Investments FNCE30001 Final Examination Semester 2, 2015  

   

1  

Seat No: Student No:

(Do NOT write your name anywhere on this exam booklet)

THE UNIVERSITY OF MELBOURNE FACULTY OF BUSINESS AND ECONOMICS

FINAL EXAMINATION SUBJECT NUMBER: FNCE30001 SUBJECT NAME: INVESTMENTS SEMESTER/YEAR: 2/2015 EXAMINATION DURATION: 3 hours READING TIME: 15 minutes TOTAL MARKS: 100 CONTRIBUTION TO FINAL MARK: 70% NO. OF PAGES: XX AUTHORISED MATERIALS 1. This is a CLOSED BOOK examination. 2. Non-programmable calculators are permitted. Calculators with the ability to enter and/or

retrieve text are NOT permitted. INSTRUCTIONS TO INVIGILATORS 1. Students should be provided ONLY with this booklet and a general purpose answer

sheet. 2. Writing is NOT permitted during reading time. 3. This booklet and the General Purpose Answer Sheet must be COLLECTED at the end of

the examination. INSTRUCTIONS TO STUDENTS 1. Write your student number at the top of this cover page. You must also complete the

General Purpose Answer Sheet. 2. You may detach the formula list and pages for rough work from this booklet (pages XX

to XX). Do not detach any other pages. Examination booklets with missing pages will not be marked.

3. Answer all questions. Answer questions in Part A using the General Purpose Answer Sheet. Answers to Parts B should be written only in the spaces provided in this booklet.

4. For full credit show ALL your calculations, including formulae used. 5. Examiners will NOT take into account anything written on the “pages for rough work”. 6. This paper must be handed in at the end of the examination. Do NOT remove this paper

from the examination room. BAILLIEU LIBRARY: This paper may NOT be lodged with the library. Examiners' Use Only

PART A (30)

B1 (9)

B2 (10)

B3 (9)

B4 (9)

B5 (7)

B6 (8)

B7 (7)

B8 (11)

TOTAL (100)

Investments FNCE30001 Final Examination Semester 2, 2015  

   

2  

Formula Sheet

Equities

𝐸 𝑟! = ∑𝑝 𝑠 𝑟!(𝑠) 𝜎!! = ∑𝑝 𝑠 𝑟! 𝑠 − 𝐸 𝑟! !

𝜎!" = ∑𝑝 𝑠 𝑟! 𝑠 − 𝐸 𝑟! 𝑟! 𝑠 − 𝐸 𝑟! 𝜌!" =!!"!!!!

( ) 212P PU E r Aσ= − *

2

( )P f

P

E r ry

Aσ−

= ( )σ

−= P f

PP

E r rS

( ) ( ) (1 ) [ ( ) ]c p f f p fE r yE r y r r y E r r= + − = + − 𝜎! = 𝑦𝜎!

( ) ( ) ( )P D D E EE r w E r w E r= + 2 2 2 2 2 2 ( , )P D D E E D E D Ew w w w cov r rσ σ σ= + +

2

1 1 1( ) ( ) ( , )

n n n

P i i P i j i ji i j

E r w E r σ ww cov r r= = =

= =∑ ∑∑

2( )M f ME r r Aσ− =

( ) ( )2

cov ,[ ]i M

i i f i M fM

r rE r r E r rβ β

σ⎡ ⎤= − = −⎣ ⎦

𝑟! = 𝐸 𝑟! + 𝛽!𝑚 + 𝑒! ( ) ( ) ( )i i i M iR t R t e tα β= + +

𝜎!! = 𝛽!!𝜎!! + 𝜎!(𝑒!) 𝑐𝑜𝑣 𝑟! , 𝑟! = 𝛽!𝛽!𝜎!!

𝑟! = 𝐸 𝑟! + 𝛽!!𝐹! + 𝛽!!𝐹! + 𝑒! 𝐸 𝑟! = 𝑟! + 𝛽!!𝜆! + 𝛽!!𝜆!

The formula list continues on the next page.

Investments FNCE30001 Final Examination Semester 2, 2015  

   

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Bonds

( )0

01 TT

ParPz

=+

1

00

1T

TParzP

⎛ ⎞= −⎜ ⎟⎝ ⎠

( )

( )0

*0

1 1

1T

T

Par d mπP

z

− −⎡ ⎤⎣ ⎦=+

( )1

*0

0

1 11

T

TPar d mπ

zP

⎧ ⎫− −⎡ ⎤⎪ ⎪⎣ ⎦= −⎨ ⎬⎪ ⎪⎩ ⎭

01

365

ParP ns=

+ ×

0

3651ParsP n

⎛ ⎞= − ×⎜ ⎟⎝ ⎠

0 1360nP Par q⎛ ⎞= − ×⎜ ⎟

⎝ ⎠

( ) ( ) ( ) ( )0 2 3 1

01 02 03 00, 1

...1 1 1 11

T TTT

C C C C C ParPz z z zz

−

−

+= + + + + +

+ + + ++

( ) ( ) ( ) ( )0 2 3 1...1 1 1 1 1T TC C C C C ParPytm ytm ytm ytm ytm−

+= + + + + +

+ + + + +

( ) ( )0

111 1T T

C ParPytm ytm ytm

⎡ ⎤= ⎢ − ⎥ +

⎢ ⎥+ +⎣ ⎦

( ) ( ) ( )0 1 1

1 111 1 1f h n n

C ParP Cytmytm ytm ytm− −

⎧ ⎫⎡ ⎤⎪ ⎪= + ⎢ − ⎥ +⎨ ⎬

⎢ ⎥+ + +⎪ ⎪⎣ ⎦⎩ ⎭ 12

C c Par= × ×

1

00

1T

TT

PHPRP

⎛ ⎞= −⎜ ⎟⎝ ⎠

The formula list continues on the next page.

Investments FNCE30001 Final Examination Semester 2, 2015  

   

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( ) ( ) ( ) ( ) ( )2 31 1 1 11 2 3 ...

TC i C i C i C Par iD T

P P P P+ + + + +

= × + × + × + + ×

1P i DP iΔ −Δ

≈ ×+

( )1 1

Ttt

t

t CFi

DP

= +=

∑

( )

( )

1

1

1

1

Ttt

tT

tt

t

t CFi

DCFi

=

=

+=

+

∑

∑ perp

1 iDi+

=

( )( ) ( ) ( )

( )( )( )

22 2 3

11 2 6 12where ...1 12 1 1 1 1 T

T T C ParP i C C CD X i XP i iP i i i i

⎡ ⎤+ +Δ −Δ≈ × + Δ = ⎢ + + + + ⎥

+ +⎢ ⎥+ + + +⎣ ⎦

*A A B Bw D w D D+ = pfolio

1 1 pfolio

n ni

i i ii i

PD w D DV= =

= = ×∑ ∑

( )( )

( )1

0

0

11

1

T tTT

tT tt

zf

z

−⎡ ⎤+⎢ ⎥= −⎢ ⎥+⎣ ⎦

( ) ( ) ( )0 01 1 1T t T tT t tTz z f −

+ = + × +

( )0

0

11

T TT

dz

=+

0

0

TtT

t

ddd

=

( ) ( ) ( )0 01 1 1 ET tT t

T t tTz z r−

⎡ ⎤+ = + × +⎣ ⎦ ( ) ( ) ( ) ( )

10 01 12 23 1,1 1 1 ... 1 1

TT T Tz z f f f −⎡ ⎤= + × + × + × × + −⎣ ⎦ ( ) ( ) ( ) ( ){ }10 01 12 23 1,1 1 E 1 E ... 1 E 1

TT T Tz z r r r −⎡ ⎤⎡ ⎤= + × + × + × × + −⎡ ⎤⎣ ⎦ ⎣ ⎦ ⎣ ⎦

( ), 1 , 1 , 1Et t t t t tf r L+ + += +

Quadratic Equation: 𝑎𝑥! + 𝑏𝑥 + 𝑐 = 0 →  𝑥 = !!± !!!!!"!!

The formula list continues on the next page.

Investments FNCE30001 Final Examination Semester 2, 2015  

   

5  

Portfolio Performance Evaluation

References:

TWR: Time-weighted return

DWR: Dollar-weighted return

11

−

+= −t t

tt

P DrP

( ) ( ) ( ) ( ) 111 1, 1 1

=

⎡ ⎤= + − = + −⎡ ⎤⎢ ⎥ ⎣ ⎦⎣ ⎦∏n n

tt

TWR total r TWR mean TWR total

1ln t t

tt

P DrP−

⎛ ⎞+= ⎜ ⎟

⎝ ⎠

( ) ( ) ( )

1

1,=

= = ×∑n

tt

TWR total r TWR mean TWR totaln

( ) ( )0

10

1 1=

⎡ ⎤⎢ ⎥ + − =⎢ ⎥+ +⎣ ⎦

∑n

t nt n

t

D P PDWR DWR

( )( )

P f P f PP P f P M f

P P P

r r r r αS T α r r β r r IRσ β σ e− −

⎡ ⎤= = = − + − =⎣ ⎦

( ) ( )

( )( )

P f P f PP P P P P P

P P P

E r r E r rS T r E r IR

eα

ασ β σ

− −= = = − =

( ) ( )1 1( )

n n

P B Pi Pi Bi Bi Pi Bi Bi Pi Pi Bii i

r r w r w r w w r w r r= =

− = − = − + −⎡ ⎤⎣ ⎦∑ ∑