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In estimating correlation matrices, risk managers often assume an underlying distribution for the correlations. Which of the following statements most accurately describes the best fit distributions for equity correlation distributions, bond correlation distributions, and default probability correlation distributions?
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The best fit distribution for the equity, bond, and default probability correlation distributions, respectively are:
A) Lognormal, generalized extreme value, and normal.
B) Johnson SB, generalized extreme value, and Johnson SB.
C) Beta, normal, and beta.
D) Johnson SB, normal, and beta.
答案：B
解析：Equity correlation distributions and default probability correlation distributions are best fit with the Johnson SB distribution. Bond correlation distributions are best fit with the generalized extreme value distribution.
Arisk manager uses the past 480 months of correlation data from the Dow Jones
Industrial Average (Dow) to estimate the long-run mean correlation of common
stocks and the mean reversion rate. Based on historical data, the long-run mean
correlation of Dow stocks was 32%, and the regression output estimates the
following regression relationship: Y = 0.215 – 0.75X. Suppose that inApril 2014,
the average monthly correlation for all Dow stocks was 36%. What is the expected
correlation for May 2014 assuming the mean reversion rate estimated in the
regression analysis?
A) 32%
B) 33%
C) 35%
D) 37%
答案：B
解析：There is a -4% difference from the long-run mean correlation andApril 2014 correlation (32% - 36% = -4%). The inverse of theβcoefficient in the regression relationship implies a mean reversion rate of 75%. Thus, the expected correlation for May 2014 is 33%: St = 0.75(32%–36 %) 0.36 = 0.33
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