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4461Before CombiningBefore combining several signals, what should you check first besides each signal's standalone Sharpe?机器学习中等essay未尝试面试订阅4462Before Optimizing WeightsWhat should you inspect first before trusting an optimizer's exact signal weights?机器学习中等essay未尝试面试订阅4463Before Using Raw ScoresWhat is the first comparability question before blending raw signal scores?机器学习中等essay未尝试面试订阅4464Before Adding Meta-ModelingBefore fitting a meta-model on top of several signals, what is the first data question you should ask?机器学习中等essay未尝试面试订阅4465Before Declaring DiversificationWhat should you check first before saying that adding five more signals makes the ensemble diversified?机器学习中等essay未尝试面试订阅5896Why Half-Kelly Keeps Three-Quarters of the GrowthFor a small-edge repeated bet the expected log-growth is well approximated by the quadratic G(f)\approx f-\tfrac12 2 f 2, where and 2 are the per-round mean and variance of the bet's return. Using this approximation, find the optimal fraction f * and show what fraction of the maximal growth G(f *) is retained by betting half-Kelly, f=f */2.概率中等derivation未尝试面试订阅5897Overbetting to Twice KellyUnder the small-edge approximation G(f)\approx f-\tfrac12 2 f 2 for the expected log-growth of a repeated bet, the growth-optimal fraction is f *= / 2. At what (nonzero) betting fraction does the expected log-growth fall back to zero, and what does this say about the symmetry of growth around f *?概率中等数值题未尝试面试订阅5906How Many Bets Until Loss Is UnlikelyA Kelly bettor on an even-money coin with p=0.6 stakes the optimal fraction f *=0.2 each round. The per-round log-return is +\ln 1.2 with probability 0.6 and \ln 0.8 with probability 0.4, with mean G\approx0.0201 and variance v\approx0.0395. Using Chebyshev's inequality, find a number of rounds n after which the probability of ending below the starting wealth is at most 5\%.概率困难数值题未尝试面试订阅6013Power of a One-Sided Z-TestYou run a one-sided z-test at level alpha = 0.05 (critical value 1.645) for a positive mean edge. The true edge is delta = 3 bp, the per-observation standard deviation is sigma = 8 bp, and you collect n = 64 observations. The power equals Phi(delta*sqrt(n)/sigma - 1.645). Compute the power, using Phi(1.355) approx 0.9123.统计中等数值题未尝试免费6015Track Record to Confirm a SharpeA strategy has a true annualized Sharpe ratio of 0.5. The t-statistic of the mean return over a track record of T years is approximately t = SR * sqrt(T). How many years of returns are needed before the t-statistic reaches 2 (the usual significance bar)?统计中等数值题未尝试免费6035Half-Life of a Mean-Reverting SpreadA residual spread follows X (t+1) = 0.8 X t + epsilon (t+1) with zero-mean shocks. In trading days, what is the half-life of mean reversion, i.e. the horizon h at which the expected residual has decayed to half its current value?统计简单数值题未尝试免费6037Random-Walk Risk Scaling Over a HorizonA price follows a driftless random walk whose daily increments are iid with standard deviation 2 bp. By what multiple does the standard deviation of the cumulative move grow when the horizon increases from 1 day to 9 days?统计简单数值题未尝试免费6040Two-Period Variance Ratio of an AR(1)Returns are generated by a stationary AR(1) with autoregressive coefficient 0.5. The Lo-MacKinlay variance ratio at lag 2 is VR(2) = Var(r t + r (t+1)) / (2 Var(r t)). Compute VR(2) and state whether it signals momentum or mean reversion.统计困难数值题未尝试面试订阅