annual volatility

问题如下：

Based on 21 daily returns of an asset, a risk manager estimates the standard deviation of the asset's daily returns to be 2%. Assuming that returns are normally distributed and that there are 260 trading days in a year, what is the appropriate Chi-square test statistic if the risk manager wants to test the null hypothesis that the true annual volatility is 25% at a 5% significance level?

选项：

A.

25.80

B.

33.28

C.

34.94

D.

54.74

解释：

The formula for the Chi-squared test statistic is:

(n - 1)* (sample variance / hypothesis variance)

Since we are given a daily standard deviation, we must first annualize it by multiplying it by the square root of the number of trading days. Therefore:

Sample volatility = sqrt (260) 2% = 32.25%

And the Chi-squared test statistic = (21 - 1)* 0.3225²/0.25² = 33.28