Finance Exam Enclosure: Formula Sheet Page 3
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1
2
3
4Market value of asset j
Or finding portfolio beta
ω
=
j
Market value of all assets
β
=
ω
β
N
N
p
i
i
E[˜ r
] = E
ω
˜ r
=
ω
E[˜ r
]
p
j
j
j
j
i
j=1
j=1
and then finding return
2
2
σ
= E[(˜ r
E[˜ r
])
]
p
p
p
E[r
] = r
+ β
(E[r
]
r
)
σ
= E[(˜ r
E[˜ r
])(˜ r
E[˜ r
])
p
f
p
m
f
ij
i
i
j
j
N
N
Term structure of interest rates
2
σ
=
ω
ω
σ
C : cash flow at time t, r : spot interest rate, f : forward
j
i
ij
p
rate between time t
1 and t.
j=1
i=1
σ
ij
ρ
=
ij
C
σ
σ
t
i
j
P V =
t
(1 + r
)
cov(˜ r
, ˜ r
)
t
i
j
t=1
=
var(˜ r
) var(˜ r
)
i
j
t
(1 + r
)
t
cov(˜ r
, ˜ r
)
f
=
1
i
j
t
t 1
=
(1 + r
)
t 1
SD(˜ r
)SD(˜ r
)
i
j
t
(1 + r
)
= (1 + f
)(1 + f
)
(1 + f
)
t
1
2
t
Variance of two-asset portfolio
Forward/Futures contracts
2
2
F : forward price. S: spot price (of underlying). T : expiry
2
σ
=
ω
ω
σ
date of contract (delivery date). T
t: time to delivery (in
j
i
ij
p
years). r: risk free interest rate (continously compounded).
j=1
j=1
r : risk free interest rate (discretely compounded)
2
2
2
2
= ω
σ
+ ω
σ
+ 2ω
ω
σ
1
2
12
1
1
2
2
Minimizing variance
r(T t)
F = Se
In a two asset problem the portfolio weight on
stock 1 that minimises the variance of the port-
T
F = S(1 + r
)
f
folio is
International
F : Forward exchange rate. S: Spot exchange rate. r for-
2
eign interest rate. r : domestic interest rate (both conti-
σ
σ
σ
ρ
1
2
12
2
ω
=
nously compounded).
1
2
2
σ
+ σ
2σ
σ
ρ
1
2
12
1
2
CAPM
(r
r )(T t)
F
= S
e
t,T
t
σ
mp
E[˜ r
] = r
+ (E[˜ r
]
r
)
p
f
m
f
2
σ
Options
m
S: spot price (of underlying). T : expiry date of contract (de-
E[˜ r
] = r
+ (E[˜ r
]
r
)β
livery date). T
t: time to delivery (in years). X: eXercise
j
f
m
f
j
price. C call price and P put price.
Portfolio p of different assets i: Calculate
return either by first finding return of each
C
= max(0, S
X)
asset i
T
T
E[r
] = r
+ β
(E[r
]
r
)
P
= max(0, X
S
)
i
f
i
m
f
T
T
Binomial option pricing
and then taking portfolio return
S: spot price (of underlying). r: per period interest rate
(continously compounded). σ: volatility. C: call price. u, d:
E[r
] =
ω
E[r
]
multiplicative price movements. ∆t: time interval. r : one
p
i
i
period risk free interest rate (discretely compounded).
i
3
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