portfolio math

Question 1

expected value of the portfolio return

Answer 1

weighted average of each returns

Question 2

portfolio variance

Answer 2

matrix of covariance (notatki)

weightened sum of 3 variances and 6 covariances (or 3 uniqe covariances *2)

Question 3

covariance

Answer 3

0 = ads no risk
>0 add risk
<0 reduce risk
to the portfolio

cov is positive when on the same side of their expected value at the same time

Question 4

covariance matrix of the portfolio

Answer 4

macierz kowariancji między składowymi portfela (po przekątnych wariancje)

n securities
n = variances
n^2-n = covariances
(N^2-n)/2 = distinct covariances

when we want to use decimal instead of % we need to podzielić over 10000 not 100

Question 5

correlation

Answer 5

cov/dev1*dev2

Question 6

cov of portfolio based on probability (joint probability)

Answer 6

tak jak wzór na cov ale każdy składnik sumy należy pomnożyć przez joint probability 1/(1-n) weights zamiast dzielić przez n-1.

expected value is the mean in this case

Question 7

safety first rules

Answer 7

focus on shortfall risk. the risk of the portfolio decrease under some certain value

Question 8

Safety first ratio

Answer 8

SFRatio =(E(rp)-Rl)/dev

Rl - minimun value (%)

we want to maximize that ratio

the distance betwee n the mean and shortfall level