FORMULA SHEET
P0 =
P ar
(1 + z0T )T
P ar 1/T
=
−1
P0
Expected Cash Flow
=
∗ T
)
(1 + z0T
(1 − b) P ar + b r π P ar
=
∗ T
)
(1 + z0T
z0T
P0
#1/T
"
∗
z0T
=
P0 =
HP R =
HP R0X =
P0 =
P0 =
P ar [1 − b (1 − rπ)]
−1
P0
P ar
n
1 + s × 365
PX − P0
P0
PX 1/X
−1
P0
!
C
1
FV
1−
+
ytm
(1 + ytm)n
(1 + ytm)n
#
)
(
"
P ar
1
C
1
+
C+
1−
ytm
(1 + ytm)n−1
(1 + ytm)n−1
(1 + ytm)f /h
ftT =
∆P
P
≈
D =
D =
X =
(1 + z0T )T =
#1/(T −t)
(1 + z0T )T
−1
(1 + z0t )t
−∆y
1
× D + X(∆y)2
1+y
2
C/ (1 + y)
C/(1 + y)2
C/(1 + y)3
×1+
×2+
×3
P
P
P
(C + P ar) /(1 + y)T
+... +
×T
P
1+y
(1 + y) + T (c − y)
−
y
c[(1 + y)T − 1] + y
"
#
1
2C
12C
T (T + 1) (C + P ar)
6C
+
+... +
+
P (1 + y)2 1 + y (1 + y)2 (1 + y)3
(1 + y)T
(1 + z01 ) · (1 + E[r̃12 ] + L12 ) · · · · · (1 + E[r̃T −1,T ] + LT −1,T )
"
1
E[r̃] =
X
prob(s)r(s)
s
2
var(r̃) = σ (r) =
X
prob(s) (r(s) − E[r̃])2
s
cov(r̃X , r̃Y ) = σXY =
X
prob(s) (rX (s) − E[r̃X ]) (rY (s) − E[r̃Y ])
s
Sharpe =
E[r̃C ] =
σC2 =
U =
E[r̃P ] =
corr(r̃X , r̃Y ) =
σP2 =
∗
wD
=
wE =
E(r̃P ) =
σP2 =
E[r̃P ] − rf
σP
rf + y(E[r̃P ] − rf )
y 2 σP2
1
E[r̃P ] − rf
E[r̃P ] − AσP2 → y ∗ =
2
AσP2
wD E[r̃D ] + wE E[r̃E ]
cov(r̃X , r̃Y )
ρXY =
σX σY
2 2
wD σD + wE2 σE2 + 2wD wE cov(r̃D , r̃E )
[E(r̃D ) − rf ]σE2 − [E(r̃E ) − rf ]cov(r̃D , r̃E )
2
[E(r̃D ) − rf ]σE2 + [E(r̃E ) − rf ]σD
− [E(r̃D ) − rf + E(r̃E ) − rf ]cov(r̃D , r̃E )
1 − wD
n
X
wi E(r̃i )
i
n X
n
X
wi wj cov(r̃i , r̃j )
i
j
2