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5357Kelly After Trading Frictions 2A trade risks 1 unit. If it wins, it earns gross 2 but pays a fee of 0.03. If it loses, it loses the 1 unit and still pays the same fee. The win probability estimate is 0.48. What full-Kelly fraction is optimal?金融与交易困难数值题未尝试面试订阅5361Why Overbetting Hurts More Than UnderbettingWhy is betting above full Kelly usually worse for long-run growth than betting the same distance below full Kelly?金融与交易中等essay未尝试面试订阅5362Why Edge Uncertainty Shrinks SizeEven if your point estimate suggests a positive full-Kelly fraction, why might a real desk still scale down the position materially?金融与交易中等essay未尝试面试订阅5363Same Expected Value Different KellyTwo trades can have similar expected value per dollar risked but very different full-Kelly fractions. Why?金融与交易中等essay未尝试面试订阅5364Why a Leverage Cap BindsWhy can a leverage cap matter even when the theoretical full-Kelly fraction is well below 100% on one trade?金融与交易中等essay未尝试面试订阅5365Why Zero Kelly Can Be CorrectWhat kinds of changes can turn a seemingly attractive trade into a zero-Kelly trade without flipping the raw headline narrative?金融与交易中等essay未尝试面试订阅5366Effective Spread From Trade Price 1The NBBO is 99.98 bid / 100.02 ask, and a buyer-initiated trade prints at 100.015. What is the effective spread in price terms and in basis points of the prevailing midpoint?金融与交易简单数值题未尝试面试订阅5367Effective Spread From Trade Price 2The NBBO is 49.95 bid / 50.05 ask, and a seller-initiated trade prints at 49.97. What is the effective spread in price terms and in basis points of the prevailing midpoint?金融与交易简单数值题未尝试面试订阅5371Realized Spread And Information Cost 1A buy trade occurs at 100.02 when the midpoint is 100. Five seconds later the midpoint is 100.03. What are the effective spread, realized spread, and adverse-selection component?金融与交易中等数值题未尝试面试订阅5372Realized Spread And Information Cost 2A sell trade occurs at 49.96 when the midpoint is 50. Five seconds later the midpoint is 49.94. What are the effective spread, realized spread, and adverse-selection component?金融与交易中等数值题未尝试面试订阅5386Why Narrow Quoted Spread Can Still Be BadWhy can a stock show a narrow quoted spread but still deliver poor execution quality to liquidity takers?金融与交易中等essay未尝试面试订阅5387Why Large-Tick Names Stay WideWhy do large-tick names often sit at the minimum spread for long periods?金融与交易中等essay未尝试面试订阅5388Why Realized Spread ShrinksWhy does realized spread usually fall below effective spread when trades are informationally toxic?金融与交易中等essay未尝试面试订阅5389Why Midpoint Timing MattersWhy can the measured realized spread change materially depending on whether you use the midpoint 1 second later or 30 seconds later?金融与交易中等essay未尝试面试订阅5390Why Price Improvement Is Not EnoughA trade executes inside the NBBO and gets price improvement. Why is that not enough to conclude the trade was cheap?金融与交易中等essay未尝试面试订阅5391Posterior Value After A Buy 1The asset value is either 99 or 101. Prior P(high)=0.45. If the value is high, a buyer arrives with probability 0.8; if the value is low, a buyer arrives with probability 0.25. You observe a buy order. What is the posterior probability that the value is high, and what is the posterior fair value?金融与交易中等数值题未尝试面试订阅5393Posterior Value After A Buy 3The asset value is either 74 or 76.5. Prior P(high)=0.4. If the value is high, a buyer arrives with probability 0.85; if the value is low, a buyer arrives with probability 0.35. You observe a buy order. What is the posterior probability that the value is high, and what is the posterior fair value?金融与交易中等数值题未尝试面试订阅5394Posterior Value After A Buy 4The asset value is either 19.5 or 20.5. Prior P(high)=0.55. If the value is high, a buyer arrives with probability 0.7; if the value is low, a buyer arrives with probability 0.2. You observe a buy order. What is the posterior probability that the value is high, and what is the posterior fair value?金融与交易中等数值题未尝试面试订阅5401Break-Even Spread Under Informed Flow 1Suppose the true value is equally likely to be 99.8 or 100.2. A fraction 0.3 of traders are informed and always trade in the correct direction; the rest are noise traders who buy or sell with equal probability. A dealer posts symmetric quotes around the prior mean. What break-even half-spread, bid, and ask should the dealer use?金融与交易中等数值题未尝试面试订阅5406Spread Under Event Risk 1A dealer currently uses a half-spread of 0.05. Ahead of an event, the informed-trader fraction is estimated at 0.12 and the value jump size at 0.4. In the symmetric informed-flow model, what is the dealer's expected value per trade if the old spread is left unchanged, and how much extra half-spread is needed to get back to break-even?金融与交易中等数值题未尝试面试订阅