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C_M_ · 2024年10月19日

expected surplus

  1. FRM II
  2. Risk Management And Investment Management

NO.PZ2023101902000037

问题如下：

An analyst reports the following fund information to the advisor of a pension fund that currently invests in government and corporate bonds and carries a surplus of USD 10 million.

To evaluate the sufficiency of the fund’s surplus, the advisor estimates the possible surplus values at the end of one year. The advisor assumes that annual returns on assets and the annual growth of the liabilities are jointly normally distributed and their correlation coefficient is 0.8. The advisor can report that, with a confidence level of 95%, the surplus value will be greater than or equal to:

选项：

A.USD -11.4 million

B.USD -8.3 million

C.USD -1.7 million

D.USD 0 million

解释：

The lower bound of the 95% confidence interval is equal to: Expected Surplus – (95% confidence factor × Volatility of Surplus). The required variables can be calculated as follows: Variance of the surplus = 1002 × 10%2 + 902 × 5%2 – 2 × 100 × 90 × 10% × 5% × 0.8 = 48.25 Volatility of the surplus = 6.94 The expected surplus = 9.7 Therefore, the lower bound of the 95% confidence interval = 9.7 – 1.645 × 6.94 = -1.725

​expected surplus不应该是100✘6%-7%✘90吗

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1 个答案

李坏_品职助教 · 2024年10月19日

嗨，从没放弃的小努力你好：


你这个算法不对的。你计算的是资产和负债的增量之差，expected surplus是年终资产 - 年终负债。

Expected surplus = 年末asset - 年末liabilities = 100 * (1+6%) - 90*（1+7%） = 9.7

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