QA12 - Measuring Returns, Volatility, and Correlation

Question 1

Calculate, distinguish, and convert between simple and continuously compounded returns

Answer 1

Simple: 1 + R-T = product (1 + Ri)
Continuously: r_t = lnP_t - lnP_(t-1)
Over multiple time periods r_T = sum r_t

To convert: 1 + R_t = exp(r_t)

Question 2

Describe how the first two moments may be insufficient to describe non-normal distributions

Answer 2

Does not describe the skew or kurtosis of the distribution

Question 3

Explain how the Jarque-Bera test is used to determine whether returns are normally distributed

Answer 3

Set H0: S=0 and K=0

JB = (T-1) * (S^2/6 + (k-3)^2/24) ~ chi(2)

Question 4

Describe the power law and its use for non-normal distributions

Answer 4

P(X> x) = kx^(-a) where k,a constants

Have much fatter tails so P decreases a lot more slowly as x increases

Question 5

Define correlation and covariance and differentiate between correlation and dependence

Answer 5

Correlation does not imply dependence