题目741 · 脑筋急转弯
Committee-with-Chair Count 1
From 8 labeled people, how many ordered pairs (committee, chair) are there where the committee has size 3 and the chair is a member of the committee?
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中文题目题目2403 · 机器学习
Variance of a Correlated Five-Model Committee
Five models each have variance 1.6 and pairwise correlation 0.4. What is the variance of their equal-weight average?
打开 →题目5301 · 金融与交易
Alpha After Cash De-Levering
A 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?
打开 →题目3729 · 随机过程
Choosing a Measure for a Risk Limit Based on Worst Expected Shortfall
A risk committee sets a limit based on expected shortfall of actual desk PnL over ten days. Should the underlying probability law be thought of as P or Q?
打开 →题目5331 · 金融与交易
Covariance Contribution Implied By VaR Budget
A Gaussian portfolio uses z=2.0 and has total volatility 0.25. A position currently has weight 0.4, and the risk committee gives it a component VaR budget of 0.08. What covariance contribution (Sigma w)_i would exactly exhaust that budget?
打开 →题目5324 · 金融与交易
Leverage Cap From Two VaR Conventions
A 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
打开 →题目089 · 概率
The Prosecutor's Fallacy
A city has 1,000,000 residents. A crime is committed by one person. The police use a forensic test that has a false positive rate of 1 in 10,000 (i.e., $P(\text{positive} \mid \text{innocent}) = 10^{-4}$) and a true positive rate of 100% ($P(\text{positive} \mid \text{guilty}) =
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