∗ † ‡
∗
† ‡
Dollar f lowi,t = T N Ai,t− T NAi,t−1(1 + Ri,t) P ercentagef lowi,t= Dollar f lowi,t
T N Ai,t−1
R2
i RAN Kt
5th min(RAN Kt, 0.2) 4th
min(0.2, RAN Kt− bottom performance quintile)
nd 4th
Sharpe ratioi= E[Ri,t− Rft] � V ar[Ri,t− Rft] Ri,t i t Rft t Mi2 = E[Ri,t− Rft] � V ar[Rmt− Rft] � V ar[Ri,t− Rft] Rmt t Sortino ratioi = E[Ri,t− Rft] � SV [Ri,t− Rft]
SV [Ri,t− Rft] = E[(max(Rft− Ri,t, 0))2]
Sharpe M V aRi = E[Ri,t− Rft] M V aR[Ri,t− Rft] M V aR[Ri,t− Rft] = zCF � V ar[Ri,t− Rft] zCF α% zCF = zα− 1 6(z 2 α− 1)S + 1 24(z 3 α− 3zα)K− 1 36(2z 3 α− 5zα)S2 zα α% α = 99% zα = 2.33 α 99% 95.84%
Ri,t− Rft= αi+ βi(Rmt− Rft) + �i,t αi i βi i Rmt t �i,t i t T racking errori= � V ar[�i,t]
One− factor information ratioi =
Jensen alphai T racking errori T reynor ratioi =
E[Ri,t− Rft] βi
Ri,t− Rft= α4Fi + β1,i(Rmt− Rft) + β2,iSM Bt+ β3,iHM Lt+ β4,iW M Lt+ �4Fi,t
α4Fi i SM Bt HM Lt
W M Lt t
F our− factor information ratio = α 4F i �
V ar[�4F i,t]
R2
R2
R2
R2
R2
i RAN Kt
min(RAN Kt, 0.2) min(0.2, RAN Kt− bottom performance quintile)
