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5252Vertical Spread Bound Check 2Calls with strikes 100 and 110>100 are priced at 5.4 and 2.1. With annual rate 0.04 and maturity T=0.5, is the bull call spread price C(K1)-C(K2) inside its no-arbitrage bounds? Also report the bound interval.金融与交易中等数值题未尝试面试订阅5253Vertical Spread Bound Check 3Calls with strikes 80 and 90>80 are priced at 4 and 1.3. With annual rate 0.03 and maturity T=1.5, is the bull call spread price C(K1)-C(K2) inside its no-arbitrage bounds? Also report the bound interval.金融与交易中等数值题未尝试面试订阅5254Vertical Spread Bound Check 4Calls with strikes 110 and 120>110 are priced at 3.5 and 1. With annual rate 0.02 and maturity T=1, is the bull call spread price C(K1)-C(K2) inside its no-arbitrage bounds? Also report the bound interval.金融与交易中等数值题未尝试面试订阅5256Call Monotonicity 1At the same maturity, calls are quoted as C(95)=7 and C(105)=5.8 with 105>95. Does this satisfy basic no-arbitrage monotonicity across strikes?金融与交易简单数值题未尝试面试订阅5257Call Monotonicity 2At the same maturity, calls are quoted as C(100)=6.2 and C(110)=6.4 with 110>100. Does this satisfy basic no-arbitrage monotonicity across strikes?金融与交易简单数值题未尝试面试订阅5260Call Monotonicity 5At the same maturity, calls are quoted as C(85)=7.8 and C(100)=5 with 100>85. Does this satisfy basic no-arbitrage monotonicity across strikes?金融与交易简单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5293Alpha Relative to a Benchmark Move 3A stock returns 1.8% while the benchmark returns 0.9%. If the stock beta is 1.1 and the risk-free rate is negligible over the horizon, what single-period alpha do you attribute to the stock?金融与交易中等数值题未尝试面试订阅5294Index Futures Overlay To Reach A Beta TargetA cash equity book has beta 0.60 to the market. The desk can short index futures with beta 1.00 per unit notional. What short futures notional, as a fraction of NAV, is needed to bring the portfolio beta down to 0.15?金融与交易中等数值题未尝试面试订阅5295Overlay Notional for Beta Neutrality 4A core book has beta 0.9 and notional 200. An index future has beta 1.0. What short futures notional makes the combined beta exposure zero?金融与交易中等数值题未尝试面试订阅5296Idiosyncratic Variance From Total and Market Pieces 5A stock follows a one-factor model with beta 1.5. Market variance is 0.04 and the stock's total variance is 0.16. What idiosyncratic variance is implied?金融与交易中等数值题未尝试面试订阅5297Portfolio Alpha Across Two Sleeves 6Sleeve A has weight 40% and alpha 2%, sleeve B has weight 60% and alpha -0.5%. What is the portfolio alpha?金融与交易中等数值题未尝试面试订阅5298Benchmark Change and Alpha Revision 7A stock returned 1.3%. Under the old benchmark, the benchmark return was 0.8% and beta was 1.0. Under a new benchmark, the benchmark return is 0.5% with the same beta. By how much does the stock's measured alpha increase?金融与交易中等数值题未尝试面试订阅5299Minimum Expected Return To Clear An Alpha HurdleA PM requires at least 1.0% expected alpha over CAPM before buying a stock. If the risk-free rate is 1%, the market expected return is 7%, and the stock's beta is 0.6, what minimum expected return must the stock have to qualify?金融与交易中等数值题未尝试面试订阅