LM 4: Probability Trees & Conditional Expectations

Question 1

What is the variance formula (o^2)?

Answer 1

(probability * [return - expected return]^2) + (probability * [return - expected return]^2) + (probability * [return - expected return]^2)

Question 2

What is standard deviation derived from variance?

Answer 2

sqrt variance (o^2) = standard deviation

Question 3

What does E (X) & E (X|S) mean?

Answer 3

E (x) = expected value of random variable

E (X|S) = expected value of x given that scenario S occurs.

Question 4

What is the total probability rule or formula?

Answer 4

E (R) = (E (R | Positive Surprise) * P (Positive Surprise))
+ (E (R | Negative Surprise) * P (Negative Surprise))

(E (R | Positive Surprise) = expected return of portfolio if return is positive surprise

(E (R | Negative Surprise) = expected return of portfolio if return is negative surprise

P (positive surprise) = probability of positive surprise

P (negative surprise) = probability of negative surprise

Question 5

What is Bayes formula?

Answer 5

P (Event | Information) = (P (Information | Event) / P (Information)) * (P (Event))

P (A | B) = ( P( B | A) / P (B)) * (P (A))

Question 6

What is the difference between prior probabilities and posterior probabilities?

Answer 6

prior probabilities = represent the probabilities before the arrival of any new information

posterior probability = reflects the new information