Quantitative Methods III

Question 1

Empirical probability, a priori and subjective

Answer 1

Empirical: past observations

A priori: using formal reasoning and inspection

Subjective: personal judgment

Question 2

Odds

Answer 2

Probability / (1 - probability)

Question 3

Multiplication rule P(AB)

Answer 3

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

Prob of A&B = prob of A given B * prob of B

Question 4

Addition rule P(A or B)

Answer 4

P(A or B) = P(A) + P(B) - P(AB)

Probability that at least one of the two events occur

If A & B are mutually exclusive P(AB) = 0

Question 5

Joint probability of independent events P(A and B)

Answer 5

P(A and B) = P(A) * P(B)

Think dice

Question 6

Expected value

Answer 6

Weighted average of the possible outcomes, where weights are probabilities of occurrence.

Question 7

Expected standard deviation and variance

Answer 7

Probability weighted standard deviation where Xbar = expected return.

Sum[Wi * (Xi - Xbar)^2…] / n

Question 8

Covariance

Answer 8

Sum[probability(Rx,Ry) * ((Rx - E(Rx)) * (Ry - E(Ry))]

How two assets move together

Question 9

Correlation

Answer 9

Cov(X,Y) / [stdev(x) * stdev(y)]

Measures strength of linear correlation

Has no units

Question 10

Portfolio expected return

Answer 10

E(Rp) = Sum[WiE(Ri) + … WnE(Rn)]

Question 11

Portfolio expected variance

Answer 11

Var(Rp) = Sum[Sum[WiWjCov(Ri,Rj)]]

Question 12

Bayes formula

Answer 12

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

Used to update prob given prior probs

Check out page 219 example

Question 13

Combination formula (factorial)

Answer 13

N! / [(n-r)! * r!]

R = number of items in group

N = number of total items

Question 14

Permutation formula (factorial)

Answer 14

N! / (n-r)!

How many different groups of size r in specific order can be chosen from n objects

Order matters

Question 15

How many combinations of 5 kids from a group of 15?

Answer 15

5! / [(15 - 5)! * 5!]

Question 16

How many permutations of 3 letters from the alphabet?

Answer 16

26! (26 - 3)!