Module 5 - Chapter Flashcards
most commonly used average in risk management is
the mean
state of absolute certainty is
rare in finance
The equation for the mean of a discrete random variable is a special case of the
weighted mean, where the outcomes are weighted by their probabilities, and the sum of the weights is equal to one
median of a discrete random variable is the value such that
the probability that a value is less than or equal to the median is equal to 50%
The same is true for discrete and continuous random variables. The expected value of a random variable is
equal to the mean of the random variable
The concept of expectations is also a much more general concept than
the concept of the mean
the expectation operator is not multiplicative (true or false)
true
In the special case where E[XY] = E[X]E[Y], we say that
X and Y are independent
Variance is defined as
the expected value of the difference between the variable and its mean squared
square root of variance
the standard deviation
Standard deviation v.s. Volatility
Standard deviation is a mathematically precise
term, whereas volatility is a more general concept
Adding a constant to a random variable, however, does not alter the standard deviation or the variance (true or false)
true
What is the variable Y
will have a mean of zero and a standard deviation of one, and is a standard random variable
Adding a constant to a random variable will not change the standard deviation (true or false)
true
multiplying a non-mean-zero variable by a constant will change the mean (true or false)
true
Covariance is analogous to variance, but instead
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
multiplying a standard normal variable by a constant and then adding another constant produces
a different result than if we first add and then multiply
If the deviations have no discernible relationship
the covariance is zero
If the covariance is anything other than zero
then the two sides of this equation cannot be equal
In the special case where the covariance between X and Y is zero
the expected value of XY is equal to the expected value of X multiplied by the expected value of Y
Closely related to the concept of covariance is
correlation
Correlation has the nice property that it varies between
-1 and +1
If two variables have a correlation of +1 then
they are perfectly correlated
If two variables are highly correlated
it is often the case that one variable causes the other variable, or that both variables share a common underlying driver
If the distribution of returns of two assets have the same mean, variance, and skewness but different kurtosis, then
the distribution with the higher kurtosis will tend to have more extreme points, and be considered more risky
normal distribution, which has a kurtosis of
3
Distributions with positive excess kurtosis are termed
leptokurtotic
Distributions with negative excess kurtosis are termed
platykurtotic
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
the best linear unbiased estimator, or BLUE
All of the estimators that we produced in this chapter for the mean, variance, covariance, skewness, and kurtosis are either
BLUE or the ratio of BLUE estimators
