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4030Futures Vol Needed for an Exact Hedge Count 5A desk hedges 6,000 spot units with 30 futures contracts of size 100. Spot volatility is 18% and spot-futures correlation is 0.75. If 30 contracts is exactly the minimum-variance hedge count, what futures volatility is implied?金融与交易中等数值题未尝试面试订阅4031Residual Hedge Variance 1Spot volatility is 20% and correlation to the hedging futures is 0.8. Under the minimum-variance hedge, what residual spot volatility remains?金融与交易中等derivation未尝试面试订阅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4041Two-Asset Diagonal Kelly Vector 1Under the quadratic Kelly approximation with diagonal covariance, variances are (0.36, 0.25) and optimal weights are (0.25, 0.2). If mu 1 = 0.09, what mu 2 is implied?金融与交易中等derivation未尝试面试订阅4042Two-Asset Diagonal Kelly Vector 2Under diagonal Sigma, expected excess returns are (0.08, 0.06) and optimal weights are (0.2, 0.375). If variance of asset 2 is 0.16, what variance of asset 1 is implied?金融与交易中等derivation未尝试面试订阅4043Two-Asset Diagonal Kelly Vector 3With diagonal covariance, expected excess returns are (0.07, 0.03) and optimal weights are (0.2, 0.15). If variance of asset 1 is 0.35, what variance of asset 2 is implied?金融与交易中等derivation未尝试面试订阅4044Two-Asset Diagonal Kelly Vector 4Diagonal covariance has variances (0.25, 0.09), and the optimal Kelly vector is (0.24, -0.1). What expected excess return vector mu is implied?金融与交易中等derivation未尝试面试订阅4045Two-Asset Diagonal Kelly Vector 5With diagonal covariance, mu 1 = 0.05, variance 1 = 0.25, and variance 2 = 0.16. What mu 2 makes the total optimal gross leverage equal 0.5 if both weights are nonnegative?金融与交易中等derivation未尝试面试订阅4046Correlated Two-Asset Kelly Vector 1Under quadratic Kelly, mu = (0.08, 0.05) and Sigma = [[0.25, 0.04], [0.04, 0.16]]. What is the unconstrained optimal Kelly vector?金融与交易困难derivation未尝试面试订阅4047Correlated Two-Asset Kelly Vector 2Under quadratic Kelly, mu = (0.1, 0.04) and Sigma = [[0.36, -0.06], [-0.06, 0.25]]. What is the unconstrained optimal Kelly vector?金融与交易困难derivation未尝试面试订阅4048Correlated Two-Asset Kelly Vector 3Under quadratic Kelly with two assets, mu = (0.09, 0.03), variances are (0.36, 0.16), and covariance is c. What covariance c makes the second optimal Kelly weight exactly zero?金融与交易困难derivation未尝试面试订阅4049Correlated Two-Asset Kelly Vector 4If Sigma = [[0.25, 0.05], [0.05, 0.36]] and the optimal Kelly vector is (0.2, 0.1), what expected excess return vector mu is implied?金融与交易困难derivation未尝试面试订阅4050Correlated Two-Asset Kelly Vector 5Suppose mu = (0.068, 0.05), variances are (0.25, 0.16), and the desk wants the unconstrained Kelly optimum to be exactly (0.2, 0.2). What covariance c makes that true?金融与交易困难derivation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