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1601Why Every Covariance Matrix Is PSDWhy must every valid covariance matrix be positive semidefinite?数学简单essay未尝试免费1602Equal-Weight Two-Asset Variance 1Two assets have variances 4 and 9, with covariance 2. What is the variance of the portfolio with weights (1/2, 1/2)?数学简单数值题未尝试免费1605Hedged Pair Variance 4Two assets have variances 1 and 9, with covariance -1. What is the variance of the portfolio with weights (1/3, 2/3)?数学困难数值题未尝试面试订阅1607Why Sample Covariance Can Be Rank DeficientWhy can a sample covariance matrix become rank deficient when the number of observations is smaller than the number of assets?数学中等essay未尝试免费1608Minimum-Variance Hedge Ratio 1You hedge X with h units of Y and want to minimize Var(X - hY). If Cov(X, Y) = 8 and Var(Y) = 4, what is the optimal hedge ratio h?数学中等derivation未尝试免费1611Equicorrelation Validity Threshold 1For an n=4 equicorrelation matrix with 1s on the diagonal and rho off the diagonal, what is the lowest rho that still keeps the matrix positive semidefinite?数学简单数值题未尝试免费1614One-Factor Covariance Entry 1Under a one-factor model X = bF + epsilon with factor variance 3, asset loadings (1, 2), and idiosyncratic variances (4, 9), what are Var(X 1), Var(X 2), and Cov(X 1, X 2)?数学困难derivation未尝试面试订阅1615Signed-Factor Covariance Entry 2Under a one-factor model X = bF + epsilon with factor variance 5, asset loadings (2, -1), and idiosyncratic variances (1, 4), what are Var(X 1), Var(X 2), and Cov(X 1, X 2)?数学困难derivation未尝试面试订阅1616How to Read Diagonal and Off-Diagonal EntriesIn a covariance matrix, what do the diagonal entries and off-diagonal entries mean?数学简单essay未尝试免费1617Correlation from Covariance 1Two assets have variances 9 and 16, and covariance 6. What is their correlation?数学中等derivation未尝试免费1618Negative Correlation Extraction 2Two assets have variances 4 and 25, and covariance -6. What is their correlation?数学中等derivation未尝试免费1619Why Large Condition Number Destabilizes WeightsWhy does a covariance matrix with a very large condition number make optimized portfolio weights unstable?数学困难essay未尝试面试订阅