Finance Exam Enclosure: Formula Sheet Page 2
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1
2
3
4E[X](1
k)
E[D
]
1
1
E[F
]
T
1
B
= E[C]
+
P
=
=
0
0
T
T
r
r(1 + r)
(1 + r)
r
r k
r
r k
Inflation
Duration (D)
C : nominal cash flow. X : real cash flow. i: inflation. r:
real interest rate. r : nominal interest rate.
T
1
D =
tP V (C
)
t
B
t
0
C
= X
(1 + i)
t=1
t
t
1 + r
T
n
1
tC
r =
1
t
D =
1 + i
t
B
(1 + r)
0
t=1
r
= (1 + r)(1 + i)
1
n
Stock valuation
Statistics
D : dividend at time t. P : Stock price at time t. r: interest
˜ X, ˜ Y , ˜ Z : random variables. a, b, c: constants.
rate. g: growth rate. X earnings. I investment. k retention
ratio. (1
k) payout ratio. r return on new investment
(reinvestment return).
var( ˜ X) = σ
( ˜ X) = E ( ˜ X
E[ ˜ X])
2
2
E[D
]
E[P
]
P
1
1
0
E[r] =
+
SD(X) = σ( ˜ X) =
var( ˜ X)
P
P
0
0
var(a ˜ X) = a
var( ˜ X)
2
E[D
] + E[P
]
1
1
P
=
0
cov( ˜ X, ˜ Y ) = E ( ˜ X
E[ ˜ X])( ˜ Y
E[ ˜ Y ])
1 + r
E[D
]
cov(a, ˜ X) = 0
t
P
=
0
t
(1 + r)
var( ˜ X + ˜ Y ) = var( ˜ X)+2cov( ˜ X, ˜ Y )+var( ˜ Y )
t=1
E[D
]
cov( ˜ X, ˜ Y )
1
P
=
ρ( ˜ X, ˜ Y ) =
0
r
g
σ( ˜ X)σ( ˜ Y )
E[D
]
1
cov( ˜ X + ˜ Y , ˜ Z) = cov( ˜ X, ˜ Z) + cov( ˜ Y , ˜ Z)
r =
+ g
P
0
cov(a, ˜ X) = 0
E[D
]
t
cov(a ˜ X, b ˜ Y ) = a b cov( ˜ X, ˜ Y )
P
=
0
t
(1 + r)
t=1
cov( ˜ X, ˜ Y )
= corr( ˜ X, ˜ Y ) =
ρ
D
= X
I
X,Y
t
t
t
σ( ˜ X)σ( ˜ Y )
E[X
]
E[I
]
Portfolio theory in mean variance set-
t
t
P
=
0
ting
t
(1 + r)
t=1
˜ r : (random) return on asset i. ω : (constant) weight on
asset i. σ : covariance of returns of assets i and j.
P
= Value assets in place
0
+ PV Growth opportunities
N
˜ r
=
ω
˜ r
p
j
j
E[X]
j=1
Assets in place =
r
cov(˜ r
, ˜ r
)
i
m
(r
r)kE[X]
β
=
i
P V GO =
var(˜ r
)
m
r(r
r k)
N
E[X]
kE[X](r
r)
β
=
ω
β
p
j
j
P
=
+
0
r
r(r
r k)
j=1
2
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