Eksamenssett.no
Ressurser
Skolenytt
Hoderegning
FIN 3600
Formelark
Investering og finansiering
eksamenssett.no
CAPM og avkastningskrav
•
E
(
r
i
)
=
r
f
+
β
i
[
E
(
r
m
)
−
r
f
]
E(r_i) = r_f + \beta_i [E(r_m) - r_f]
E
(
r
i
)
=
r
f
+
β
i
[
E
(
r
m
)
−
r
f
]
(CAPM)
•
β
i
=
Cov
(
r
i
,
r
m
)
Var
(
r
m
)
\displaystyle \beta_i = \frac{\text{Cov}(r_i, r_m)}{\text{Var}(r_m)}
β
i
=
Var
(
r
m
)
Cov
(
r
i
,
r
m
)
•
α
i
=
E
(
r
i
)
−
[
r
f
+
β
i
(
E
(
r
m
)
−
r
f
)
]
\alpha_i = E(r_i) - [r_f + \beta_i(E(r_m) - r_f)]
α
i
=
E
(
r
i
)
−
[
r
f
+
β
i
(
E
(
r
m
)
−
r
f
)]
(Jensens alfa)
•
E
(
r
i
)
−
r
f
=
β
M
K
T
M
R
P
+
β
S
M
B
S
M
B
+
β
H
M
L
H
M
L
E(r_i) - r_f = \beta^{MKT} MRP + \beta^{SMB} SMB + \beta^{HML} HML
E
(
r
i
)
−
r
f
=
β
M
K
T
MRP
+
β
SMB
SMB
+
β
H
M
L
H
M
L
(Fama-French)
Porteføljeteori
•
E
(
r
p
)
=
∑
w
i
E
(
r
i
)
\displaystyle E(r_p) = \sum w_i E(r_i)
E
(
r
p
)
=
∑
w
i
E
(
r
i
)
•
σ
p
2
=
w
1
2
σ
1
2
+
w
2
2
σ
2
2
+
2
w
1
w
2
σ
1
σ
2
ρ
12
\sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \sigma_1 \sigma_2 \rho_{12}
σ
p
2
=
w
1
2
σ
1
2
+
w
2
2
σ
2
2
+
2
w
1
w
2
σ
1
σ
2
ρ
12
•
S
=
E
(
r
p
)
−
r
f
σ
p
\displaystyle S = \frac{E(r_p) - r_f}{\sigma_p}
S
=
σ
p
E
(
r
p
)
−
r
f
(Sharpe-ratio)
•
w
1
∗
=
σ
2
2
−
σ
1
σ
2
ρ
12
σ
1
2
+
σ
2
2
−
2
σ
1
σ
2
ρ
12
\displaystyle w_1^* = \frac{\sigma_2^2 - \sigma_1 \sigma_2 \rho_{12}}{\sigma_1^2 + \sigma_2^2 - 2 \sigma_1 \sigma_2 \rho_{12}}
w
1
∗
=
σ
1
2
+
σ
2
2
−
2
σ
1
σ
2
ρ
12
σ
2
2
−
σ
1
σ
2
ρ
12
(min. varians)
Opsjoner
•
C
=
S
0
N
(
d
1
)
−
K
e
−
r
T
N
(
d
2
)
C = S_0 N(d_1) - K e^{-rT} N(d_2)
C
=
S
0
N
(
d
1
)
−
K
e
−
r
T
N
(
d
2
)
(Black-Scholes call)
•
d
1
=
ln
(
S
0
/
K
)
+
(
r
+
σ
2
/
2
)
T
σ
T
,
d
2
=
d
1
−
σ
T
\displaystyle d_1 = \frac{\ln(S_0/K) + (r + \sigma^2/2)T}{\sigma\sqrt{T}}, \quad d_2 = d_1 - \sigma\sqrt{T}
d
1
=
σ
T
ln
(
S
0
/
K
)
+
(
r
+
σ
2
/2
)
T
,
d
2
=
d
1
−
σ
T
•
C
+
K
e
−
r
T
=
P
+
S
0
C + K e^{-rT} = P + S_0
C
+
K
e
−
r
T
=
P
+
S
0
(put-call-paritet)
•
p
=
e
r
T
−
d
u
−
d
\displaystyle p = \frac{e^{rT} - d}{u - d}
p
=
u
−
d
e
r
T
−
d
(binomisk risikonøytral sannsynlighet)
•
C
T
=
max
(
S
T
−
K
,
0
)
C_T = \max(S_T - K, 0)
C
T
=
max
(
S
T
−
K
,
0
)
,
P
T
=
max
(
K
−
S
T
,
0
)
P_T = \max(K - S_T, 0)
P
T
=
max
(
K
−
S
T
,
0
)
(innløsningsverdi)
Obligasjoner
•
P
=
C
⋅
1
−
(
1
+
y
)
−
n
y
+
F
(
1
+
y
)
n
\displaystyle P = C \cdot \frac{1-(1+y)^{-n}}{y} + \frac{F}{(1+y)^n}
P
=
C
⋅
y
1
−
(
1
+
y
)
−
n
+
(
1
+
y
)
n
F
•
D
Mac
=
1
P
∑
t
⋅
C
F
t
(
1
+
y
)
t
\displaystyle D_{\text{Mac}} = \frac{1}{P} \sum t \cdot \frac{CF_t}{(1+y)^t}
D
Mac
=
P
1
∑
t
⋅
(
1
+
y
)
t
C
F
t
(Macaulay-durasjon)
•
D
∗
=
D
Mac
1
+
y
\displaystyle D^* = \frac{D_{\text{Mac}}}{1+y}
D
∗
=
1
+
y
D
Mac
(modifisert durasjon)
•
Δ
P
P
≈
−
D
∗
Δ
y
+
1
2
Konv
(
Δ
y
)
2
\displaystyle \frac{\Delta P}{P} \approx -D^* \Delta y + \frac{1}{2} \text{Konv} (\Delta y)^2
P
Δ
P
≈
−
D
∗
Δ
y
+
2
1
Konv
(
Δ
y
)
2
Kapitalstruktur
•
V
L
=
V
U
+
T
c
⋅
D
V_L = V_U + T_c \cdot D
V
L
=
V
U
+
T
c
⋅
D
(MM Prop. I med skatt)
•
r
E
=
r
0
+
(
r
0
−
r
D
)
(
1
−
T
c
)
D
E
\displaystyle r_E = r_0 + (r_0 - r_D)(1-T_c) \frac{D}{E}
r
E
=
r
0
+
(
r
0
−
r
D
)
(
1
−
T
c
)
E
D
(MM Prop. II med skatt)
•
W
A
C
C
=
E
V
r
E
+
D
V
r
D
(
1
−
T
c
)
\displaystyle WACC = \frac{E}{V} r_E + \frac{D}{V} r_D (1-T_c)
W
A
CC
=
V
E
r
E
+
V
D
r
D
(
1
−
T
c
)
Verdsettelse
•
V
0
=
∑
t
=
1
n
F
C
F
t
(
1
+
W
A
C
C
)
t
+
T
V
n
(
1
+
W
A
C
C
)
n
\displaystyle V_0 = \sum_{t=1}^{n} \frac{FCF_t}{(1+WACC)^t} + \frac{TV_n}{(1+WACC)^n}
V
0
=
t
=
1
∑
n
(
1
+
W
A
CC
)
t
FC
F
t
+
(
1
+
W
A
CC
)
n
T
V
n
(DCF)
•
T
V
n
=
F
C
F
n
+
1
W
A
C
C
−
g
\displaystyle TV_n = \frac{FCF_{n+1}}{WACC - g}
T
V
n
=
W
A
CC
−
g
FC
F
n
+
1
(Gordons vekstformel for terminalverdi)
•
P
0
=
D
1
r
E
−
g
\displaystyle P_0 = \frac{D_1}{r_E - g}
P
0
=
r
E
−
g
D
1
(Gordons dividendemodell)
•
EK-verdi
=
V
0
−
Netto gjeld
\text{EK-verdi} = V_0 - \text{Netto gjeld}
EK-verdi
=
V
0
−
Netto gjeld
Fusjoner og oppkjøp
•
Synergi
=
V
A
B
−
(
V
A
+
V
B
)
\text{Synergi} = V_{AB} - (V_A + V_B)
Synergi
=
V
A
B
−
(
V
A
+
V
B
)
•
Netto verdiskaping
=
Synergi
−
Premie
\text{Netto verdiskaping} = \text{Synergi} - \text{Premie}
Netto verdiskaping
=
Synergi
−
Premie
•
Premie
=
Tilbudspris
−
Markedsverdi
m
a
˚
l
\text{Premie} = \text{Tilbudspris} - \text{Markedsverdi}_{mål}
Premie
=
Tilbudspris
−
Markedsverdi
m
a
˚
l