Learning outcomes: Describe how equity correlations and correlation volatilities behave throughout various economic states. Calculate a mean reversion rate using standard regression and calculate the corresponding autocorrelation. Identify the best-fit distribution for equity, bond, and default correlations.
Questions:
503.1. You ask a junior staffer to review the evidence on equity correlations using as the data set the daily closing prices of the 30 stocks in the Dow Jones Industrial Average (Dow) from January 1972 to October 2012. He reports back the following four summary findings:
I. Equity correlation levels are lowest during economic expansions (growth) and highest during recessions
II. Equity correlation volatility is generally high; i.e., above 70.0% in during growth/normal/recessionary periods
III. There is a general, positive association between correlation level and correlation volatility
IV. Equity correlations exhibit high, strong mean reversion and, therefore, low (positive) auto-correlation
Which is (are) correct?
a. None are correct
b. I. and II.
c. III. and IV.
d. All are correct
503.2. The long-term mean of the correlation data is 35.0%. In January 2014, the averaged correlation of the 30 × 30 Dow correlation matrices was 27.0%. From the regression function from 1972 to 2012, the average mean reversion was 77.5% (this last figure is actually true!). Using the simple s(t) - s(t-1) = alpha*[mu(s) - s(t-1)] = α[μ(s) - s(t-1)] model, what is the expected correlation for February 2014?
a. 27.75%
b. 28.80%
c. 33.20%
d. 37.50%
503.3. Consider the following four statements about the best distributional fit to equity prices, equity correlations, bond correlations, and default probability correlations:
I. Assuming a sharp volatility skew (i.e., continuously decreasing), equity prices are best fit by a lognormal distribution
II. Equity correlations can be fit by a normal or lognormal
III. Bond correlations can be fit by a normal or generalized extreme value (GEV) distribution
IV. Default probability correlations can be fit by a normal or generalized extreme value (GEV) distribution
Which of the above is (are) true?
a. None are true
b. III. only
c. I. and II. only
d. All are true
Answers here:
Questions:
503.1. You ask a junior staffer to review the evidence on equity correlations using as the data set the daily closing prices of the 30 stocks in the Dow Jones Industrial Average (Dow) from January 1972 to October 2012. He reports back the following four summary findings:
I. Equity correlation levels are lowest during economic expansions (growth) and highest during recessions
II. Equity correlation volatility is generally high; i.e., above 70.0% in during growth/normal/recessionary periods
III. There is a general, positive association between correlation level and correlation volatility
IV. Equity correlations exhibit high, strong mean reversion and, therefore, low (positive) auto-correlation
Which is (are) correct?
a. None are correct
b. I. and II.
c. III. and IV.
d. All are correct
503.2. The long-term mean of the correlation data is 35.0%. In January 2014, the averaged correlation of the 30 × 30 Dow correlation matrices was 27.0%. From the regression function from 1972 to 2012, the average mean reversion was 77.5% (this last figure is actually true!). Using the simple s(t) - s(t-1) = alpha*[mu(s) - s(t-1)] = α[μ(s) - s(t-1)] model, what is the expected correlation for February 2014?
a. 27.75%
b. 28.80%
c. 33.20%
d. 37.50%
503.3. Consider the following four statements about the best distributional fit to equity prices, equity correlations, bond correlations, and default probability correlations:
I. Assuming a sharp volatility skew (i.e., continuously decreasing), equity prices are best fit by a lognormal distribution
II. Equity correlations can be fit by a normal or lognormal
III. Bond correlations can be fit by a normal or generalized extreme value (GEV) distribution
IV. Default probability correlations can be fit by a normal or generalized extreme value (GEV) distribution
Which of the above is (are) true?
a. None are true
b. III. only
c. I. and II. only
d. All are true
Answers here:
