Quant - Portfolio Math

Question 1

What risks impact a portfolio’s variance?

Answer 1

1. the risk of the individual component assets
2. their combined risks together as measured by their covariance

Question 2

What is the formula for calculating the covariance of all objects within a portfolio?

Answer 2

A formula for computing the covariance between random variables RA and RB, such as the different assets of a portfolio, is

Cov(RA,RB)=∑i∑jP(RA,i,RB,j)(RA,i−ERA)(RB,j−ERB).

The value is derived by summing all possible deviation cross-products weighted by the appropriate joint probability.

Question 3

What is “shortfall risk”?

Answer 3

portfolio value (or portfolio return) falling below some minimum acceptable level over some time horizon

Question 4

What is Roy’s safety-first criterion?

Answer 4

Roy’s safety-first criterion states that the optimal portfolio minimizes the probability that portfolio return, RP, will fall below RL. For a portfolio with a given safety-first ratio (SFratio), the probability that its return will be less than RL is Normal(–SFRatio), and the safety-first optimal portfolio has the lowest such probability.