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1916Look-Ahead Audit Scenario 1A daily factor is z-scored using the full-sample mean and standard deviation before the backtest is run. What is the main problem?统计简单essay未尝试免费1917Look-Ahead Audit Scenario 2A backtest ranks stocks each month using the latest fully restated accounting data available today, even for years long ago. What is wrong with that setup?统计简单essay未尝试免费1918Look-Ahead Audit Scenario 3A research notebook chooses the top decile each day using today's close and then records the same day's close-to-close return as PnL. What is the leak?统计中等essay未尝试面试订阅1919Look-Ahead Audit Scenario 4A training set includes observations whose labels use returns that overlap with the future test window. What should be added to the split procedure?统计中等数值题未尝试面试订阅1920Look-Ahead Audit Scenario 5A PM wants to backfill today's index membership list into the whole historical universe before evaluating a factor. Why is that unsafe?统计困难essay未尝试面试订阅1921Required Observation Count 1A research lead uses the approximation n >= K * sigma 2 / delta 2 with K = 7.84, signal standard deviation 24 bp, and target detectable mean shift 3 bp. What is the minimum integer sample size?统计简单数值题未尝试免费1923Required Observation Count 3A research lead uses the approximation n >= K * sigma 2 / delta 2 with K = 9, signal standard deviation 30 bp, and target detectable mean shift 4 bp. What is the minimum integer sample size?统计中等数值题未尝试免费1926Minimum Detectable Edge 1Using the same approximation n >= K * sigma 2 / delta 2, suppose K = 7.84, sigma = 25 bp, and you can collect only n = 400 observations. What is the smallest detectable mean edge delta, in basis points?统计简单essay未尝试免费1928Minimum Detectable Edge 3Using the same approximation n >= K * sigma 2 / delta 2, suppose K = 9, sigma = 30 bp, and you can collect only n = 900 observations. What is the smallest detectable mean edge delta, in basis points?统计中等数值题未尝试免费1931Effective Sample Under Serial Dependence 1A return series has 240 observations and lag-1 autocorrelation 1/5. Using the heuristic n eff = n * (1-rho)/(1+rho), what is the effective sample size?统计简单essay未尝试免费1936Paired Design Observation Ratio 1Two strategies are tested on the same names and dates, giving correlation 1/5 between their noise terms. Relative to an unpaired comparison with the same marginal variance, by what factor does the paired design reduce required sample size?统计简单数值题未尝试免费1941Power Score Design Choice 1Compare two research designs using the score delta * sqrt(n) / sigma. Design A has delta=4 bp, n=225, sigma=2 bp. Design B has delta=3 bp, n=400, sigma=1 bp. Which design has the larger score?统计简单数值题未尝试免费1948Log Utility Versus Impact Budget 3A portfolio manager sizes one smooth alpha sleeve with a log reward and a quadratic risk surcharge. The desk chooses a scalar exposure x > -1 to maximize F(x) = 12 ln(1+x) - 1 x 2. What exposure x maximizes F?数学中等数值题未尝试免费1950Quarter-Size Utility Balance 5A PM uses a very steep quadratic penalty, so the optimal tilt should stay small even with positive edge. The desk chooses a scalar exposure x > -1 to maximize F(x) = 5 ln(1+x) - 8 x 2. What exposure x maximizes F?数学困难derivation未尝试免费1954Symmetric Flow Implies Flat Skew 9If a market maker maximizes G(x)=a ln(1+x)+a ln(1-x) on x in (-1,1), what skew is optimal?数学中等derivation未尝试免费1962Balanced Exponential Penalties 17A desk minimizes J(x)=6 e x + 3 e -2x . What x is optimal?数学中等derivation未尝试免费1965Derive the Optimizer for a Linear-Softplus Objective 20For 0<m<n, derive the unique maximizer of K(x)=m x - n ln(1+e x).数学困难derivation未尝试免费1969Which Side of Zero Is Optimal in the Linear-Softplus Problem 24For K(x)=m x - n ln(1+e x) with 0<m<n/2, is the unique optimizer positive, zero, or negative?数学中等derivation未尝试免费1980Minimum Risk Needed for a Target Alpha 10A desk wants to minimize a x 2 + b y 2 subject to mu 1 x + mu 2 y = A. What is the minimum achievable value?数学困难derivation未尝试面试订阅1994Spread-Constrained Allocation With Uneven Penalties 24The spread target fixes how far apart the outer books must sit, while the middle book absorbs the rest. Minimize 1x 2 + 2y 2 + 3z 2 subject to x+y+z=11 and x-z=1.数学中等derivation未尝试免费