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5301Alpha After Cash De-LeveringA trading sleeve has realized return 12% and market beta 1.4. The risk committee wants the reported beta reduced to exactly 1.0 by parking the rest of the capital in T-bills earning 2%. If the market returned 8%, what alpha will the combined position report relative to CAPM?金融与交易中等数值题未尝试面试订阅5302Market Return Consistent With Zero AlphaA PM says a stock with beta 1.5 and realized return -1% still generated exactly zero alpha this month. If the risk-free rate was 2%, what market return would make that statement true?金融与交易中等数值题未尝试面试订阅5303Benchmark Weight Needed to Zero Out Active Beta 8A manager sleeve has beta 1.25. It is mixed with cash of beta 0. What weight on the manager sleeve makes the overall beta exactly 1?金融与交易中等数值题未尝试面试订阅5304Gross Return Needed For Post-Fee Alpha TargetA PM runs a stock with beta 0.7. After the quarter, a 0.8% fee is deducted from the stock's gross return before alpha is reported. If the risk-free rate is 1.5% and the market returned 5.5%, what gross stock return is needed so the reported post-fee alpha is +1.0%?金融与交易中等数值题未尝试面试订阅5305Directional Sleeve Weight For Target AlphaA portfolio mixes a market-neutral arbitrage sleeve with realized return 4% and beta 0.2, and a directional sleeve with realized return 14% and beta 1.4. Let w be the weight in the directional sleeve and 1-w in the arbitrage sleeve. If the risk-free rate is 2% and the market returned 8%, what value of w makes the combined portfolio alpha exactly 2.2%?金融与交易中等数值题未尝试面试订阅5306Three-Factor Return Attribution 1A portfolio has alpha 0.01, market beta 1.1 with market factor move 0.02, value exposure 0.4 with value-factor move -0.01, and size exposure 0.3 with size-factor move 0.015. What return does this linear factor model attribute to the portfolio?金融与交易中等数值题未尝试面试订阅5307Three-Factor Return Attribution 2A portfolio has alpha 0.005, market beta 0.9 with market factor move 0.015, value exposure -0.2 with value-factor move 0.01, and size exposure 0.2 with size-factor move 0.012. What return does this linear factor model attribute to the portfolio?金融与交易中等数值题未尝试面试订阅5309Three-Factor Return Attribution 4A portfolio has alpha 0.008, market beta 0.7 with market factor move 0.01, value exposure 0.3 with value-factor move 0.005, and size exposure -0.1 with size-factor move 0.011. What return does this linear factor model attribute to the portfolio?金融与交易中等数值题未尝试面试订阅5310Three-Factor Return Attribution 5A portfolio has alpha 0.009, market beta 1 with market factor move 0.017, value exposure -0.4 with value-factor move 0.008, and size exposure 0.25 with size-factor move 0.014. What return does this linear factor model attribute to the portfolio?金融与交易中等数值题未尝试面试订阅5311Why Beta Is Not Total RiskWhy can a stock have a low beta but still be risky in an absolute sense?金融与交易困难essay未尝试面试订阅5312Why Alpha Is FragileWhy can measured alpha disappear once you change the factor model used to benchmark a portfolio?金融与交易困难essay未尝试面试订阅5313Why CAPM Is Still UsedEven though markets are more complex than one-factor CAPM, why is CAPM still used in practice?金融与交易困难essay未尝试面试订阅5314Why Factor Exposures Help HedgingWhy is it often more informative to hedge factor exposures than to hedge names one by one?金融与交易困难essay未尝试面试订阅5315Why Expected Return And Attribution DifferWhy is estimating an expected return from a factor model different from explaining a realized return after the fact?金融与交易困难essay未尝试面试订阅5316NAV Limit From Historical VaR CapA desk uses the historical return window [-0.01, 0.005, -0.03, -0.015, 0.01, -0.025, -0.005, -0.04]. Dollar loss in each scenario is defined as loss = -NAV * return, with NAV measured in millions. Historical VaR is computed at alpha=0.75 using the ceil(alpha*n) order-statistic convention. If the desk's VaR limit is 4 million, what is the largest NAV it may run?金融与交易中等数值题未尝试面试订阅5318Tail Hedge Impact On Historical ESA desk's historical dollar-loss sample in millions is [0.4, 1.1, 1.9, 2.7, 3.2, 3.9, 4.8, 6.3]. It buys a hedge that pays 1.5 million only on days when the unhedged loss exceeds 5.0. Using the hedged loss sample and historical VaR/ES at alpha=0.75 with the ceil(alpha*n) convention, what are VaR and ES?金融与交易中等数值题未尝试面试订阅5321One-Day Sigma Allowed By Five-Day VaR BudgetA linear book is modeled with zero-mean normal PnL. The desk reports 5-day delta-normal VaR at 97.5%, uses z=1.96, and applies square-root-of-time scaling. If the 5-day VaR limit is 30 million, what is the largest 1-day PnL standard deviation the book may run?金融与交易简单数值题未尝试面试订阅5322Maximum Scale Of Second Sleeve Under VaR CapTwo independent sleeves have zero-mean normal daily PnL. Sleeve A has standard deviation 6 million and cannot be changed. Sleeve B has standard deviation 8 million but can be scaled by a factor lambda. Using 1-day 99% delta-normal VaR with z=2.326, what is the largest lambda allowed if total VaR must not exceed 20 million?金融与交易简单数值题未尝试面试订阅5323Expected Carry Needed To Hit VaR TargetA trading book's 1-day PnL is modeled as normal with mean mu and standard deviation 9 million. Risk reports define delta-normal VaR by VaR = z alpha*sigma - mu. If z 0.95=1.645 and the desk wants reported 95% VaR to be exactly 12 million, what daily expected PnL mu is required?金融与交易简单数值题未尝试面试订阅5324Leverage Cap From Two VaR ConventionsA linear book currently has 1-day 97.5% delta-normal VaR of 6 million. The risk committee instead limits 10-day 99% VaR to 25 million and assumes zero mean plus square-root-of-time scaling. If the book is levered by a factor L, what is the largest L allowed? Use z 0.975=1.96 and z 0.99=2.326.金融与交易简单数值题未尝试面试订阅