An analyst at Bergman International Bank has been asked to explain the calculation of VaR for linear derivatives to the newly hired junior analysts. Which of the following statements best describes the calculation of VaR for a linear derivative on the S&P 500 Index? A、For a futures contract, multiply the VaR of the S&P 500 Index by a sensitivity factor reflecting the percent change in the value of the futures contract for a 1% change in the index value. 答案：A 解析：calculate the VaR for a linear derivative: VaRp = ∆ * VaRf The delta in the formula is a sensitivity factor that reflects the change in value of the derivatives contract for a given change in the value of the underlying. “The delta adjustment to the VaR of the underlying asset accounts for the fact that the relative changes in value between the underlying and the derivatives may not be one for one but nevertheless然而 are linear in nature. Note that options are non-linear.“，老师请问引号内这段话要怎么理解

为什么我算出来是1.5094%

John Holt is managing a fixed-income portfolio worth USD 10 million. The duration of the portfolio today is 5.9 years and six months六个月之后 it is expected to be 6.2 years. The 6-month Treasury bond futures contract is trading at USD 98.47. The bond that is expected to be cheapest-to-deliver has a duration of 4.0 years today and an expected duration of 4.8 years at the maturity of the futures contract. How many futures contracts should John short to hedge against changes in interest rates over the next six months? Each futures contract is for the delivery of USD 100,000 face value of bonds. A、157 contracts B、150 contracts C、131 contracts D、125 contracts 答案：C 老师，请问这题为什么要用未来的久期

为什么是1/250,不是1/365？

这种算组合VaR和组合UL的题 是不是都不需考虑weights啊？请解释下原因和哪些组合计算市要考虑的？

这种算组合VaR和组合UL的题 是不是都不需考虑weights啊？请解释下原因和哪些组合计算市要考虑的？

老师，图片中的公式不是说利率上升，期货价格上升吗 但是下面这个题目的答案是利率上升使得期货价格下降 A German housing corporation needs to hedge against rising interest rates. It has chosen to use futures on 10-year German government bonds. Which position in the futures should the corporation take, and why? A、Take a long position in the futures because rising interest rates lead to rising futures prices. B、Take a short position in the futures because rising interest rates lead to rising futures prices. C、Take a short position in the futures because rising interest rates lead to declining futures prices. D、Take a long position in the futures because rising interest rates lead to declining futures prices. 答案：C 解析： Government bond futures decline in value when interest rates rise, so the housing corporation should short futures to hedge against rising interest rates.

It is June 2 and a fund manager with USD 10 million invested in government bonds is concerned that interest rates will be highly volatile over the next three months. The manager decides to use the September Treasury bond futures contract to hedge the value of the portfolio. The current futures price is USD 95.0625. Each contract is for the delivery of USD 100,000 face value of bonds. The duration of the manager’s bond portfolio in three months will be 7.8years. The cheapest-to-deliver bond in the Treasury bond futures contract is expected to have a duration of 8.4 years at maturity of the contract. At the maturity of the Treasury bond futures contract, the duration of the underlying benchmark Treasury bond is nine years. What position should the fund manager undertake to mitigate his interest rate risk exposure? A、Short 94 contracts B、Short 96 contracts C、Short 98 contracts D、Short 105 contracts 答案：C 老师，请问这题标的资产的久期为什么用7.8年，而不用9年呢？

请问这道题中的 tranche of a CMO是什么意思

波动率 是方差还是标准差