Equations Flashcards
Total return
(pₜ₊₁/pₜ) - 1
How do you annualise multi-year data?
nth root of data where n is number of years
Annualised return
(1+R)^252/days - 1
How do you annualise risk?
Daily data = σ x √252
Weekly data = σ x √52
Monthly data = σ x √12
Tracking error
Standard deviation of active return (Rₚ - Rb)
Information ratio
Active return/Tracking error
(Rₚ - Rb)/Tracking error
Annual value at risk
Average return - (No of std devs x std dev)
R - (N(σ) x σ)
Annual conditional value at risk
-Get VaR in quarterly basis
-Average quarterly returns below VaR
-[(1+(average)-VaR)⁴]-1
Explain value at risk
The percent of fund value that’s expected to be lost at a given probability level, assuming normal market conditions
Explain conditional value at risk
It is the average of the losses in excess of VaR, and provides the mean loss in the remainder of the distribution tail, starting at VaR. Helps us understand how stretched the left tail of returns may be.
Active share
Sum of absolute weight differences to benchmark over 2
(∑|wf - wb|)/2
Beta
Cov(rᵢ,rₘ)/Var(rₘ)
Sharpe ratio
Excess return/Standard deviation
(Rₚ - Rf)/σ
Treynor ratio
Excess return/Beta
(Rₚ - Rf)/β
Downside deviation
√[1/n(∑(R-t)²)]
t=target
Only look at returns below target (default is 0)
