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4417Expanding Window Final Training Length 2An expanding-window walk-forward starts with 18 months of training, then uses a 1-month embargo and a 4-month test block, advancing by 4 months each round across 59 months of history. What is the training-window length in the last complete fold?机器学习简单数值题未尝试面试订阅4418Embargo Budget Across Folds 3A walk-forward backtest produces 7 complete folds, and the research protocol inserts a 3-day embargo between each training block and its following test block. How many calendar days are lost to embargo across the whole run?机器学习简单数值题未尝试面试订阅4419Average Training Length Under Expansion 4An expanding walk-forward starts with 12 months of training and then advances by 6 months for each of 5 complete test folds. What is the average training-window length used across the 5 folds?机器学习简单数值题未尝试面试订阅4420Latest Label-Safe Training Day 5A test block starts on day 121. Training labels are 5-day forward returns, and you also impose a 2-day embargo immediately before the test block. What is the latest training day whose full forward label still remains valid?机器学习简单数值题未尝试面试订阅4441Fee-Adjusted Composite Alpha 1A desk forms a composite alpha A = 0.6 A fast + 0.4 A slow. The expected gross daily alpha of A fast is 8 bps and of A slow is 5 bps. Their daily turnover is 90% and 20%, and every 1% of turnover costs 0.02 bps. What is the composite's expected net daily alpha?机器学习中等数值题未尝试面试订阅4442Implied Correlation From Composite Vol 2Two standardized signals are combined as C = 0.5 S1 + 0.5 S2. Their standard deviations are 1.2 and 0.8, and the composite standard deviation is observed to be 0.9. What correlation between S1 and S2 is implied?机器学习中等数值题未尝试面试订阅4443Orthogonalized Fast Signal Coefficient 3A fast signal F has standard deviation 1.5 and a slow signal S has standard deviation 1.0. Their correlation is 0.4. If you orthogonalize the fast signal as F res = F - beta*S so that F res is uncorrelated with S, what beta should you use?机器学习中等数值题未尝试面试订阅4444Beta-Neutral Blend Weight 4A fast signal book has market beta 0.8 and a slow signal book has market beta -0.4. You form C = w*fast + (1-w)*slow and want the composite beta to be 0. What weight w on the fast book achieves that?机器学习中等数值题未尝试面试订阅4445Equal-Weight Signal-To-Return Correlation 5Signals S1 and S2 are both standardized. Their correlations with next-period return R are 0.12 and 0.08, and Corr(S1,S2)=0.2. If you form C = 0.5 S1 + 0.5 S2, what is Corr(C,R)?机器学习中等数值题未尝试面试订阅4466Risk-Neutral Probability And No-Arbitrage 1In a one-period binomial model, S0=100, Su=120, Sd=90, and the simple risk-free rate is 0. Compute the risk-neutral probability of the up state, and state whether the no-arbitrage condition holds.数理金融简单数值题未尝试面试订阅4467Risk-Neutral Probability And No-Arbitrage 2In a one-period binomial model, S0=50, Su=65, Sd=45, and the simple risk-free rate is 0.05. Compute the risk-neutral probability of the up state, and state whether the no-arbitrage condition holds.数理金融简单数值题未尝试面试订阅4471State-Price Density Solve 1A stock and bond trade in a one-period two-state model with S0=100, Su=120, Sd=80, and gross risk-free return 1. Solve for the state-price densities λu and λd.数理金融中等数值题未尝试面试订阅4472State-Price Density Solve 2A stock and bond trade in a one-period two-state model with S0=50, Su=62, Sd=42, and gross risk-free return 1.02. Solve for the state-price densities λu and λd.数理金融中等数值题未尝试面试订阅4492Free Dimension of EMM Family in a 4-State Rank-3 MarketA finite-state market has 4 states and traded payoff span rank 3. Assuming no arbitrage and strict positivity are otherwise satisfied, how many free parameters remain in the equivalent martingale measure family, and is the martingale measure unique?数理金融简单数值题未尝试面试订阅4496Span-Restoring Asset Choice 6In a three-state market, the currently traded payoffs are cash [1,1,1] and stock [80,100,120]. Which candidate extra payoff would actually make the market complete: A=[1,1,1], B=[0,1,0], or C=[2,2.5,3]?数理金融中等数值题未尝试面试订阅4497How Many New Independent Payoffs Are Needed in a 5-State Rank-2 Market?A market has 5 states and current traded-payoff rank 2. How many additional independent payoff directions are needed to make the market complete?数理金融中等数值题未尝试面试订阅4499One New Direction Added to a 7-State Rank-5 MarketA market has 7 states and current traded-payoff rank 5. A newly listed asset is known to add one genuinely independent payoff direction. After adding it, how many more independent payoff directions are still needed to make the market complete?数理金融中等数值题未尝试面试订阅4501Claim Price Interval From State-Price Family 11A family of state-price vectors is pi(lambda) = (0.25+lambda, 0.50-2lambda, 0.20+lambda) with lambda constrained to [0, 0.05]. For the claim payoff (0,1,3), what arbitrage-free price interval does the family imply?数理金融中等数值题未尝试面试订阅4526Equity Participation With a Put CushionA payoff gives 90% of the stock value at maturity and, if the stock finishes below 100, adds 30% of the shortfall from 100. Describe a static replication with simple building blocks.数理金融中等essay未尝试面试订阅4527Two-Ramp Corridor PayoffA payoff is zero below 95, rises one-for-one with S T between 95 and 110, stays flat between 110 and 135, and then resumes rising one-for-one above 135. What static option portfolio replicates it?数理金融中等essay未尝试面试订阅