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1763Which Proposed Instrument Is More Plausible?You want to estimate the causal effect of quote-update intensity X on realized spread capture Y. Candidate instrument A is a randomized gateway assignment decided by the exchange. Candidate instrument B is same-day order-flow imbalance, which also directly moves spread capture. Which candidate is more plausible as an instrument, and what IV condition fails for the other one?统计中等multi part未尝试面试订阅1765Fixed Effects Still Miss a Moving Stress ChannelPanel fixed effects remove each desk's persistent skill, but an omitted intraday stress variable still changes day by day. Suppose higher stress raises both inventory pressure X and slippage Y within the same desk. After adding desk fixed effects, what confounding channel remains, and in what direction does it bias the within-desk slope on X?统计中等essay未尝试面试订阅1768A Lagged Variable Is Not Automatically a Valid InstrumentSomeone proposes using yesterday's order-flow imbalance as an instrument for today's imbalance in a return-impact regression. Why is this not automatically a valid instrument in financial data?统计中等multi part未尝试面试订阅1786Ridge Effective Degrees of Freedom 1A standardized ridge model has singular-value squares d j 2 = [9, 4, 1] and penalty lambda = 1. What is the effective degrees of freedom tr(S lambda) = sum d j 2/(d j 2+lambda)?统计简单essay未尝试免费1792Why Ridge for Correlated Alpha ClustersA desk has 80 highly correlated alphas that all measure similar value exposure. Why can Ridge be preferable to pure Lasso if the goal is stable prediction rather than sparse interpretation?统计简单essay未尝试免费1793Elastic Net GroupingTwo features are almost duplicates but both are economically meaningful. Why does Elastic Net often behave better than pure Lasso here?统计中等derivation未尝试免费1795Why the One-SE Rule Is ConservativeWhy do practitioners often prefer the one-standard-error rule over the absolute CV minimizer when selecting a regularization parameter?统计困难essay未尝试面试订阅1838AR(1) Forecast Error Variance 3For the AR(1) model X t = phi X (t-1) + e t with phi = 0.5 and Var(e t) = 2.25, what is the h = 4 step forecast error variance?统计中等essay未尝试面试订阅1842ARMA Identification or Simplification 2You observe the diagnostic statement: ACF cuts after lag 1, PACF tails off. What is the correct modeling conclusion?统计中等derivation未尝试面试订阅1896First Tradable Session 1A signal becomes public at Tuesday 4:15pm ET. A daily strategy may only trade after all input data are known. What is the earliest tradable session?统计简单essay未尝试免费1973How the Cheap Book Gets More Size 3In the problem min a x 2 + b y 2 subject to x+y=c, which book gets the larger allocation when a<b, and why?数学中等derivation未尝试免费1976Three-Book Budget Allocation 6Three sleeves have different quadratic slippage penalties but must add up to a fixed total size. Minimize Q(x,y,z) = 1x 2 + 2y 2 + 4z 2 subject to x+y+z = 28.数学简单数值题未尝试免费1982Asymmetric Spread-Constrained Allocation 12The left book is more expensive per unit, so the optimizer cannot simply split the spread evenly. Minimize 2x 2 + 1y 2 + 1z 2 subject to x+y+z=10 and x-z=2.数学简单数值题未尝试免费1986Alpha Maximization on a Unit-Risk Ellipse 16Two sleeves carry different expected edges but must lie on one fixed quadratic risk budget. Maximize 3x + 4y subject to 1x 2 + 1y 2 = 25.数学简单数值题未尝试免费1988How the Optimizer Scales With the Risk Radius 18In max mu 1 x + mu 2 y subject to a x 2 + b y 2 = R 2, how does the optimizer change when R is doubled?数学中等derivation未尝试免费1991Zero Alpha Target Implies Zero Minimum Risk 21If the target alpha level A in mu 1 x + mu 2 y = A is zero, what is the minimum of a x 2 + b y 2?数学中等derivation未尝试免费2000Ridge Needed to Repair Local PnL Curvature 5A research model has a locally non-convex quartic approximation, and risk wants the smallest ridge that fixes it everywhere. A local PnL model is h(q)=q 4-6q 2+lambda q 2. What is the smallest lambda that makes h globally convex?数学困难数值题未尝试免费2375Why the Optimal Control Weight Equals Cov/Var 5Why does the variance-minimizing control weight satisfy b*=Cov(X,Y)/Var(Y)?数学困难derivation未尝试免费2379Variance Formula for an Antithetic Average 9If X and X' have the same variance sigma 2 and correlation rho, what is Var((X+X')/2)?数学中等derivation未尝试面试订阅2385When a Control Variate Can Make Things Worse 15Why can a badly chosen control coefficient increase variance instead of reducing it?数学困难derivation未尝试面试订阅