Quantiative Methods - 3.3 - Portfolio Variance, Bayes and Counting Problems

Question 1

what is covariance a measure of? how is it defined?

Answer 1

how 2 assets move together

- expected value of the product of the deviations of the two random variables from their respective expected values

Question 2

what are the 4 properties of covariance?

Answer 2

• The covariance of a random variable with itself is its variance of RA; that is, Cov(RA,RA) = Var(RA)
• Covariance may range from negative infinity to positive infinity
• A positive covariance indicates that when one random variable is above its mean, the other random variable tends to be above its mean as well

A negative covariance indicates that when one random variable is above its mean, the other random variable tends to be below its mean

Question 3

what shows the covariances between returns on a group of assets?

Answer 3

covariance matrix

Question 4

does the covariance between the returns on two assets depend on order?

Answer 4

no - Cov(RA,RB) = Cov(RB,RA)

Question 5

in a covariance matrix, what can generally be said about the number of variance and unique covariance terms?

Answer 5

In general for n assets, there are n variance terms (on the diagonal) and n(n – 1)/2 unique covariance terms.

Question 6

which components make up the calculation for portfolio variance?

Answer 6

asset weights, returns variances and returns covariances

Question 7

the lower the covariance terms, the lower the what?

Answer 7

portfolio variance and standard deviation

Question 8

when is Bayes formula used?

Answer 8

to update a given set of prior probabilities for a given event in response to the arrival of new information

Question 9

what does labeling refer to?

Answer 9

the situation where there are n items that can each receive one of k different labels

Question 10

when can we use the combination (binomial) formula?

Answer 10

when k=2 (number of labels)

Question 11

what is the difference between the combination and permutation formulas?

Answer 11

combination (AKA binomial) - when order doesn’t matter

permutation - when order matters

Question 12

what are the 5 guidelines used to determine which counting method to employ when dealing with counting problems?

Answer 12

• the multiplication rule is used when there are 2 or more groups. Only 1 item may be selected from each group
• factorial is used by itself when there are no groups
• labelling formula applies to three or more subgroups of predetermined size
• combination formula applies to only two groups of predetermined size (look for words like choose or combination)
• permutation formula applies to only two groups of predetermined size (when order matters)