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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5278Variance Needed For One-Third Tangency WeightTwo uncorrelated risky assets have expected returns 0.10 and 0.14, risk-free rate 0.05, and asset 1 variance 0.05. What variance would asset 2 need so that the tangency portfolio puts exactly one-third of the risky allocation in asset 2?金融与交易困难数值题未尝试面试订阅5279Fee That Shrinks Tangency Weight To 20%Two uncorrelated risky assets have expected returns 0.06 and 0.09, risk-free rate 0.02, and variances 0.025 and 0.07. Suppose asset 2 carries an annual implementation fee c that reduces its expected return from 0.09 to 0.09-c. What fee c would make the tangency portfolio weight on asset 2 equal to 20%?金融与交易困难数值题未尝试面试订阅5280Variance Penalty For Equal Tangency WeightsTwo uncorrelated risky assets have expected returns 0.09 and 0.13, risk-free rate 0.04, and variances 0.035 and 0.10. Risk control adds a variance penalty x to asset 1, so its effective variance becomes 0.035 + x. What x would make the tangency portfolio split the risky allocation equally across the two assets?金融与交易困难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5286PM Dismisses A Low-Sharpe Hedge SleeveA PM says, "This market-neutral sleeve has a poor standalone Sharpe, so it should never receive weight in a Markowitz optimizer." The sleeve is mildly negatively correlated with the core book. How would you respond in two or three sentences?金融与交易困难essay未尝试面试订阅5289Why Long-Only Can Reshape The Entire SolutionAn unconstrained optimizer wants a large short in one equity sleeve to hedge two crowded longs, but mandate rules require long-only weights. Explain why the long-only solution can look qualitatively different rather than just a clipped version of the unconstrained one.金融与交易困难essay未尝试面试订阅5290Tiny Alpha Changes, Huge Weight FlipsA Markowitz backtest flips from +18% to -12% in one sleeve after a tiny revision to expected-return estimates, while the covariance matrix barely changes. What does this tell you, and what would you do before trading the result live?金融与交易困难essay未尝试面试订阅