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1884Displayed Capacity Bias from Missing ClosuresA live database shows 28 small-capacity funds and 42 large-capacity funds. Survival rates for those groups were 40% and 70%, respectively. Suppose small-capacity funds average 1.0 billion of capacity and large-capacity funds average 3.0 billion. By how much does the displayed live-panel average capacity overstate the original launch-universe average capacity?统计中等essay未尝试面试订阅1885Hidden Capacity UnderstatementAmong currently live funds, 18 are low-capacity and 12 are high-capacity. Their survival rates were 90% and 30%, respectively. Suppose low-capacity funds average 0.5 billion of capacity and high-capacity funds average 2.5 billion. By how much does the displayed live-panel average capacity understate the original launch-universe average capacity?统计中等essay未尝试面试订阅1890Global Survival Rate from a Skewed Launch MixAt launch there were twice as many regional funds as global funds. Today, 18 regional funds and 18 global funds remain live. If the regional-fund survival rate was 45%, what was the global-fund survival rate?统计中等essay未尝试面试订阅1891Choose the Least Survivorship-Biased Fund PanelA researcher wants the 2016-2025 average return of all funds launched in 2016. Which data pull is least exposed to survivorship bias? A. Keep only funds that are still alive in 2025, then use their full back history. B. Keep funds alive on each evaluation date, but retroactively delete any fund once it later closes. C. Use a point-in-time panel that keeps every 2016 launch in history until its actual closure date and retains closed funds in the archive. D. Use only funds that are current index constituents in 2025. Give the best choice.统计简单essay未尝试免费1892Unbiased Denominator for Issuer Survival StudyYou want to estimate the default frequency of bonds issued in 2018. Which denominator is the least survivorship-biased? A. Only bonds still outstanding in 2026. B. Only bonds that traded in the last month. C. All bonds issued in 2018, including those that matured or defaulted later. D. Only bonds that are currently eligible for a benchmark index. Give the best choice.统计简单essay未尝试面试订阅1893Sampling Rule for Average Strategy LifetimeA quant team wants to estimate the average lifetime of strategies from launch to shutdown. Which sampling rule is least survivorship-biased? A. Sample only strategies that are live today. B. Sample strategies that were alive at any point after 2024. C. Sample all launched strategies and record each realized shutdown date, including strategies that already died. D. Sample only strategies with at least 36 months of history. Give the best choice.统计简单essay未尝试免费1894Point-in-Time Equity Universe ConstructionFor a monthly equity backtest, which universe construction is least survivorship-biased? A. Use today’s index constituents for the entire historical sample. B. Use monthly historical constituents and keep delisted names in the panel until their actual exit dates. C. Keep only stocks with complete price histories from start to finish. D. Drop delisted names as soon as their prices become noisy near bankruptcy. Give the best choice.统计简单essay未尝试面试订阅1895Better Dataset for Failure-Rate EstimationA vendor offers two hedge-fund datasets. Dataset A contains only funds that are currently reporting, but it includes long backfilled histories for those funds. Dataset B stores monthly reporting snapshots and preserves closed funds in the historical archive. Which dataset is better for estimating historical fund failure rates with minimal survivorship bias?统计简单essay未尝试面试订阅1897First Tradable Session 2A signal becomes public at Wednesday 8:10am 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1899First Tradable Session 4A signal becomes public at Friday 3:55pm ET. A daily strategy may only trade after all input data are known. What is the earliest tradable session?统计中等数值题未尝试免费1902Vendor Lag Alignment 2A vendor distributes a dataset with a fixed 3-business-day lag. If your model key is the Monday file and you trade at the open, what is the first valid trading session that may use that observation?统计中等derivation未尝试免费1903Vendor Lag Alignment 3A vendor distributes a dataset with a fixed 1-business-day lag. If your model key is the Wednesday signal and you trade at the open, what is the first valid trading session that may use that observation?统计中等数值题未尝试面试订阅1905Vendor Lag Alignment 5A vendor distributes a dataset with a fixed 2-business-day lag. If your model key is the Thursday borrow-fee file and you trade at the open, what is the first valid trading session that may use that observation?统计困难essay未尝试面试订阅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1953Mild Positive Skew From Asymmetric Flow 8Order-flow asymmetry is present but not extreme, so the optimal skew should stay close to flat. A market maker chooses a skew x in (-1,1) to maximize G(x) = 7 ln(1+x) + 5 ln(1-x). What skew is optimal?数学中等derivation未尝试免费1960Derive the Optimizer for an Exponential Asymmetry Objective 15For A>0 and B>0, derive the unique minimizer of J(x)=A e x + B e -2x .数学困难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