Module 8.3: Portfolio Variance, Bayes, and Counting Problems Flashcards
How do you calculate portfolio variance?
Assume 30% invested in stocks with a standard deviation of 20% and the remainder in bonds with standard deviation of 12%. The correlation of bond returns with stock returns is .6.
How do you calculate standard deviation?
Var(RP) = wa^2*σ^2(Ra) + wb^2σ2(Rb) + 2wawbσ(Ra)σ(Rb)ρ(Ra,Rb)
p = correlation between a and b
=√(0.32)(0.202)+(0.72)(0.122)+2(0.3)(0.7)(0.20)(0.12)(0.60)
Variance = .0167
Standard Deviation = =√0.0167=12.92%
How do you calculate covariance using a joint probability model
Problem will provide a table with probabilities on top and left side.
1) Calculate the expected return by multiplying the joint probability by each return for each asset
2) Multiply the joint probability by the return - expected return for each asset.
What is the Bayes’ formula and when is it used?
Used to update a given set of prior probabilities for a given event in response to the arrival of new information.
updated prob = (prob of new information for a given event / unconditional probability of new information) x prior probability of event.
What is labeling?
Refers to the situation where there are n items that can each receive one of k different labels.
What are the five guidelines that may be used to determine which counting method to use?
1) The multiplication rule of counting is used when there are two or more groups. The key is that only one item may be selected from each group.
2) Factorial is used by itself when there are no groups - we are only arranging a given set of n items.
3) the labeling formula applies to three or more subgroups of predetermined sizes.
4) The combination formula applies to only two groups of predetermined size.
5) the permutation formula applies to only two groups of predetermined size. Look for “order”.
What is the permutation formula?
n! / (n-r)!
What is the combination formula?
n! / (n-r)!r!
What is the formula for Correlation (Ra,Rb)
Cov(Ra,Rb) / (standard deviation(Ra) * standard deviation(rb)
What is the formula for variance of returns?
given covariance and correlation are provided
[Cov(Ra,Rb) /(standard deviation(Rb)Corr(Ra,Rb)]^2
