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4099Two-Asset Equal Risk Contribution 4A two-asset equal-risk-contribution portfolio uses long-only weights that sum to 1. Asset A has vol 14.00\%, asset B has vol 28.00\%, and their correlation is 0. 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4106Risk-Contribution Concentration Check 1A portfolio holds rates, equity, and commodity sleeves with zero pairwise correlations. Weights are rates: 0.5, equity: 0.3, commodity: 0.2 and vols are rates 10.00\%, equity 18.00\%, commodity 30.00\%. Which sleeve contributes the most to portfolio variance, and what share of total variance does it contribute?金融与交易中等数值题未尝试面试订阅4441Fee-Adjusted Composite Alpha 1A desk forms a composite alpha A = 0.6 A fast + 0.4 A slow. The expected gross daily alpha of A fast is 8 bps and of A slow is 5 bps. Their daily turnover is 90% and 20%, and every 1% of turnover costs 0.02 bps. What is the composite's expected net daily alpha?机器学习中等数值题未尝试面试订阅4442Implied Correlation From Composite Vol 2Two standardized signals are combined as C = 0.5 S1 + 0.5 S2. Their standard deviations are 1.2 and 0.8, and the composite standard deviation is observed to be 0.9. What correlation between S1 and S2 is implied?机器学习中等数值题未尝试面试订阅4443Orthogonalized Fast Signal Coefficient 3A fast signal F has standard deviation 1.5 and a slow signal S has standard deviation 1.0. Their correlation is 0.4. If you orthogonalize the fast signal as F res = F - beta*S so that F res is uncorrelated with S, what beta should you use?机器学习中等数值题未尝试面试订阅4444Beta-Neutral Blend Weight 4A fast signal book has market beta 0.8 and a slow signal book has market beta -0.4. You form C = w*fast + (1-w)*slow and want the composite beta to be 0. What weight w on the fast book achieves that?机器学习中等数值题未尝试面试订阅4445Equal-Weight Signal-To-Return Correlation 5Signals S1 and S2 are both standardized. Their correlations with next-period return R are 0.12 and 0.08, and Corr(S1,S2)=0.2. If you form C = 0.5 S1 + 0.5 S2, what is Corr(C,R)?机器学习中等数值题未尝试面试订阅4446Equal Variance Contribution Weight 6Two independent signal sleeves have standard deviations 2 and 1. In a composite C = w S1 + (1-w) S2, what weight w makes the two sleeves contribute equally to the total variance?机器学习中等数值题未尝试面试订阅4447Implied Covariance From Chosen Blend 7A desk uses C = 0.7 S1 + 0.3 S2. The standard deviations of S1 and S2 are 1.0 and 1.5, and the standard deviation of C is 0.95. What covariance between S1 and S2 is implied?机器学习中等数值题未尝试面试订阅4448Correlation Shock Benefit 8An equal-weight composite combines two standardized signals. If their correlation drops from 0.6 to 0.2, by how much does the composite standard deviation fall?机器学习中等数值题未尝试面试订阅4449Target Alpha Weight 9A fast signal has expected alpha 9 bps and a slow signal has expected alpha 3 bps. In a composite C = w fast + (1-w) slow, what weight on the fast signal produces expected alpha 6.6 bps?机器学习中等数值题未尝试面试订阅4450MSE Gain From A Diversifying Forecast 10Forecast error variance is 4 for model A, 9 for model B, and their error covariance is 1. You blend them equally. By how much does the blended forecast's MSE improve relative to using model A alone?机器学习中等数值题未尝试面试订阅5267Target Return And Covariance Share 2A fully invested two-asset portfolio places weight w in asset 1 and 1-w in asset 2. The assets have expected returns 0.06 and 0.10, volatilities 0.03 and 0.07, and correlation 0.1. If the PM wants expected return 0.082, what weight w is required, and what percentage of the resulting variance comes from the covariance term?金融与交易中等数值题未尝试面试订阅5268Equal Risk Contribution Mix 3Two risky assets have volatilities 0.05 and 0.11, correlation 0.25, and expected returns 0.09 and 0.13. Under a fully invested long-only portfolio, choose weights so the two assets contribute equally to total variance. What are the weights and the portfolio expected return?金融与交易中等数值题未尝试面试订阅5269Boundary Correlation For No Risk Increase 4A portfolio holds weights 0.6 and 0.4 in two assets with volatilities 0.02 and 0.08. What correlation would make the portfolio volatility exactly equal to 0.02, the volatility of the safer asset? Is that attainable without going outside the correlation bounds?金融与交易中等数值题未尝试面试订阅5270Return Maximization Under Variance Cap 5A fully invested long-only portfolio allocates weight w to asset 2 and 1-w to asset 1. Asset 1 has expected return 0.05 and volatility 0.025. Asset 2 has expected return 0.14 and volatility 0.12. Their correlation is 0.3. If portfolio variance must not exceed 0.006, what is the largest admissible weight on asset 2, and what expected return does that deliver?金融与交易中等数值题未尝试面试订阅5271Minimum-Variance Weight 1Two risky assets have variances 0.04 and 0.09 and covariance 0.015. What weight on asset 1 gives the two-asset minimum-variance portfolio?金融与交易中等数值题未尝试面试订阅5281Correlation Shock And Volatility Repricing 1An equal-weight portfolio holds two assets with volatilities 0.04 and 0.09. The current correlation estimate is -0.2, but stress testing revises it to +0.3. With weights unchanged, what is the new portfolio volatility, and by how many volatility points does it rise versus the original estimate?金融与交易中等数值题未尝试面试订阅5283Correlation Break And Diversification Loss 3A two-asset portfolio has weights 0.3 and 0.7, volatilities 0.03 and 0.10, and current correlation 0.25. After a macro shock, correlation is revised to 0.75 with all else unchanged. What is the new portfolio volatility, and how many volatility points of diversification are lost relative to the original estimate?金融与交易中等数值题未尝试面试订阅5284Correlation Normalization And Variance Jump 4A portfolio holds weights 0.4 and 0.6 in two assets with volatilities 0.06 and 0.12 and current correlation -0.4. If correlation normalizes to 0 while weights and volatilities stay fixed, by what percentage does portfolio variance increase?金融与交易中等数值题未尝试面试订阅