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4016Minimum-Variance Hedge Ratio 1A spot exposure has volatility 18%, the hedging futures has volatility 24%, and the desired minimum-variance hedge ratio is 0.6. What correlation is implied by h*=rho*sigma S/sigma F?金融与交易中等derivation未尝试面试订阅4017Minimum-Variance Hedge Ratio 2A spot exposure has volatility 30%, correlation 0.75 to the hedging futures, and desired hedge ratio 0.9. What futures volatility is implied?金融与交易中等derivation未尝试面试订阅4018Minimum-Variance Hedge Ratio 3A short hedge ratio of -0.3 is desired. If futures volatility is 20% and correlation is -0.4, what spot volatility is implied?金融与交易中等derivation未尝试面试订阅4021Hedge Contract Count 1A spot exposure of 2000 units is hedged with futures contracts of 100 units each. Spot volatility is 30.00%, futures volatility is 25.00%, and correlation is 0.8. How many futures contracts correspond to the minimum-variance hedge?金融与交易中等derivation未尝试面试订阅4026Beta Hedge Contract Count 1A desk uses 36 futures contracts of size 1000 to hedge a spot exposure of 50000 units. Spot volatility is 24% and futures volatility is 30%. What correlation would make this contract count exactly minimum-variance optimal?金融与交易中等derivation未尝试面试订阅4027Beta Hedge Contract Count 2A desk wants to hedge 4000 spot units with 25 futures contracts of size 200. Spot volatility is 15% and correlation is 0.8. What futures volatility would make that contract count minimum-variance optimal?金融与交易中等derivation未尝试面试订阅4028Contract Size Implied by a Min-Variance Hedge 3A desk hedges a spot exposure of 12,000 units with 40 futures contracts. The spot volatility is 25%, the futures volatility is 20%, and the spot-futures correlation is 0.64. If the desk is using the minimum-variance hedge ratio, what contract size must each futures contract represent?金融与交易中等数值题未尝试面试订阅4030Futures Vol Needed for an Exact Hedge Count 5A desk hedges 6,000 spot units with 30 futures contracts of size 100. Spot volatility is 18% and spot-futures correlation is 0.75. If 30 contracts is exactly the minimum-variance hedge count, what futures volatility is implied?金融与交易中等数值题未尝试面试订阅4031Residual Hedge Variance 1Spot volatility is 20% and correlation to the hedging futures is 0.8. Under the minimum-variance hedge, what residual spot volatility remains?金融与交易中等derivation未尝试面试订阅4033Residual Hedge Variance 3An exposure has unhedged volatility 25%. After applying the minimum-variance hedge, the residual volatility is 15%. What correlation between spot and futures does this imply?金融与交易中等derivation未尝试面试订阅4035Residual Hedge Variance 5Spot volatility is 18%. What minimum absolute correlation |rho| is needed so that the minimum-variance hedge leaves residual volatility no more than 9%?金融与交易中等derivation未尝试面试订阅4036Why a Good Hedge Ratio Is Not Always OneWhy can the minimum-variance hedge ratio exceed 1?金融与交易中等essay未尝试面试订阅4037Why Cross-Hedges Leave Residual RiskWhy can the optimal hedge ratio be negative?金融与交易中等essay未尝试面试订阅4038Why Beta Hedges and Minimum-Variance Hedges Are Not the Same QuestionWhy does a high correlation matter more than a low futures volatility when hedge effectiveness is the goal?金融与交易中等essay未尝试面试订阅4039Why Hedge Effectiveness Is Mostly a Correlation StoryWhy can a hedge that looks perfect in notional terms still leave material basis risk?金融与交易中等essay未尝试面试订阅4040How to Sanity-Check a Hedge-Ratio AnswerWhy might a desk choose not to use the exact minimum-variance hedge ratio even after estimating it carefully?金融与交易中等essay未尝试面试订阅