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5327Cleaned Historical VaR After Removing Bad ScenarioDesk A and Desk B losses across five aligned scenarios are A=[4, 1, 3, 2, 5] and B=[1, 2, 0, 4, 1]. Scenario 4 is traced to bad data and removed from both books before aggregation. Using the remaining scenarios and historical VaR/ES at alpha=0.75 with the ceil(alpha*n) convention, what are the cleaned VaR and ES of the aggregated portfolio?金融与交易中等数值题未尝试面试订阅5328Minimum Hedge Overlay Scale For VaR LimitA core book has scenario losses [2, 5, 4, 6]. A hedge overlay contributes [0, -2, -1, -3] per unit notional across the same four scenarios. If the overlay is scaled by a factor x and portfolio losses are computed scenario by scenario as core + x*hedge, what is the minimum x that makes historical VaR at alpha=0.75 no larger than 3 under the ceil(alpha*n) convention?金融与交易中等数值题未尝试面试订阅5329Tail Insurance Needed To Reduce Historical ESThe aggregated historical dollar-loss sample of a portfolio is [4, 7, 6, 5] million across four scenarios. A bespoke insurance contract pays c million only in scenarios where the original loss exceeds 5.5 million. Using the hedged sample and alpha=0.75 with the ceil(alpha*n) convention, what is the minimum c that makes historical ES no larger than 5 million?金融与交易中等数值题未尝试面试订阅5330Incremental VaR From Adding Third DeskDesk A and Desk B have aligned scenario losses A=[1, 3, 2, 5] and B=[1, 1, 3, 1]. A new Desk C with losses [1, 0, 2, 0] is proposed. Historical VaR is computed at alpha=0.75 using the ceil(alpha*n) convention. By how much does portfolio VaR increase after adding Desk C to the existing A+B portfolio?金融与交易中等数值题未尝试面试订阅5331Covariance Contribution Implied By VaR BudgetA Gaussian portfolio uses z=2.0 and has total volatility 0.25. A position currently has weight 0.4, and the risk committee gives it a component VaR budget of 0.08. What covariance contribution (Sigma w) i would exactly exhaust that budget?金融与交易困难数值题未尝试面试订阅5333Missing Marginal VaR From Euler BreakdownA risk report shows total Euler portfolio VaR of 2.4. Desk A contributes 0.7 and Desk B contributes 0.9. Desk C has weight 0.5, and its component VaR is the residual needed to make the Euler contributions sum to total VaR. What marginal VaR must Desk C have?金融与交易困难数值题未尝试面试订阅5334Approximate VaR Change From RebalanceA portfolio manager plans two trades and uses a local Euler approximation for total VaR. She sells 0.30 of a crowded factor sleeve whose marginal VaR is 0.26 per unit weight, and buys 0.20 of a hedge sleeve whose marginal VaR is -0.10 per unit weight. What is the approximate change in total portfolio VaR from the rebalance?金融与交易困难数值题未尝试面试订阅5336Portfolio VaR Below Sum Of Desk VaRsAt the daily risk meeting, the CRO notes that the standalone historical VaRs of three desks add up to 42 million, but the portfolio historical VaR comes out to only 31 million after a new basis book was added. What is the most likely explanation, and what is one concrete systems check you should run before trusting that diversification effect?金融与交易困难essay未尝试面试订阅5338Date-Shifted Scenario VectorsDesk A is shocked on yesterday's historical scenario set, while Desk B is revalued on the same market moves but shifted forward by one calendar day because of a loader bug. The risk engine still adds the two P/L vectors and reports a portfolio historical VaR. What exactly is wrong with that number, and what is the correct fix?金融与交易困难essay未尝试面试订阅5339Component ES Rises While Total ES Is FlatA portfolio's total expected shortfall stays flat at 25 million over the week, but the credit sleeve's component ES rises from 4 million to 9 million. Why is that still an actionable warning, and what should the portfolio manager ask for next before deciding whether to cut risk?金融与交易困难essay未尝试面试订阅5340Why Sqrt-Time Scaling Fails In A Liquidity EventDuring a liquidity event, a desk estimates 10-day VaR by taking one-day VaR times sqrt(10) for a book of gap-prone options and crowded cash bonds. Why is that unsafe here, and what is a more defensible check to run instead?金融与交易困难essay未尝试面试订阅5343Kelly Fraction With Two Loss SizesA repeatable trade stakes a fraction f of capital each round. With probability 0.50 the staked amount gains 100%, with probability 0.30 it loses 50%, and with probability 0.20 it loses 100%. Ignoring leverage caps, what full-Kelly fraction f maximizes expected log growth?金融与交易简单数值题未尝试面试订阅5344Kelly Fraction With Two Upside StatesA repeatable trade stakes a fraction f of capital each round. With probability 0.30 the staked amount gains 200%, with probability 0.30 it gains 50%, and with probability 0.40 it loses 100%. Ignoring leverage caps, what full-Kelly fraction f maximizes expected log growth?金融与交易简单数值题未尝试面试订阅5346Implied Edge From Kelly Target 1A trader says the full-Kelly size for a trade with net odds 1 should be 0.1 of capital. What win probability estimate is consistent with that statement?金融与交易中等数值题未尝试面试订阅5347Implied Edge From Kelly Target 2A trader says the full-Kelly size for a trade with net odds 1.5 should be 0.18 of capital. What win probability estimate is consistent with that statement?金融与交易中等数值题未尝试面试订阅5351Compare Kelly Allocations 1Trade A wins net 1.1 with probability 0.57. Trade B wins net 2 with probability 0.41. Compute both full-Kelly fractions and identify which trade gets the larger capital fraction if you size them separately.金融与交易中等数值题未尝试面试订阅5352Compare Kelly Allocations 2Trade A wins net 0.9 with probability 0.62. Trade B wins net 3.2 with probability 0.34. Compute both full-Kelly fractions and identify which trade gets the larger capital fraction if you size them separately.金融与交易中等数值题未尝试面试订阅5356Kelly After Trading Frictions 1A trade risks 1 unit. If it wins, it earns gross 1.2 but pays a fee of 0.05. If it loses, it loses the 1 unit and still pays the same fee. The win probability estimate is 0.56. What full-Kelly fraction is optimal?金融与交易困难数值题未尝试面试订阅5357Kelly After Trading Frictions 2A trade risks 1 unit. If it wins, it earns gross 2 but pays a fee of 0.03. If it loses, it loses the 1 unit and still pays the same fee. The win probability estimate is 0.48. What full-Kelly fraction is optimal?金融与交易困难数值题未尝试面试订阅5361Why Overbetting Hurts More Than UnderbettingWhy is betting above full Kelly usually worse for long-run growth than betting the same distance below full Kelly?金融与交易中等essay未尝试面试订阅