institution Which of the following statements regarding the goals-based approach to asset allocation is w w o correct? A) Individuals are often concerned with single goals while institutions are often concerned with multiple goals w B) The relevant risk measure for both individuals and institutions is the probability of missing the goal C) The return determination for individuals is based on minimum expectations while for institutions, it is based on mathematical expectations Explanation For institutions, "mathematical expectations" refers to the weighted expected return of the portfolio components The relevant measure for institutions is volatility of return or surplus Individuals are often concerned with multiple goals while institutions are often concerned with single goals (Study Session 9, Module 19.7, LOS 19.m) Related Material in SchweserNotes - Book w w w o m bo ok c en tre Question #34 of 37 Based on the following information, and using a weighted average of the corner portfolios that bracket the return objective, compute the weight of US bonds in an e cient portfolio with an expected return of 13.50% The following are the long-term capital market expectations: Correlations Asset Class Expected Return Exp Std Dev 1 US Equity 12.00% 16.00% 1.00 US Bonds 8.25% 6.50% 0.32 1.00 Intl Equities 14.00% 18.00% 0.46 0.22 1.00 Intl Bonds 9.25% 12.25% 0.23 0.56 0.32 1.00 11.50% 21.00% 0.25 0.11 0.08 0.06 1.00 in en tre Alt Inv bo ok c The details of each corner portfolio are given below.  Exp Std Dev Sharpe Ratio Asset Class Weights 14.00% 18.00% 0.639 0.00% 0.00% 100.00% 0.00% 13.66% 16.03% 0.696 0.00% 0.00% 86.36% 0.00% 14.00% 13.02% 13.58% 0.775 21.69% 0.00% 56.56% 0.00% 21.76% 12.79% 13.00% 0.792 21.48% 0.00% 52.01% 5.24% 21.27% 10.54% 8.14% 0.988 9.40% 51.30% 26.55% 0.00% 12.76% 8.70% 6.32% 0.981 0.00% 89.65% 4.67% 0.00% w w w o m Corner Expected Portfolio Return A) 6.25% B) 3.75% C) 0.00% Explanation 0.00% 5.68% The expected return of 13.50% lies between corner portfolios and with expected returns of 13.66% and 13.02% Since both these corner portfolios have no exposure to US bonds, the weight of US bonds in a portfolio which is the weighted average of portfolios and would also be 0% Alternatively: We solve for w in the following equation: 13.50 = w(13.66) + (1-w)(13.02)  w = 0.75 (Study Session 9, Module 19.3, LOS 19.b) Related Material Question #35 of 37 bo ok c SchweserNotes - Book en tre Weight of US bonds = (0.75)(0%) + (0.25)(0%) = 0% in In other words, the e cient portfolio with an expected return of 13.50% has 75% weight of corner portfolio and 25% weight of corner portfolio With respect to the US bonds asset class, the weight is then derived as follows: e cient frontier? m Which of the following does NOT accurately re ect a statement describing the resampled o A) A single portfolio with speci c asset class weights at each level of return w w B) A portfolio may be considered statistically equivalent if the manager’s portfolio is within a 90% dence interval of the most e cient portfolio w C) At each level of return the most e cient of the simulated e cient portfolios is at the center of a distribution Explanation A single portfolio with speci c asset class weights at each level of return describes traditional mean variance optimization The other answer choices describe the resampled e cient frontier where Monte Carlo simulation is used to create an e cient frontier at each return level and run thousands of times resulting in an e cient frontier that is the result of an averaging process The e cient frontier becomes a blur rather than a single sharp curve At each level of return, the most e cient of the simulated e cient portfolios is at the center of the distribution (Study Session 9, Module 19.2, LOS 19.a) Related Material SchweserNotes - Book Question #36 of 37 The following information is available regarding corner portfolios from an e cient frontier: Corner Expected Portfolio Return Exp Std Dev Sharpe Ratio Asset Class Weights 14.00% 18.00% 0.639 0.00% 0.00% 100.00% 0.00% 0.00% 13.66% 16.03% 0.696 0.00% 0.00% 86.36% 14.00% 13.02% 13.58% 0.775 21.69% 0.00% 56.56% 0.00% 21.76% 12.79% 13.00% 0.792 21.48% 0.00% 52.01% 5.24% 21.27% 10.54% 8.14% 0.988 9.40% 51.30% 26.55% 0.00% 12.76% 8.70% 6.32% 0.981 0.00% 89.65% 4.67% 0.00% bo ok c en tre in 0% The following portfolios are under consideration by an investor: 11.0% B 13.5% o A m Portfolio Expected Return w w For an investor with a risk-aversion of 6, which portfolio would have the highest utility? w A) Portfolio A with a utility of 0.092 B) Portfolio A with a utility of 0.085 C) Portfolio B with a utility of 0.115 Explanation 5.68% For portfolios A and B we rst need the approximate standard deviation.  Portfolio A with an expected return of 11% lies between corner portfolios and Let w denote the weight of corner portfolio 5, we solve for w in the following equation: 11 = (10.54)(w) + (12.79)(1-w) w = 0.80 Approximate standard deviation of portfolio A = (0.80)(8.14)+(0.20)(13) = 9.11 Similarly, Portfolio B with an expected return of 13.50% lies between corner portfolios and Let w denote the weight of corner portfolio 2, we solve for w in the following equation: 13.50 = (13.66)(w) + (13.02)(1-w) in w = 0.75 Approximate standard deviation of portfolio B = (0.75)(16.03)+(0.25)(13.58) = 15.418 en tre RZ =6 UA = E(RA) – 0.5(RZ)(σ2A) = 0.11 – 0.5(6)(0.0911)2 = 0.085 bo ok c UB = E(RB) – 0.5(RZ)(σ2B) = 0.135 – 0.5(6)(0.154)2 = 0.064 (Study Session 9, Module 19.5, LOS 19.f) Related Material o m SchweserNotes - Book w w w Question #37 of 37 Based on the following information, which asset class is the least signi cant in an e cient portfolio with an expected return of 12.50%? The following are the long-term capital market expectations: US Equity 12.00% 16.00% US Bonds 8.25% 6.50% Intl Equities 14.00% 18.00% Intl Bonds 9.25% 12.25% Alt Inv 11.50% 21.00% in Asset Class Expected Return Exp Std Dev Exp Std Dev Sharpe Ratio Asset Class Weights 14.00% 18.00% 0.639 0.00% 0.00% 100.00% 0.00% 0.00% 13.66% 16.03% 0.696 0.00% 0.00% 86.36% 14.00% 13.02% 13.58% 0.775 21.69% 0.00% 56.56% 0.00% 21.76% 12.79% 13.00% 0.792 21.48% 0.00% 52.01% 5.24% 21.27% 10.54% 8.14% 0.988 9.40% 51.30% 26.55% 0.00% 12.76% 8.70% 6.32% 0.981 0.00% 89.65% 4.67% 0.00% w w o m bo ok c Corner Expected Portfolio Return en tre The details of each corner portfolio are given below A) Alternative investments with a weight of 20.17% w B) US bonds with a weight of 3.71% C) International bonds with a weight of 4.56% Explanation 0% 5.68% The expected return of 12.50% lies between corner portfolios and with expected returns of 12.79% and 10.54% We solve for w in the following equation: 12.50 = w(12.79) + (1-w)(10.54)  w = 0.87 In other words, the e cient portfolio with an expected return of 12.50% has 87% weight of corner portfolio and 13% weight of corner portfolio With respect to asset classes, the weights are then derived as follows: US equity = (0.87)(21.48) + (0.13)(9.40) = 19.91% US bonds = (0.87)(0) + (0.13)(51.30) = 6.67% Intl bonds = (0.87)(5.24) + (0.13)(0) = 4.56% en tre Alt invest = (0.87)(21.27) + (0.13)(12.76) = 20.17% in Intl equity = (0.87)(52.01) + (0.13)(26.55) = 48.70% Hence, International bonds are the least signi cant asset class with the lowest weight of 4.56% (Study Session 9, Module 19.3, LOS 19.b) bo ok c Related Material w w w o m SchweserNotes - Book ... weight of corner portfolio With respect to the asset classes, the weights are then derived as follows: Weight of asset class = (0 .33 )(65%) + (0.67)(15%) = 31 .50% Weight of asset class = (0 .33 )(0%)... (0.67)(20%) = 13. 4% Asset class has the highest weight and is the most signi cant .in Weight of asset class = (0 .33 ) (35 %) + (0.67)(50%) = 45.05% (Study Session 9, Module 19 .3, LOS 19. b) Related... Session 9, Module 19 .3, LOS 19. i) Related Material SchweserNotes - Book Question #32 of 37 Which of the following statements regarding liabilities in the context of the asset allocation decision