Module 8.2: Conditional Expectations, Correlation Flashcards
What is an independent event and dependent event?
An independent event is when the P(A | B) = P(A)
If this condition is not satisfied then the events are dependent.
Good examples of independent events are dice rolls and coin flips
What is the total probability rule and how can it be used to calculate an unconditional probability:
The total probability rule highlights the relationship between unconditional and conditional probabilities of mutually exclusive and exhaustive events.
P(R) = P(R | I) × P(I) + P(R | not I ) × P(not I)
What is the expected value of a random variable?
The weighted average of the possible outcomes for the variable (given probabilities and outcomes).
How can conditional expectation be used in an investment application?
It can be used in an investment application by using the total probability rule and estimating the expected return on the stock as the sum of the expected return given an event and without the event (tariff for example).
What is Covariance and how is it calculated using the probability model? Walk through the steps:
Covariance is a measure of how two assets move together. It is the expected value of the product of the deviations of the two random variables from their respective expected values.
Cov(Ri,Rj) = probability{[Ri − E(Ri)][Rj − E(Rj)]}
1) Calculate expected return for each stock
2) Calculate Covariance using the formula above
What are the properties of the covariance?
1) The covariance is a general representation of the same concept as variance. That is variance measures how a random variable moves with itself, covariance is how a variable moves with another random variable.
2) The covariance of Ra with itself is equal to the variance of Ra.
3) the covariance may range from negative infinity to positive infinity.
How is covariance calculated using historical data? (i.e sample covariance?)
Formula: (return on x in period t - mean return on x)*(return on y in period t - mean return on y) / (N-1)
What is correlation coefficient? What is the formula?
Correlation = Covariance / product of standard deviations of the random variables
or
Covariance = Correlation * product of the standard deviations of the two variables
What are the 6 properties of correlation?
1) Correlation measures strength of linear relationship
2) Correlation has no units
3) The correlation range is from -1 to +1
4) if correlation = 1, the random variables are perfectly correlated
5) same for -1.
6) if it’s 0 there is no relationship.
What is suprious correlation?
If the correlation that is either the result of chance or present due to changes in both variables over time that is casued by their association with a third variable.
