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5300Compare Two Stocks Under CAPM Plus AlphaThe risk-free rate is 2.5% and the market expected return is 9.5%. Stock A has beta 1.1 and zero alpha forecast. Stock B has beta 0.4 and a forecast alpha of 1.5%. Under a CAPM-plus-alpha view, which stock has the higher expected return, and by how much?金融与交易中等数值题未尝试面试订阅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5325Four-Day VaR With Positive CarryA linear book has zero-mean 1-day 95% delta-normal VaR of 14.805 million. Starting tomorrow, the desk expects positive carry of 1.2 million per day, and risk reports assume mean scales linearly while volatility scales with sqrt(time). Using z 0.95=1.645, what 4-day VaR should be reported?金融与交易简单数值题未尝试面试订阅5326Historical VaR And ES With Central Hedge DeskThree books are shocked under the same five scenarios. Desk A losses are [2, 5, 1, 4, 3], Desk B losses are [1, 0, 3, 2, 2], and a central hedge desk contributes [-1, 0, -1, 0, -1] where negative numbers mean gains. After aggregating scenario by scenario, what are historical VaR and ES at alpha=0.8 using the ceil(alpha*n) convention?金融与交易中等数值题未尝试面试订阅5333Missing Marginal VaR From Euler BreakdownA risk report shows total Euler portfolio VaR of 2.4. Desk A contributes 0.7 and Desk B contributes 0.9. Desk C has weight 0.5, and its component VaR is the residual needed to make the Euler contributions sum to total VaR. What marginal VaR must Desk C have?金融与交易困难数值题未尝试面试订阅5343Kelly Fraction With Two Loss SizesA repeatable trade stakes a fraction f of capital each round. With probability 0.50 the staked amount gains 100%, with probability 0.30 it loses 50%, and with probability 0.20 it loses 100%. Ignoring leverage caps, what full-Kelly fraction f maximizes expected log growth?金融与交易简单数值题未尝试面试订阅5344Kelly Fraction With Two Upside StatesA repeatable trade stakes a fraction f of capital each round. With probability 0.30 the staked amount gains 200%, with probability 0.30 it gains 50%, and with probability 0.40 it loses 100%. Ignoring leverage caps, what full-Kelly fraction f maximizes expected log growth?金融与交易简单数值题未尝试面试订阅5346Implied Edge From Kelly Target 1A trader says the full-Kelly size for a trade with net odds 1 should be 0.1 of capital. What win probability estimate is consistent with that statement?金融与交易中等数值题未尝试面试订阅5347Implied Edge From Kelly Target 2A trader says the full-Kelly size for a trade with net odds 1.5 should be 0.18 of capital. What win probability estimate is consistent with that statement?金融与交易中等数值题未尝试面试订阅5351Compare Kelly Allocations 1Trade A wins net 1.1 with probability 0.57. Trade B wins net 2 with probability 0.41. Compute both full-Kelly fractions and identify which trade gets the larger capital fraction if you size them separately.金融与交易中等数值题未尝试面试订阅5352Compare Kelly Allocations 2Trade A wins net 0.9 with probability 0.62. Trade B wins net 3.2 with probability 0.34. Compute both full-Kelly fractions and identify which trade gets the larger capital fraction if you size them separately.金融与交易中等数值题未尝试面试订阅