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4033Residual Hedge Variance 3An exposure has unhedged volatility 25%. After applying the minimum-variance hedge, the residual volatility is 15%. What correlation between spot and futures does this imply?金融与交易中等derivation未尝试面试订阅4035Residual Hedge Variance 5Spot volatility is 18%. What minimum absolute correlation |rho| is needed so that the minimum-variance hedge leaves residual volatility no more than 9%?金融与交易中等derivation未尝试面试订阅4036Why a Good Hedge Ratio Is Not Always OneWhy can the minimum-variance hedge ratio exceed 1?金融与交易中等essay未尝试面试订阅4037Why Cross-Hedges Leave Residual RiskWhy can the optimal hedge ratio be negative?金融与交易中等essay未尝试面试订阅4038Why Beta Hedges and Minimum-Variance Hedges Are Not the Same QuestionWhy does a high correlation matter more than a low futures volatility when hedge effectiveness is the goal?金融与交易中等essay未尝试面试订阅4039Why Hedge Effectiveness Is Mostly a Correlation StoryWhy can a hedge that looks perfect in notional terms still leave material basis risk?金融与交易中等essay未尝试面试订阅4040How to Sanity-Check a Hedge-Ratio AnswerWhy might a desk choose not to use the exact minimum-variance hedge ratio even after estimating it carefully?金融与交易中等essay未尝试面试订阅4051Hedge-Like Asset in Vector Kelly 1Under quadratic Kelly, mu = (0.06, 0.01) and Sigma = [[0.16, -0.03], [-0.03, 0.09]]. What is the optimal Kelly vector?金融与交易困难derivation未尝试面试订阅4054Hedge-Like Asset in Vector Kelly 4Under quadratic Kelly, mu = (0.08, 0.05) and Sigma = [[0.25, 0.04], [0.04, 0.16]]. By how much does positive covariance reduce the first Kelly weight relative to ignoring covariance?金融与交易困难derivation未尝试面试订阅4055Hedge-Like Asset in Vector Kelly 5Under quadratic Kelly, mu = (0.09, 0.04) and Sigma = [[0.25, 0.14], [0.14, 0.36]]. What is the optimal Kelly vector?金融与交易困难derivation未尝试面试订阅4056Quadratic Kelly Growth Score 1A desk fixes the first Kelly weight at 0.25. Asset 2 has mu 2 = 0.03, variance v 2 = 0.16, and covariance -0.04 with asset 1. Under the quadratic Kelly approximation, what second weight maximizes growth given the fixed first weight?金融与交易困难derivation未尝试面试订阅4057Quadratic Kelly Growth Score 2A desk fixes the first Kelly weight at 0.4. Asset 2 has mu 2 = 0.02, variance v 2 = 0.25, and covariance 0.05 with asset 1. Under the quadratic Kelly approximation, what second weight maximizes growth given the fixed first weight?金融与交易困难derivation未尝试面试订阅4058Quadratic Kelly Growth Score 3A desk fixes the first Kelly weight at 0.3. Asset 2 has mu 2 = -0.01, variance v 2 = 0.09, and covariance -0.03 with asset 1. Under the quadratic Kelly approximation, what second weight maximizes growth given the fixed first weight?金融与交易困难derivation未尝试面试订阅4061Negative Correlation and Gross Kelly ExposureWhy can a negatively correlated asset enter the Kelly portfolio with a positive weight even if its standalone edge is slightly negative?金融与交易中等essay未尝试面试订阅4062Independent Assets and AdditivityWhy does estimation error in the covariance matrix matter so much for multi-asset Kelly?金融与交易中等essay未尝试面试订阅4063Why Naive Single-Asset Kelly Can MisleadWhy do practitioners often shrink or cap multi-asset Kelly weights even after solving the unconstrained optimum?金融与交易中等essay未尝试面试订阅4064Why a Weak Asset Can Still Belong in the PortfolioWhy can gross leverage explode when the covariance matrix is nearly singular?金融与交易中等essay未尝试面试订阅4065How Correlation Changes the GeometryWhy is looking only at each asset’s standalone Kelly fraction misleading in a multi-asset book?金融与交易中等essay未尝试面试订阅4096Two-Asset Equal Risk Contribution 1A two-asset equal-risk-contribution portfolio uses long-only weights that sum to 1. Asset A has vol 10.00\%, asset B has vol 25.00\%, and their correlation is 0.3. What weights equalize the two assets' variance contributions?金融与交易中等数值题未尝试面试订阅4097Two-Asset Equal Risk Contribution 2A two-asset equal-risk-contribution portfolio uses long-only weights that sum to 1. Asset A has vol 12.00\%, asset B has vol 18.00\%, and their correlation is -0.2. What weights equalize the two assets' variance contributions?金融与交易中等数值题未尝试面试订阅