Statistical Foundations

Question 1

Difference between ex-post and ex-ante returns?

Answer 1

Ex-post returns are realized outcomes. Ex-ante returns are expectational.

Question 2

Contrast the kurtosis and excess kurtosis of the normal distribution.

Answer 2

Kurtosis serves as an indicator of the peaks and trails of a distribution.

A normally distributed variable has kurtosis of 3.

Excess kurtosis is equal to kurtosis - 3.

Therefore a normal distribution has an excess kurtosis of 0.

Excess kurtosis is more intuitive because the figure varies around zero.

Question 3

How would a large increase in the kurtosis of a return distribution affect its shape?

Answer 3

higher peaks or fatter tails

Question 4

What is another term for volatility of a return?

Answer 4

standard deviation

Question 5

The covariance between the returns of two financial assets is equal to the product of the standard deviations of the returns of the two assets. What is the primary statistical terminology for this relationship?

Answer 5

The covariance will equal the product of the standard deviations when the correlation coefficient is equal to 1.

Question 6

What is heteroskedasticity

Answer 6

When the variance of a variable changes with respect to a variable

Question 7

What is homoskedasticity

Answer 7

When the variance of a variable is constant

Question 8

What is beta

Answer 8

It is

the covariance of the return in an individual stock and the return on the overall market

over

Variance of the market

Question 9

What is the value of the beta of the following 3 investments: a fund that tracks the overall market index, a riskless asset, a bet at a casino table

Answer 9

1, 0, 0

Question 10

In the case of a financial asset with returns that have zero autocorrelation, what is the relationship between the variance of the asset’s daily returns and the variance of the asset’s monthly return?

Answer 10

Variance of the monthly returns are T times the variance of the daily returns, where T is the number of trading days in the month.

Question 11

In the case of a financial asset with returns that have autocorrelation approaching +1, what is the relationship between the standard deviation of the asset’s monthly returns and the standard deviation of the asset’s annual return?

Answer 11

In the perfectly correlated case the standard deviation of a multiperiod retun is proportional to T. In this case the annual vol is 12 times the monthly volatility.

Question 12

What is autocorrelation

Answer 12

The autocorrelation of a time series of returns from an investment refers to the possible
correlation of the returns with one another through time.

Question 13

What is the general statistical issue addressed when the GARCH method is used in a time series analysis of returns.

Answer 13

The tendency of an asset’s variance to change through time.