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FINC6001 β Finance: Theory to Applications

Final Exam Formula Sheet

Margin Margin=
equity in account

value of stock
Expected rate of return on
a portfolio

πΈ(ππ) = π€π·πΈ(ππ·)+π€πΈπΈ(ππΈ)

Variance of the return on
a portfolio

ππ
2 = (π€π·ππ·)

2 +(π€πΈππΈ)
2 +2(π€π·ππ·)(π€πΈππΈ)ππ·πΈ

Portfolio variance (n
assets) when securities
have the same standard
(Ο) and share a common

correlation coefficient (Ο)

ππ
2 =

1

π
π2 +

π β1

π
ππ2

Correlation between
assets D and E

ππ·πΈ = πΆπππ(ππ·,ππΈ) =
πΆππ£(ππ·,ππΈ)

ππ·ππΈ
Sharpe ratio of a portfolio ππ =
πΈ(ππ)βππ

ππ
Sharpe ratio maximising
portfolio weights with

two risky assets (D and E)
and a risk-free asset

π€π· =
[πΈ(ππ·)βππ]ππΈ

2 β[πΈ(ππΈ)βππ]ππ·ππΈππ·πΈ

[πΈ(ππ·)βππ]ππΈ
2 +[πΈ(ππΈ)βππ]ππ·

2 β[πΈ(ππ·)βππ +πΈ(ππΈ)βππ]ππ·ππΈππ·πΈ
π€πΈ = 1βπ€π·

Optimal capital allocation
to the risky

asset/portfolio
π¦ =

πΈ(ππ)βππ

π΄ππ
2

Single index model (SIM)
in excess returns

ππ = πΌπ +π½πππ +ππ

Security risk in the SIM

Total risk = Systematic risk + Firm-specific risk

π2 = π½2ππ
2 +ππ

2

πΆππ£(ππ,ππ) = Product of betas x Market-index risk = π½ππ½πππ
2

Treynor-Black
optimisation procedure

π€π
0 =

πΌπ
π2(ππ)

(1)
β π€π =

π€π
0

β π€π
0π

π

(2)
β

{
πΌπ΄ = βπ€ππΌπ

π

π=1

π2(ππ΄) = βπ€π
2

π

π=1

π2(ππ)

π½π΄ = βπ€ππ½π

π

π=1

(3)
β π€π΄

0 = [

πΌπ΄
π2(ππ΄)
β

πΈ(ππ)
ππ
2β
]

(4)
β π€π΄

β =
π€π΄
0

1+(1βπ½π΄)π€π΄
0

(5)
β {
π€π
β = 1βπ€π΄

β

π€π
β = π€π΄

βπ€π

(6)
β {
πΈ(ππ) = (π€π

β +π€π΄
βπ½π΄)πΈ(ππ)+π€π΄

βπΌπ΄
ππ
2 = (π€π

β +π€π΄
βπ½π΄)

2ππ
2 +[π€π΄

βπ(ππ΄)]
2

Multifactor model (2
factors):

ππ = πΈ(ππ)+π½π1πΉ1 +π½π2πΉ2 +ππ

Multifactor SML (2
factors):

πΈ(ππ) = ππ +π½π1[πΈ(π1)βππ]+π½π2[πΈ(π2)βππ]

Fama-French 3 factor
model:

πππ‘ = πΌπ +π½πππππ‘ +π½ππππ΅πππ΅π‘ +π½ππ»ππΏπ»ππΏπ‘ +πππ‘

Fama-French 3 factor
model (APT):

πΈ(ππ)βππ = ππ +ππ[πΈ(ππ)βππ]+π ππΈ(πππ΅)+βππΈ(π»ππΏ)

M2 of portfolio P: π2 = ππ(ππ βππ)

Treynor measure: ππ =
ππ βππ

π½π
Jensenβs alpha: πΌπ = οΏ½ΜοΏ½π β[οΏ½ΜοΏ½π +π½π(οΏ½ΜοΏ½π βοΏ½ΜοΏ½π)]

Information ratio:
πΌπ

π(ππ)
Morningstar risk-
adjusted return: πππ΄π(πΎ) = [

1

π
Ξ£π‘=1
π (

1+ππ‘
1+πππ‘

)

βπΎ

]

β12/πΎ

β1

Stock index futures

Hedge ratio =
Hedge value

Total position value
Optimal hedge ratio = ββ = π(
ππ
ππ
)

Number of contracts required to hedge the risk in a stock portfolio =
ππ

ππΉ
Γ
π½π

π½πΉ
Interest rate futures

Duration of interest rate futures contract = π·πΉ = π·π +ππΉ

Number of contracts required to hedge the risk in a bond portfolio =
π·π

π·πΉ
Γ
ππ

ππΉ
Bargaining model (2
players with βAβ making

the initial offer; 3
dates)

Player A: 1βπ½(1βπΌ); Player B: π½(1βπΌ)

The assignment help me finish this finance task , time is 10-12am Β 23th Nov GMT+8 timeΒ

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