Module 5

Question 1

most commonly used average in risk management is

Answer 1

the mean

Question 2

state of absolute certainty is

Answer 2

rare in finance

Question 3

The equation for the mean of a discrete random variable is a special case of the

Answer 3

weighted mean, where the outcomes are weighted by their probabilities, and the sum of the weights is equal to one

Question 4

median of a discrete random variable is the value such that

Answer 4

the probability that a value is less than or equal to the median is equal to 50%

Question 5

The same is true for discrete and continuous random variables. The expected value of a random variable is

Answer 5

equal to the mean of the random variable

Question 6

The concept of expectations is also a much more general concept than

Answer 6

the concept of the mean

Question 7

the expectation operator is not multiplicative (true or false)

Answer 7

true

Question 8

In the special case where E[XY] = E[X]E[Y], we say that

Answer 8

X and Y are independent

Question 9

Variance is defined as

Answer 9

the expected value of the difference between the variable and its mean squared

Question 10

square root of variance

Answer 10

the standard deviation

Question 11

Standard deviation v.s. Volatility

Answer 11

Standard deviation is a mathematically precise
term, whereas volatility is a more general concept

Question 12

Adding a constant to a random variable, however, does not alter the standard deviation or the variance (true or false)

Answer 12

true

Question 13

What is the variable Y

Answer 13

will have a mean of zero and a standard deviation of one, and is a standard random variable

Question 14

Adding a constant to a random variable will not change the standard deviation (true or false)

Answer 14

true

Question 15

multiplying a non-mean-zero variable by a constant will change the mean (true or false)

Answer 15

true

Question 16

Covariance is analogous to variance, but instead

Answer 16

of looking at the deviation from the mean of one variable, we are going to look at the relationship between the deviations of two variables

Question 17

multiplying a standard normal variable by a constant and then adding another constant produces

Answer 17

a different result than if we first add and then multiply

Question 18

If the deviations have no discernible relationship

Answer 18

the covariance is zero

Question 19

If the covariance is anything other than zero

Answer 19

then the two sides of this equation cannot be equal

Question 20

In the special case where the covariance between X and Y is zero

Answer 20

the expected value of XY is equal to the expected value of X multiplied by the expected value of Y

Question 21

Closely related to the concept of covariance is

Answer 21

correlation

Question 22

Correlation has the nice property that it varies between

Answer 22

-1 and +1

Question 23

If two variables have a correlation of +1 then

Answer 23

they are perfectly correlated

Question 24

If two variables are highly correlated

Answer 24

it is often the case that one variable causes the other variable, or that both variables share a common underlying driver

Question 25

If the distribution of returns of two assets have the same mean, variance, and skewness but different kurtosis, then

Answer 25

the distribution with the higher kurtosis will tend to have more extreme points, and be considered more risky

Question 26

normal distribution, which has a kurtosis of

Answer 26

3

Question 27

Distributions with positive excess kurtosis are termed

Answer 27

leptokurtotic

Question 28

Distributions with negative excess kurtosis are termed

Answer 28

platykurtotic

Question 29

we can often prove that a particular candidate has the minimum variance among all the potential unbiased estimators. We call an estimator with these properties

Answer 29

the best linear unbiased estimator, or BLUE

Question 30

All of the estimators that we produced in this chapter for the mean, variance, covariance, skewness, and kurtosis are either

Answer 30

BLUE or the ratio of BLUE estimators