# P2.T5.22.12. Correlation Properties

#### David Harper CFA FRM

##### David Harper CFA FRM
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Learning objectives: 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:

22.12.1. Albert has retrieved the monthly average correlation for stocks in the Dow Jones Industrial Average (DJIA) index for the last ten years; i.e., each month's ρ(t) is the average of 30*30 pairwise correlation matrix. With this time series of correlation values, he then computes the one-period lag autocorrelation, AC[ρ(t), ρ(t-1)]. So this is an autocorrelation of a time series of correlations.

If Albert's one-period lag autocorrelation value is low, then which of the following is most likely?

a. The regression coefficient is positive
b. The Pearson correlation coefficient is high
c. The mean reversion rate (aka, gravity) is high
d. The volatilities of correlation(t) and correlation(t-1) are low

22.12.2. Meissner conducted a detailed study of equity correlations of the 30 stocks in the Dow (DJIA) over 44.5 years (i.e., the 534 months from January 1972 to July 2017) that generated 534 * 30^2 = 480,600 correlations values. In regard to his empirical findings with respect to equity correlations, each of the following statements is TRUE, except which is false?

a. Mean reversion should be included in equity correlation models
b. For equity correlations, the Johnson SB distribution is better than the normal or lognormal
c. A stressed scenario of bad economic times should incorporate higher correlation levels and higher correlation volatility
d. Autocorrelation is a monotonically increasing function of the monthly lag; i.e., higher lags imply higher autocorrelations

22.12.3. Meissner's introduction of correlation features a detailed study of equity correlations and some history, including the role of correlation in the Global Financial Crisis (GFC) of 2007 to 2009 and the subsequent reaction in Basel III. He argues that "correlations and correlation risk are critical in many areas in finance such as investments, trading and especially risk management, where different correlations result in very different degrees of risk. Correlations also play a key role in a systemic crisis, where correlations typically increase and can lead to high unexpected losses."

Based on Meissner's review, which of the following statements is TRUE?

a. Because stochasticity is non-deterministic, we should avoid stochastic models for correlation
b. Correlation risk is less important in market risk and credit risk but more important in operational risk
c. Companies with high default probabilities who are more affected by idiosyncratic factors and less affected by systematic factors tend to have lower default correlations
d. An increase in default correlations between mortgages in CDOs, ceteris paribus (i.e., holding default probability constant), implies an increase in equity tranche spreads