Empirical Properties of Correlations

Question 1

How correlation levels are during recession, normal period and expansionary period

Answer 1

Correlation in recession> Correlation in normal period> Correlation in expansion

Question 2

How correlation volatilities are during recession, normal period and expansionary period

Answer 2

Correl volatility in normal period>recession>expansionary period

Because, investors are less certain of direction in normal times

Question 3

What is mean reversion

Answer 3

Implies that over time, variables or returns regress back to the mean or average return.

Statistically defined as a negative relationship between the change in a variable over time delta(S(t)-S(t-1)) and the variable in the previous period S(t-1)

Question 4

Mean reversion rate

Answer 4

The degree of the attraction back to the mean and is also referred to as the speed or gravity of mean reversion. (denoted by alpha) is the negative of the beta in the regression equation

Book equation

S(t) - S(t-1) = a*(mu-S(t-1)) X delta(t) + alpha X epsilon X sqrt (delta(t))

What may come on the exam

Expected change in period t = Alpha X (Mean - Value at t-1)

Question 5

How to calculate mean reversion rate

Answer 5

Regression, S(t)-S(t-1) as the Y variable, and S(t01) as the X variable.

The beta coefficient is equal to the negative of the mean reversion rate.

Question 6

What is autocorrelation?

Answer 6

Autocorrelation measures the degree that a current variable value is correlated to past values. Calculated using ARCH or GARCH model.

Alternative is to run a regression.

For one period lag, autocorrelation = cov(correl (t),correl(t-1))/(sigma(correl t) X sigma (correl t-1))

Question 7

Autocorrelation vs mean reversion

Answer 7

Mean reversion measures the tendency to pull away from current value back to the long run mean.

Autocorrelation instead measures the persistence to pull toward more recent historical values.

The sum of mean reversion rate and the one period autocorrelation rate will always equal 1.

Question 8

Best fit distribution for bond correlation

Answer 8

Generalized extreme value distribution (however normal distribution is also a good fit)

Question 9

Johnson SB distribution

Answer 9

Best fit for equity correlations and default probability correlation distributions(two shape parameters, one location parameter and one scale parameter)