LM 5: Portfolio Mathematics

Question 1

What is the covariance formula?

Answer 1

correlation * SD1 * SD2

Question 2

What is the formula for portfolio standard deviation given correlation?

Answer 2

SQRT w^2 SD^2 + w^2 SD^2 + 2 w w correlation SD *SD

Question 3

What is the formula for portfolio standard deviation given covariance?

Answer 3

SQRT w^2 SD^2 + w^2 SD^2 + 2 w w covariance

Question 4

In a 2-asset portfolio, what makes up covariance?

Answer 4

correlation * sd1 * sd2

Question 5

Which way do 2 assets move when it’s perfectly positively correlated, perfectly negatively correlated, and uncorrelated?

Answer 5

perfectly positively correlated = move up and down together = +1

perfectly negatively correlated = move in opposite direction = -1

uncorrelated = no relationship = 0

Question 6

What is the safety first ratio (SF Ratio) (aka Roy’s safety first ratio)?

Answer 6

SFRatio = (E (Rp) - RL / op)

E (Rp) = expected return of portfolio
RL = threshold level
op = standard deviation of portfolio

like sharpe ratio just replaces RF with RL

Question 7

What is the probability of the return of a portfolio falling below a threshold formula?

Answer 7

P (Rp < RL) = N (-SFRatio)

(Rp) = expected return of portfolio
RL = threshold level
N = time frame in years