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张思琪05883 · 2023年06月16日

16.7是怎么出来的

  1. FRM II
  2. Risk Management And Investment Management

NO.PZ2016071602000001

问题如下：

Over the past year, the HIR Fund had a return of 7.8%, while its benchmark, the S&P 500 index, had a return of 7.2%. Over this period, the fund's volatility was 11.3%, while the S&P index's volatility was 10.7% and the fund's TEV was 1.25%. Assume a risk-free rate of 3%. What is the information ratio for the HIR Fund and for how many years must this performance persist to be statistically significant at a 95% confidence level?

选项：

A.

0.480 and approximately 16.7 years

B.

0.425 and approximately 21.3 years

C.

3.840 and approximately 0.2 years

D.

1.200 and approximately 1.9 years

解释：

A is correct. The information ratio is (7.8 — 7.2)/1.25 = 0.48. Statistical significance is achieved when the t-statistic is above the usual value of 1.96. By Equation (29.5), the minimum number of years T for statistical significance is (1.96/IR)2 = 16.7. Note, however, that there is no need to perform the second computation because there is only one correct answer for the IR question.

16.7是怎么出来的

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1 个答案

李坏_品职助教 · 2023年06月16日

嗨，努力学习的PZer你好：


首先 information ratio is (7.8 - 7.2)/1.25 = 0.48，也就是IR=0.48.

然后题目问的是95%的置信度水平，所以t统计量是1.96，所以年数=(1.96/IR)^2 = 16.7


这个知识点在基础班讲义P174：

本题中问的年数，就是N。截图中的公式的t就是1.96，所以σ/√N = α/1.96，N = [1.96 / (α/σ)]^2，这个α/σ就是IR。


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努力的时光都是限量版，加油！

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