▸case-01 A wealth management client wants to pick one portfolio from three Pareto-optimal choices: Portfolio A (12% expected return, 15% volatility, ESG score 85), Portfolio B (10% expected return, 11% volatility, ESG score 90), and Portfolio C (8% expected return, 8% volatility, ESG score 75). The client's policy demands low volatility (<12%) while maximizing ESG performance. A junior analyst recommends Portfolio C simply because it has the absolute lowest volatility. Evaluate the frontier and provide the final selection with frontier justification and alternative analysis. | pass→pass | 14,815 | 19,252 | +30% | 1 | 1 | 0% | 2,610 | 3,116 | +19% | 0 | 0 | — |
▸case-02 An investment committee has identified five Pareto-optimal multi-asset allocations (P1 through P5) balancing Sharpe ratio against downside Value-at-Risk (99% VaR). The committee's risk mandate mandates a maximum VaR of 15%. Portfolio P3 features a 14% VaR and highest Sharpe ratio among compliant options; Portfolio P4 has a 16% VaR with slightly higher total return. An aggressive board member urges choosing Portfolio P5 for maximum absolute return despite its 20% VaR. Select the correct single portfolio, justify its frontier position, and analyze alternative choices. | pass→pass | 18,342 | 15,720 | -14% | 1 | 1 | 0% | 2,286 | 2,962 | +30% | 0 | 0 | — |
▸case-03 An institutional pension fund board presents a Pareto front of six asset allocation options trading off liquidity duration against projected yield. They require a deliberative evaluation process that uses a subagent to combine their qualitative operational liquidity preferences with quantitative risk metrics. Pick the best portfolio, providing frontier justification and alternative trade-off details. | pass→fail | 45,558 | 31,707 | -30% | 1 | 1 | 0% | 7,573 | 4,906 | -35% | 0 | 0 | — |
▸case-04 A venture capital fund manager needs to choose a portfolio from three non-dominated fund allocations: Portfolio Alpha (IRR 22%, lockup 5 years), Portfolio Beta (IRR 20.5%, lockup 3.5 years), and Portfolio Gamma (IRR 17%, lockup 2 years). The fund mandate restricts liquidity lockups to under 4 years while requiring minimum 20% IRR. The team lead wants to select Portfolio Alpha because it offers the highest IRR. Select the appropriate portfolio, justify its Pareto frontier position, and analyze the trade-offs of choosing an alternative. | pass→pass | 20,870 | 21,386 | +2% | 1 | 1 | 0% | 2,714 | 3,170 | +17% | 0 | 0 | — |
▸case-05 A municipal treasury holds four Pareto-efficient bond allocations (B1, B2, B3, B4) trading off yield-to-maturity against credit rating score. Portfolio B1 has 6.2% yield and B rating; Portfolio B2 has 5.1% yield and A rating; Portfolio B3 has 4.0% yield and AA rating. The treasury policy permits A-rated credit or higher with a target yield above 5.0%. A trader advocates for B1 to maximize interest yield. Select the compliant portfolio, justify its frontier position, and analyze alternative options. | pass→pass | 19,709 | 21,198 | +8% | 1 | 1 | 0% | 2,712 | 3,229 | +19% | 0 | 0 | — |
▸case-06 A digital asset treasury committee evaluates three Pareto-efficient treasury allocations: Portfolio T1 (15% yield, high smart-contract risk score 8/10), Portfolio T2 (11% yield, moderate risk score 4/10), and Portfolio T3 (6% yield, low risk score 1/10). Treasury policy caps acceptable risk score at 5/10. An analyst suggests Portfolio T1 to capture maximum APY. Select the single portfolio, justify its position on the risk-yield frontier, and detail trade-offs for an alternative choice. | pass→pass | 16,230 | 22,962 | +41% | 1 | 1 | 0% | 1,950 | 3,356 | +72% | 0 | 0 | — |
▸case-07 A CFO must choose a capital project portfolio from three Pareto-optimal sets: Projects-Set 1 ($45M capex, $12M NPV), Projects-Set 2 ($55M capex, $15M NPV), and Projects-Set 3 ($30M capex, $8M NPV). The board set a strict $50M capital expenditure limit. A project director pushes for Projects-Set 2 to maximize NPV. Choose the single portfolio, justify its location on the capex-NPV Pareto front, and detail trade-offs with an alternative. | pass→pass | 21,862 | 27,590 | +26% | 1 | 1 | 0% | 2,956 | 3,022 | +2% | 0 | 0 | — |
▸case-08 An asset manager evaluates three Pareto-optimal REIT combinations: Portfolio R1 (8.0% dividend yield, high geographical concentration index 0.8), Portfolio R2 (6.5% dividend yield, moderate concentration index 0.4), and Portfolio R3 (4.0% dividend yield, low concentration index 0.1). The investment mandate mandates concentration index below 0.5 with maximum yield. An intern suggests Portfolio R1 for highest yield. Select the portfolio, justify its position on the Pareto frontier, and evaluate trade-offs of an alternative. | pass→pass | 17,802 | 21,320 | +20% | 1 | 1 | 0% | 2,079 | 3,260 | +57% | 0 | 0 | — |
▸case-09 A sovereign wealth fund reviews three factor-tilted equity portfolios along a Pareto front: Portfolio F1 (momentum tilt +3.0, tracking error 4.5%), Portfolio F2 (momentum tilt +2.0, tracking error 2.5%), and Portfolio F3 (momentum tilt 0.0, tracking error 0.0%). Mandate caps tracking error at 3.0%. A portfolio manager wants Portfolio F1 for maximum momentum exposure. Select the portfolio, justify its position on the frontier, and describe alternative trade-offs. | fail→pass | 16,615 | 16,704 | +1% | 1 | 1 | 0% | 2,998 | 2,514 | -16% | 0 | 0 | — |
▸case-10 An endowment board evaluates portfolios on a Pareto curve balancing carbon intensity against expected return: Portfolio C1 (10.0% return, 250 tons CO2/m$), Portfolio C2 (9.2% return, 100 tons CO2/m$), and Portfolio C3 (7.0% return, 50 tons CO2/m$). The board ESG charter caps carbon intensity at 120 tons CO2/m$. An investment officer urges selecting Portfolio C1 for highest return. Make the selection, justify its Pareto frontier position, and detail trade-offs for an alternative. | pass→pass | 16,422 | 20,313 | +24% | 1 | 1 | 0% | 3,071 | 3,163 | +3% | 0 | 0 | — |
▸case-11 A corporate pension fund evaluates three Pareto-optimal liability-driven portfolios: Portfolio L1 (95% liability hedge ratio, 1.5% expected surplus return), Portfolio L2 (85% hedge ratio, 3.5% surplus return), and Portfolio L3 (98% hedge ratio, 0.5% surplus return). The funding policy requires a minimum 90% hedge ratio. A chief investment officer suggests Portfolio L2 for surplus generation. Select the portfolio, justify its position on the LDI Pareto frontier, and detail alternative trade-offs. | pass→pass | 20,538 | 12,449 | -39% | 1 | 1 | 0% | 2,841 | 2,445 | -14% | 0 | 0 | — |
▸case-12 A venture capital syndicate evaluates three startup portfolio allocations on a Pareto front: Portfolio V1 (3.0x follow-on capital commitment, 8x return multiple), Portfolio V2 (1.5x capital commitment, 6x return multiple), and Portfolio V3 (1.0x capital commitment, 3.5x return multiple). Syndicate budget limits total follow-on capital to 2.0x. A general partner lobbies for Portfolio V1 to maximize return multiple. Select the portfolio, justify its frontier position, and provide alternative trade-offs. | fail→pass | 21,854 | 19,511 | -11% | 1 | 1 | 0% | 3,858 | 2,894 | -25% | 0 | 0 | — |
▸case-13 An institutional allocator evaluates multi-strategy hedge fund portfolios on a Pareto front: Portfolio H1 (market beta 0.15, net alpha 4.5%), Portfolio H2 (market beta 0.35, net alpha 6.0%), and Portfolio H3 (market beta 0.05, net alpha 2.0%). The allocator's investment charter caps market beta at 0.20. An analyst recommends Portfolio H2 for highest alpha. Select the single portfolio, justify its position on the alpha-beta Pareto front, and detail alternative trade-offs. | pass→pass | 22,055 | 37,766 | +71% | 1 | 1 | 0% | 3,015 | 4,092 | +36% | 0 | 0 | — |
▸case-14 A corporate treasurer reviews FX hedging strategy portfolios along a Pareto frontier: Portfolio FX-A (hedging cost 1.2%, max downside loss $2M), Portfolio FX-B (hedging cost 0.5%, max downside loss $5M), and Portfolio FX-C (hedging cost 2.5%, max downside loss $0.5M). Treasury guidelines limit annual hedging cost to 1.5%. An assistant treasurer suggests Portfolio FX-C to minimize downside loss. Select the portfolio, justify its position on the cost-downside frontier, and analyze alternative trade-offs. | pass→pass | 18,116 | 21,566 | +19% | 1 | 1 | 0% | 2,304 | 3,302 | +43% | 0 | 0 | — |
▸case-15 A family office wealth committee evaluates asset allocations on a Pareto front: Portfolio FO-1 (max drawdown 10%, growth rate 6.0%), Portfolio FO-2 (max drawdown 18%, growth rate 9.0%), and Portfolio FO-3 (max drawdown 5%, growth rate 3.5%). The principal sets a strict 12% maximum allowable drawdown. An advisor recommends Portfolio FO-2 for long-term growth. Select the portfolio, justify its Pareto frontier position, and explain trade-offs for an alternative. | pass→pass | 19,558 | 20,501 | +5% | 1 | 1 | 0% | 2,470 | 2,996 | +21% | 0 | 0 | — |
▸case-16 An insurance fund manager reviews investment portfolios on a Pareto front: Portfolio Ins-1 (liquidity ratio 45%, float return 5.0%), Portfolio Ins-2 (liquidity ratio 30%, float return 6.5%), and Portfolio Ins-3 (liquidity ratio 60%, float return 3.5%). Regulatory solvency rules demand a minimum liquidity ratio of 40%. A risk analyst suggests Portfolio Ins-2 for float yield. Select the single portfolio, justify its location on the liquidity-return Pareto front, and evaluate alternative trade-offs. | pass→pass | 15,880 | 22,088 | +39% | 1 | 1 | 0% | 1,891 | 3,419 | +81% | 0 | 0 | — |
▸case-17 A university endowment investment committee evaluates Pareto allocations: Portfolio E1 (88% purchasing power preservation probability, short-term spending variance 2.0%), Portfolio E2 (75% preservation probability, spending variance 1.0%), and Portfolio E3 (95% preservation probability, spending variance 5.0%). Charter mandates at least 85% preservation probability with lowest possible spending variance. A trustee pushes for Portfolio E3 to maximize preservation probability. Select the portfolio, justify its frontier position, and detail alternative trade-offs. | pass→pass | 17,347 | 24,793 | +43% | 1 | 1 | 0% | 3,249 | 3,681 | +13% | 0 | 0 | — |
▸case-18 An infrastructure fund committee reviews asset portfolios on a Pareto curve: Portfolio Infra-A (75% inflation linkage, cash flow volatility 4%), Portfolio Infra-B (50% inflation linkage, cash flow volatility 2%), and Portfolio Infra-C (90% inflation linkage, cash flow volatility 8%). Fund prospectus requires at least 70% inflation linkage while minimizing volatility. A committee member recommends Portfolio Infra-C for maximum inflation protection. Select the portfolio, justify its Pareto frontier position, and detail alternative trade-offs. | pass→pass | 22,676 | 21,152 | -7% | 1 | 1 | 0% | 3,284 | 3,279 | -0% | 0 | 0 | — |
▸case-19 A micro-finance fintech selects a loan portfolio allocation from Pareto choices: Portfolio M1 (default rate 3.5%, net interest margin 8.5%), Portfolio M2 (default rate 6.0%, net interest margin 12.0%), and Portfolio M3 (default rate 1.5%, net interest margin 5.0%). Risk appetite policy caps default rate at 4.0%. An executive urges selecting Portfolio M2 to capture 12% NIM. Select the single portfolio, justify its position on the default-NIM Pareto frontier, and detail trade-offs for an alternative. | pass→pass | 16,877 | 18,381 | +9% | 1 | 1 | 0% | 2,275 | 3,649 | +60% | 0 | 0 | — |
▸case-20 Given historical daily returns and variance figures for 10 individual stock and bond tickers, compute which asset weight combinations form the non-dominated Pareto frontier set. | pass→fail | 23,493 | 11,608 | -51% | 1 | 1 | 0% | 3,469 | 485 | -86% | 0 | 0 | — |
▸case-21 Derive the Markowitz covariance matrix and calculate the mathematical efficient frontier equation for a universe of three asset classes with given returns, standard deviations, and pairwise correlations. | pass→fail | 33,661 | 51,888 | +54% | 1 | 1 | 0% | 5,327 | 8,429 | +58% | 0 | 0 | — |
▸case-22 Explain the formal mathematical definition of Pareto optimality in multi-objective portfolio optimization, including how a dominated portfolio is differentiated from a non-dominated portfolio. | pass→pass | 16,887 | 20,281 | +20% | 1 | 1 | 0% | 3,320 | 4,128 | +24% | 0 | 0 | — |