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FINC6001 – Finance: Theory to Applications
Final Exam Formula Sheet
Margin Margin=
equity in account
value of stock
Expected rate of return on
a portfolio
�(��) = ���(��)+���(��)
Variance of the return on
a portfolio
��
2 = (����)
2 +(����)
2 +2(����)(����)���
Portfolio variance (n
assets) when securities
have the same standard
(σ) and share a common
correlation coefficient (ρ)
��
2 =
1
�
�2 +
� −1
�
��2
Correlation between
assets D and E
��� = ����(��,��) =
���(��,��)
����
Sharpe ratio of a portfolio �� =
�(��)−��
��
Sharpe ratio maximising
portfolio weights with
two risky assets (D and E)
and a risk-free asset
�� =
[�(��)−��]��
2 −[�(��)−��]�������
[�(��)−��]��
2 +[�(��)−��]��
2 −[�(��)−�� +�(��)−��]�������
�� = 1−��
Optimal capital allocation
to the risky
asset/portfolio
� =
�(��)−��
���
2
Single index model (SIM)
in excess returns
�� = �� +���� +��
Security risk in the SIM
Total risk = Systematic risk + Firm-specific risk
�2 = �2��
2 +��
2
���(��,��) = Product of betas x Market-index risk =
������
2
Treynor-Black
optimisation procedure
��
0 =
��
�2(��)
(1)
⇒ �� =
��
0
∑ ��
0�
�
(2)
⇒
{
�� = ∑����
�
�=1
�2(��) = ∑��
2
�
�=1
�2(��)
�� = ∑����
�
�=1
(3)
⇒ ��
0 = [
��
�2(��)
⁄
�(��)
��
2⁄
]
(4)
⇒ ��
∗ =
��
0
1+(1−��)��
0
(5)
⇒ {
��
∗ = 1−��
∗
��
∗ = ��
∗ ��
(6)
⇒ {
�(��) = (��
∗ +��
∗ ��)�(��)+��
∗ ��
��
2 = (��
∗ +��
∗ ��)
2��
2 +[��
∗ �(��)]
2
Multifactor model (2
factors):
�� = �(��)+��1�1 +��2�2 +��
Multifactor SML (2
factors):
�(��) = �� +��1[�(�1)−��]+��2[�(�2)−��]
Fama-French 3 factor
model:
��� = �� +������ +��������� +���������
+���
Fama-French 3 factor
model (APT):
�(��)−�� = ��
+��[�(��)−��]+���(���)+ℎ ��(���)
M2 of portfolio P: �2 = ��(�� −��)
Treynor measure: �� =
�� −��
��
Jensen’s alpha: �� = �̅�� −[�̅�� +��(�̅�� −�̅��)]
Information ratio:
��
�(��)
Morningstar risk-
adjusted return: ����(�) = [
1
�
Σ�=1
� (
1+��
1+���
)
−�
]
−12/�
−1
Stock index futures
Hedge ratio =
Hedge value
Total position value
Optimal hedge ratio = ℎ ∗ = �(
��
��
)
Number of contracts required to hedge the risk in a stock
portfolio =
��
��
×
��
��
Interest rate futures
Duration of interest rate futures contract = �� = �� +��
Number of contracts required to hedge the risk in a bond
portfolio =
��
��
×
��
��
Bargaining model (2
players with ’A’ making
the initial offer; 3
dates)
Player A: 1−�(1−�); Player B: �(1−�)

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FINC6001 – Finance Theory to Applications Final Exam Form

  • 1. FINC6001 – Finance: Theory to Applications Final Exam Formula Sheet Margin Margin= equity in account value of stock Expected rate of return on a portfolio �(��) = ���(��)+���(��) Variance of the return on a portfolio �� 2 = (����) 2 +(����) 2 +2(����)(����)��� Portfolio variance (n assets) when securities have the same standard (σ) and share a common correlation coefficient (ρ)
  • 2. �� 2 = 1 � �2 + � −1 � ��2 Correlation between assets D and E ��� = ����(��,��) = ���(��,��) ���� Sharpe ratio of a portfolio �� = �(��)−�� �� Sharpe ratio maximising portfolio weights with two risky assets (D and E) and a risk-free asset �� = [�(��)−��]��
  • 3. 2 −[�(��)−��]������� [�(��)−��]�� 2 +[�(��)−��]�� 2 −[�(��)−�� +�(��)−��]������� �� = 1−�� Optimal capital allocation to the risky asset/portfolio � = �(��)−�� ��� 2 Single index model (SIM) in excess returns �� = �� +���� +�� Security risk in the SIM Total risk = Systematic risk + Firm-specific risk �2 = �2�� 2 +�� 2
  • 4. ���(��,��) = Product of betas x Market-index risk = ������ 2 Treynor-Black optimisation procedure �� 0 = �� �2(��) (1) ⇒ �� = �� 0 ∑ �� 0� � (2) ⇒ {
  • 5. �� = ∑���� � �=1 �2(��) = ∑�� 2 � �=1 �2(��) �� = ∑���� � �=1 (3) ⇒ �� 0 = [ �� �2(��) ⁄ �(��) �� 2⁄ ]
  • 6. (4) ⇒ �� ∗ = �� 0 1+(1−��)�� 0 (5) ⇒ { �� ∗ = 1−�� ∗ �� ∗ = �� ∗ �� (6) ⇒ { �(��) = (�� ∗ +�� ∗ ��)�(��)+�� ∗ �� �� 2 = (�� ∗ +�� ∗ ��)
  • 7. 2�� 2 +[�� ∗ �(��)] 2 Multifactor model (2 factors): �� = �(��)+��1�1 +��2�2 +�� Multifactor SML (2 factors): �(��) = �� +��1[�(�1)−��]+��2[�(�2)−��] Fama-French 3 factor model: ��� = �� +������ +��������� +��������� +��� Fama-French 3 factor model (APT): �(��)−�� = �� +��[�(��)−��]+���(���)+ℎ ��(���) M2 of portfolio P: �2 = ��(�� −��) Treynor measure: �� =
  • 8. �� −�� �� Jensen’s alpha: �� = �̅�� −[�̅�� +��(�̅�� −�̅��)] Information ratio: �� �(��) Morningstar risk- adjusted return: ����(�) = [ 1 � Σ�=1 � ( 1+�� 1+��� ) −� ] −12/� −1 Stock index futures
  • 9. Hedge ratio = Hedge value Total position value Optimal hedge ratio = ℎ ∗ = �( �� �� ) Number of contracts required to hedge the risk in a stock portfolio = �� �� × �� �� Interest rate futures Duration of interest rate futures contract = �� = �� +�� Number of contracts required to hedge the risk in a bond portfolio = �� �� × �� ��
  • 10. Bargaining model (2 players with ’A’ making the initial offer; 3 dates) Player A: 1−�(1−�); Player B: �(1−�)