Quant - Portfolio Math Flashcards
What risks impact a portfolio’s variance?
- the risk of the individual component assets
- their combined risks together as measured by their covariance
What is the formula for calculating the covariance of all objects within a portfolio?
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.
What is “shortfall risk”?
portfolio value (or portfolio return) falling below some minimum acceptable level over some time horizon
What is Roy’s safety-first criterion?
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.