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4005Clique/Reset Payoff 5A digital corridor note pays 4 if S T > K and 1 otherwise. Rates are zero and the risk-neutral probability of S T > K is 0.35. What is the price?金融与交易中等derivation未尝试面试订阅4016Minimum-Variance Hedge Ratio 1A spot exposure has volatility 18%, the hedging futures has volatility 24%, and the desired minimum-variance hedge ratio is 0.6. What correlation is implied by h*=rho*sigma S/sigma F?金融与交易中等derivation未尝试面试订阅4017Minimum-Variance Hedge Ratio 2A spot exposure has volatility 30%, correlation 0.75 to the hedging futures, and desired hedge ratio 0.9. What futures volatility is implied?金融与交易中等derivation未尝试面试订阅4018Minimum-Variance Hedge Ratio 3A short hedge ratio of -0.3 is desired. If futures volatility is 20% and correlation is -0.4, what spot volatility is implied?金融与交易中等derivation未尝试面试订阅4021Hedge Contract Count 1A spot exposure of 2000 units is hedged with futures contracts of 100 units each. Spot volatility is 30.00%, futures volatility is 25.00%, and correlation is 0.8. How many futures contracts correspond to the minimum-variance hedge?金融与交易中等derivation未尝试面试订阅4026Beta Hedge Contract Count 1A desk uses 36 futures contracts of size 1000 to hedge a spot exposure of 50000 units. Spot volatility is 24% and futures volatility is 30%. What correlation would make this contract count exactly minimum-variance optimal?金融与交易中等derivation未尝试面试订阅4027Beta Hedge Contract Count 2A desk wants to hedge 4000 spot units with 25 futures contracts of size 200. Spot volatility is 15% and correlation is 0.8. What futures volatility would make that contract count minimum-variance optimal?金融与交易中等derivation未尝试面试订阅4028Contract Size Implied by a Min-Variance Hedge 3A desk hedges a spot exposure of 12,000 units with 40 futures contracts. The spot volatility is 25%, the futures volatility is 20%, and the spot-futures correlation is 0.64. If the desk is using the minimum-variance hedge ratio, what contract size must each futures contract represent?金融与交易中等数值题未尝试面试订阅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