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C_M_ · 2024年11月06日

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

上一题的surplus at risk跟这题的surplus value是不一样的对吗 surplus at risk用的是expected surplus growth（增量)去计算，surplus value用的是expected surplus？这样理解对吗

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1 个答案

李坏_品职助教 · 2024年11月07日

嗨，爱思考的PZer你好：


对，这两个问题的计算是不一样的。 surplus at risk是用增量数据算的，而surplus value是截面数据，用expected surplus计算。

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