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4116Implementation Shortfall Arithmetic 1A buy order benchmarks performance to the arrival price 24. It fills in slices 30000@24.03, 20000@24.06, and exchange/commission fees are 0.004 dollars per share. What is the implementation shortfall in dollars and in basis points versus arrival?金融与交易中等数值题未尝试面试订阅4117Implementation Shortfall Arithmetic 2A sell order benchmarks performance to the arrival price 51.2. It fills in slices 25000@51.16, 15000@51.1, and exchange/commission fees are 0.003 dollars per share. What is the implementation shortfall in dollars and in basis points versus arrival?金融与交易中等数值题未尝试面试订阅4118Implementation Shortfall Arithmetic 3A buy order benchmarks performance to the arrival price 18.5. It fills in slices 40000@18.52, 10000@18.57, and exchange/commission fees are 0.0025 dollars per share. What is the implementation shortfall in dollars and in basis points versus arrival?金融与交易中等数值题未尝试面试订阅4119Implementation Shortfall Arithmetic 4A sell order benchmarks performance to the arrival price 76. It fills in slices 20000@75.95, 30000@75.9, and exchange/commission fees are 0.005 dollars per share. What is the implementation shortfall in dollars and in basis points versus arrival?金融与交易中等数值题未尝试面试订阅4120Implementation Shortfall Arithmetic 5A buy order benchmarks performance to the arrival price 102.4. It fills in slices 10000@102.46, 15000@102.5, 5000@102.57, and exchange/commission fees are 0.004 dollars per share. What is the implementation shortfall in dollars and in basis points versus arrival?金融与交易中等数值题未尝试面试订阅4121Spread-Impact Decomposition 1A buy slice arrives when the mid is 50. Crossing the spread costs 0.02 dollars per share, temporary impact is 0.03, and permanent impact is estimated at 0.01. What are the expected average fill price and the post-trade mid immediately after the market digests the permanent impact?金融与交易中等数值题未尝试面试订阅4122Spread-Impact Decomposition 2A sell slice arrives when the mid is 32.5. Crossing the spread costs 0.015 dollars per share, temporary impact is 0.025, and permanent impact is estimated at 0.008. What are the expected average fill price and the post-trade mid immediately after the market digests the permanent impact?金融与交易中等数值题未尝试面试订阅4123Spread-Impact Decomposition 3A buy slice arrives when the mid is 80.2. Crossing the spread costs 0.03 dollars per share, temporary impact is 0.04, and permanent impact is estimated at 0.015. What are the expected average fill price and the post-trade mid immediately after the market digests the permanent impact?金融与交易中等数值题未尝试面试订阅4126Square-Root Impact Scaling 1A desk uses a square-root impact rule: cost in bps scales with sqrt(Q/ADV). A trade of 1.00\% of ADV costs 8 bps. What impact cost would the same model predict for a trade of 4.00\% of ADV?金融与交易简单数值题未尝试面试订阅4141Generative Threshold from Equal-Variance Gaussians 1A discriminative model was trained at class prior P(Y=1)=0.5 and outputs posterior probability 0.7 for a case x. Overnight the base rate shifts to P(Y=1)=0.2, while the class-conditional evidence for x is assumed unchanged. What posterior probability should you use after this pure prior shift?机器学习中等数值题未尝试面试订阅4146Naive Bayes Posterior 1A generative regime model assigns posterior probability P(trend|x)=0.7 to the trend regime. If the next-day expected payoff is 12 bps in trend and -4 bps in mean reversion, what conditional expected payoff E[r|x] does the model imply?机器学习中等数值题未尝试面试订阅4148Naive Bayes Posterior 3A generative regime model assigns posterior probability P(trend|x)=0.6 to the trend regime. If the next-day expected payoff is 0.015 return units in trend and -0.01 return units in mean reversion, what conditional expected payoff E[r|x] does the model imply?机器学习中等数值题未尝试面试订阅4149Naive Bayes Posterior 4A generative regime model assigns posterior probability P(trend|x)=0.4 to the trend regime. If the next-day expected payoff is 3 return units in trend and 1 return units in mean reversion, what conditional expected payoff E[r|x] does the model imply?机器学习中等数值题未尝试面试订阅4150Naive Bayes Posterior 5A generative regime model assigns posterior probability P(trend|x)=0.8 to the trend regime. If the next-day expected payoff is -2 bps in trend and 5 bps in mean reversion, what conditional expected payoff E[r|x] does the model imply?机器学习中等数值题未尝试面试订阅4166Centering-and-Scaling Coefficient Rewrite 1A linear model is y = 1.5 + 2 x. You now replace x by the engineered feature z=(x-10)/2. What intercept and slope make the model equivalent when written as y = a + b z?机器学习简单数值题未尝试面试订阅4167Centering-and-Scaling Coefficient Rewrite 2A linear model is y = -0.5 + 1.2 x. You now replace x by the engineered feature z=(x-5)/0.5. What intercept and slope make the model equivalent when written as y = a + b z?机器学习简单数值题未尝试面试订阅4171Marginal Effect with an Interaction Feature 1A model uses engineered interaction terms: y = β0 + 0.8 x1 + β2 x2 + 0.5 x1 x2. What is the marginal effect of x1 when x2 = 2?机器学习中等数值题未尝试面试订阅4172Marginal Effect with an Interaction Feature 2A model uses engineered interaction terms: y = β0 + -0.2 x1 + β2 x2 + 1.2 x1 x2. What is the marginal effect of x1 when x2 = -1?机器学习中等数值题未尝试面试订阅4176Cyclical Time-of-Day Encoding 1A cyclical hour-of-day feature is encoded as (sin(2πh/24), cos(2πh/24)). What is the encoding for h=6?机器学习简单数值题未尝试面试订阅4177One-Hot Plus Interaction Column CountA categorical variable has 5 levels. You one-hot encode it with a dropped baseline, keep one raw numeric feature x, and also create all interactions between x and the retained dummies. How many columns come out of this block in total?机器学习简单数值题未尝试面试订阅