13
5 T
T

1
µ0 = µ0,t ,
T
t=1
µ0,t t
t = 1, . . . , T
1966
R - µ0
S = ,
Ã
" µ0
T
1
" R = Rt Rt
t=1
T
t

2
T
1
" Ã = Rt - R
t=1
T -1
1994 1966
R - µ0
S =
2 .
T
1
Rt - µ0,t - (R - µ0)
t=1
T -1
µ0,t = µ0 t = 1, . . . , T
 1
(0, 1)

T
T
Rt - R Ft - F
RtFt - T R F
t=1
² =
2 = t=1 2 ,
T T
Ft - F Ft2 - T F
t=1 t=1
T
1
" R = Rt Rt
t=1
T
t
T
1
" F = Ft
T t=1
Ft t = 1, . . . , T
t Ft
 " (0, 1)
T -t
pt = t = 0, 1, . . . , T.
T + . . . +  + 1

T
Ft
pt Rt - R - F
t=0

² = ,

T
2
pt Ft - F
t=0
T T


F = ptFt, R = ptRt.
t=0 t=0
 1965
R - µ0
T = ,
²
" µ0
T
1
" R = Rt Rt
t=1
T
t
" ² F
 1968


J = R - µ0 + ² F - µ0 ,
" µ0
T
1
" R = Rt Rt
t=1
T
t
T
1
" F = Ft
t=1
T
Ft t = 1, . . . , T
t Ft
" ² F
J > 0
J < 0
F
µ0 ²
1 - ²

²F + (1 - ²)µ0 = µ0 + ² F - µ0 .
² · ²rynk + (1 - ²) · ²bezryzyk = ² · 1 + (1 - ²) · 0 = ².
 M2
1997
1985
R - µ0
M2 = µ0 - F + · ÃF ,
Ã
" µ0
T
1
" R = Rt Rt
t=1
T
t
T
1
" F = Ft
t=1
T
Ft t = 1, . . . , T
t

2
T
1
" Ã = Rt - R
t=1
T -1

2
T
1
" ÃF = Ft - F F
t=1
T -1
S
M2 = µ0 - F + S · ÃF ,
R - µ0
M2 = µ0 + · ÃF ,
Ã
F
 1994
1980
1981


T

2
1

à = Rt - R .
T - 1
t=1
r


T

2
1

¸(r) = (Rt - r)- ,
T - 1
t=1

Rt - r Rt - r < 0
(Rt - r)- =
0 Rt - r e" 0
(Rt - r)-
Rt - r 0
R - r
Sort = ,
¸(r)
T
1
" R = Rt Rt
t=1
T
t
" r
r 0
µ0 1994
r

2
T
1
" ¸(r) = (Rt - r)-
t=1
T -1


T

2
1

¸ = (Rt - R)- ,
T - 1
t=1
 T
8
t " {1, . . . , T } Cp
Ck
Ck - Cp
Rt = .
Cp
-1 Ck
0
T
R1, R2, . . . , RT
T

1
R = Rt,
T
t=1
8

1
R = Rt,
8
t=1
R1, R2, . . . R8
t " {1, . . . , T }
Cp
Ck
Ck
Rt = ln .
Cp
Ck
0
-"
R1, R2, . . . , RT [1, 2], [2, 3], . . . , [T -1, T ]
[1, T ]
 [1, 2], [2, 3], . . . , [T - 1, T ]

C2 C3 CT C2 C3 CT CT
ln + ln + . . . + ln = ln · · . . . · = ln .
C1 C2 CT -1 C1 C2 CT -1 C1
ln(1 + x) d" x, "
x > -1

Ck Ck - Cp
ln = ln 1 +
Cp Cp
Ck-Cp
" x =
Cp

Ck - Cp Ck - Cp
ln 1 + d" ,
Cp Cp
T
R1, R2, . . . , RT
T

1
R = Rt.
T
t=1


T

1

à = · (Rt - R)2.
T - 1
t=1
 n x
x = (x1, . . . , xn),
xi i
L n
Ki
xi = ,
L
Ki i
Ki = mi · Ci,p,
Ci,p mi i
i = 1, . . . , n
xi
xi
1 i
n L
K1 + . . . + Kn = L
K1 Kn K1 + . . . + Kn L
x1 + . . . + xn = + . . . + = = = 1.
L L L L
i
Ck,i - Cp,i
Ri = ,
Cp,i
Cp,i i
Ck,i
x
L m1, . . . , mn
i
(Ck,i - Cp,i) · mi
(Ck,1 - Cp,1) · m1 + . . . + (Ck,n - Cp,n) · mn
L
(Ck,1 - Cp,1) · m1 + . . . + (Ck,n - Cp,n) · mn R1 · m1 · Cp,1 + . . . + R1 · mn · Cp,n
=
L L
m1 · Cp,1 mn · Cp,n
= R1 · + . . . + Rn · = R1 · x1 + . . . + Rn · xn.
L L
x = (x1, . . . , xn)
Rx = R1 · x1 + . . . + Rn · xn.
 x


n



Ã(x) = xi · xj · Ãi,j,
i,j=1
Ãi,j i j
T

1
Ãi,j = (Ri,t - Ri) · (Rj,t - Rj)
T - 1
t=1
Ri,t i t t = 1, . . . , T
Ri i
T

1
Ri = Ri,t.
T
t=1
x = (x1, . . . , xn)
²1, . . . , ²n
x
²x = ²1 · x1 + . . . + ²n · xn,
Cov(x, xm)
²x = ,
Ã2(xm)
x
xm
x
x
1
x 1
x 1
x 1
x 0
x 0
F1, . . . , FT
1, . . . , T xm
E(xm) = F ,
T

1
F = Ft
T
t=1
"
"
"
"
"
"
"
x
Rx x
Rx = µ0 + ²x · (F - µ0),
µ0 ²x x
F
 T
1, 2, . . . , T x
Rx - Rb
IRx =
T Ex
" Rx x
" Rb
" T Ex x
x x


T

2
1

T Ex = · Rx,t - Rb,t - (Rx - Rb) ,
T - 1
t=1
" Rx,t x t
" Rb,t t
Rx - Rb
" 0, 5 - 0, 75
" 0, 75 - 1
" 1
 n
T
1, 2, . . . , T Cp
t " {1, . . . , T } Ck
Ck - Cp
Rt = .
Cp
T
R1, R2, . . . , RT
R1 + R2 + . . . + RT
R = ,
T


T

1

à = · (Rt - R)2.
T - 1
t=1
n x
x = (x1, . . . , xn),
xi i
xi
xi
1 i
x = (x1, . . . , xn)
Rx = R1 · x1 + . . . + Rn · xn.


n



Ã(x) = xi · xj · Ãi,j,
i,j=1
Ãi,j i j
T

1
Ãi,j = (Ri,t - Ri) · (Rj,t - Rj)
T - 1
t=1
Ri,t i t t = 1, . . . , T
Ri i
Ri,1 + Ri,2 + . . . + Ri,T
Ri = .
T
 x