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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4066Scaled Kelly Fraction 1A strategy's full-Kelly position is 0.8. A risk mandate caps absolute position size at 0.3. What is the largest Kelly fraction lambda the desk can apply without breaching the cap?金融与交易简单derivation未尝试面试订阅4067Scaled Kelly Fraction 2A strategy's full-Kelly position is -1.2. A risk mandate caps absolute position size at 0.6. What is the largest Kelly fraction lambda the desk can apply without breaching the cap?金融与交易简单derivation未尝试面试订阅4071Growth Retention under Fractional Kelly 1Under the quadratic Kelly scaling rule, the expected growth at fraction c of full Kelly is proportional to 2c-c 2 relative to full Kelly. What fraction of full-Kelly growth is retained at c=0.5?金融与交易中等derivation未尝试面试订阅4083Fractional Kelly Portfolio Leverage 3A strategy has full-Kelly expected log-growth 12% per year. Under 40% Kelly and the quadratic approximation, what expected log-growth remains?金融与交易简单derivation未尝试面试订阅4084Fractional Kelly Portfolio Leverage 4To retain 75% of full-Kelly growth under the quadratic approximation with lambda in [0,1], what Kelly fraction is needed?金融与交易简单derivation未尝试面试订阅4091Inverse-Vol Risk-Parity Weights 1Inverse-volatility risk parity across three sleeves targets weights (0.5, 0.25, 0.25). If the first two sleeve volatilities are 10% and 20%, what volatility must the third sleeve have?金融与交易简单数值题未尝试面试订阅4092Inverse-Vol Risk-Parity Weights 2A two-sleeve inverse-volatility book currently uses vols 12% and 18%. A third sleeve with volatility 36% is added. What are the new fully invested inverse-volatility weights?金融与交易简单数值题未尝试面试订阅4093Inverse-Vol Risk-Parity Weights 3An inverse-volatility risk-parity portfolio uses three uncorrelated sleeves with vols 10%, 15%, and 30%. What leverage would scale the fully invested portfolio to a target portfolio volatility of 12%?金融与交易简单数值题未尝试面试订阅4094Inverse-Vol Risk-Parity Weights 4Inverse-volatility risk parity wants weight proportions 4:2:1 across three sleeves. If the first sleeve volatility is 8%, what sleeve volatilities are implied for the second and third sleeves?金融与交易简单数值题未尝试面试订阅4095Inverse-Vol Risk-Parity Weights 5A two-sleeve inverse-volatility portfolio starts from vols 14% and 21%. If the second sleeve volatility falls to 14%, what are the new weights?金融与交易简单数值题未尝试面试订阅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4101Vol-Target Scaling 1A three-sleeve inverse-vol portfolio was originally built from vols 10%, 20%, and 25%, so the weights are left stale when sleeve 2 volatility jumps to 30%. Assuming zero correlations, what share of portfolio variance now comes from sleeve 2?金融与交易中等数值题未尝试面试订阅4102Vol-Target Scaling 2A three-sleeve inverse-vol portfolio was originally calibrated on vols 12%, 24%, and 36%. If sleeve 1 volatility jumps to 18% and weights are not rebalanced, which sleeve contributes the most variance, and what is its share?金融与交易中等数值题未尝试面试订阅4103Vol-Target Scaling 3A two-sleeve inverse-vol portfolio starts with vols 16% and 24%. If the first sleeve volatility drops by 25%, what are the new weights?金融与交易中等数值题未尝试面试订阅4104Vol-Target Scaling 4A three-sleeve inverse-vol portfolio uses vols 10%, 20%, and 40%. If the third sleeve volatility halves to 20%, by how many weight points does sleeve 3 gain after rebalancing?金融与交易中等数值题未尝试面试订阅4105Vol-Target Scaling 5Suppose a portfolio still holds weights (0.5, 0.3, 0.2) while sleeve volatilities are (10%, 20%, 30%) and correlations are zero. What fraction of portfolio variance comes from sleeve 3?金融与交易中等数值题未尝试面试订阅