lOMoARcPSD|70337540
Faculty of Economics and Business Academic year 2013-2014
On the first page of this exam form you will find important information about this exam.
Please read the information below before answering any exam questions!
Exam: Investment and Portfolio Theory 2 6012B0234Y
Date and time of the exam: Thursday 22 May 2014 14:00
Duration of the exam: 3 hours
You have to identify yourself using your validated UvA-identification card or other legal ID-card.
If you are not registered via SIS for the course component correctly, your exam will not be marked and
registered.
Please write your name and student number on every
sheet of paper you hand in.
Warning against cheating: Do not cheat! Students who are caught in any form of cheating will be
punished, the maximum punishment being exclusion from all exams for a period of one year.
Make sure that your mobile phone is switched off and locked in your briefcase. Your briefcase must be closed
and placed on the floor.
During the exam you are not allowed to go to the toilet without the prior consent of
the coordinating supervisor or invigilator.
Tools allowed: pencil, pen, eraser, ruler, calculator
You are NOT allowed to use graphical/programmable calculator
Specific information on this exam:
This exam consists of 16 multiple choice questions and 4 open questions.
Answer on normal exam paper, there is no separate form for the multiple choice questions. Your
answer should be clear, short, and precise.
The answers should be in English. Answers in any other language will not be taken into consideration
(you will receive 0 points for the particular question).
To obtain full points for the open questions, make sure you clearly explain all steps you take in
calculations and interpret your result.
The results of this exam will be published within 15 working days following the date of the
exam. If the re-sit is scheduled to take place within 6 weeks following the current exam, the
results of the current exam will be published within 12 working days.
Inspection of the exam: there will be an inspection session for the exam and the assignments. Date
and time to be announced on Blackboard.
You are allowed to keep the question form(s) after the examination.
Good luck!
i
, lOMoARcPSD|70337540
Open questions (50/100 points)
1. Calculate the Black-Scholes value of the following options. Show your calculations:
a. A call with X=40, S = 50, σ = 0.40, Rf = 0.01, T= 0.5
The BS call value is C = $11.690
With the table provided, a value of 11.78 is also reasonable. Both rounding d1 and d2 and interpolating N(d1)
and N(d2) are acceptable ways of use of the table.
b. A call with X=60, S = 50, σ = 0.45, Rf = 0.015, T= 1.5
The BS call value is C = $7.943
With the table provided, a value of 8.12 is also reasonable.
2. Assume you have a put option contract (consisting of 100 options) on T-Mobile. This stock currently trades at
$31.80, has a volatility of 0.44, and a strike price of $25. Assume the risk-free rate is 0.75% annually.
a. Calculate the delta of this option.
d1 = 0.7838, N(d1) = 0.7823, delta is N(d1) - 1 = - 0.2177
b. Calculate how many contracts we need to create a delta-neutral hedge for a portfolio consisting of 400 stocks.
delta of the portfolio: +400. delta of 1 option: -0.2177, of one option contract: -21.77.
delta neutrality therefore needs 400/21.77 = 18.39 contracts.
rounding is not required.
c. Assume the share price moves to $35.20. Calculate the change in the option value based on delta and gamma.
The formula for gamma is:
1 2
e d
S0 2 T
This should be calculated based on the old price, S0 = 31.80. In that case, we have d1 = 0.7838, S0 = 31.80 and
gamma = [ 1/(31.8*0.44*√2π*1) ]e-0.307 = 0.0209
then the price change is delta * (35.2-31.8) + 1/2 * gamma * (35.2-31.8)2 = -0.2177 * 3.4 + 0.5*0.0209*3.42 =
-0.7402+0.1208= -0.619
d. Calculate the change in the option value based on the Black-Scholes model before and after the price change
(assume all other inputs stay the same).
d1 = 0,7838 ; d2 = 0,3438 ; N(d1) = 0,7834 ; N(d2) = 0,6345 ; put = 2,18
NB: doesn’t have to be through the put-call parity, of course, even though that was the idea.
this becomes: 1,0147 ; 0,5747 ; 0,8449 ; 0,7173 with a put value of 1,56
drop = 0.62
i
Faculty of Economics and Business Academic year 2013-2014
On the first page of this exam form you will find important information about this exam.
Please read the information below before answering any exam questions!
Exam: Investment and Portfolio Theory 2 6012B0234Y
Date and time of the exam: Thursday 22 May 2014 14:00
Duration of the exam: 3 hours
You have to identify yourself using your validated UvA-identification card or other legal ID-card.
If you are not registered via SIS for the course component correctly, your exam will not be marked and
registered.
Please write your name and student number on every
sheet of paper you hand in.
Warning against cheating: Do not cheat! Students who are caught in any form of cheating will be
punished, the maximum punishment being exclusion from all exams for a period of one year.
Make sure that your mobile phone is switched off and locked in your briefcase. Your briefcase must be closed
and placed on the floor.
During the exam you are not allowed to go to the toilet without the prior consent of
the coordinating supervisor or invigilator.
Tools allowed: pencil, pen, eraser, ruler, calculator
You are NOT allowed to use graphical/programmable calculator
Specific information on this exam:
This exam consists of 16 multiple choice questions and 4 open questions.
Answer on normal exam paper, there is no separate form for the multiple choice questions. Your
answer should be clear, short, and precise.
The answers should be in English. Answers in any other language will not be taken into consideration
(you will receive 0 points for the particular question).
To obtain full points for the open questions, make sure you clearly explain all steps you take in
calculations and interpret your result.
The results of this exam will be published within 15 working days following the date of the
exam. If the re-sit is scheduled to take place within 6 weeks following the current exam, the
results of the current exam will be published within 12 working days.
Inspection of the exam: there will be an inspection session for the exam and the assignments. Date
and time to be announced on Blackboard.
You are allowed to keep the question form(s) after the examination.
Good luck!
i
, lOMoARcPSD|70337540
Open questions (50/100 points)
1. Calculate the Black-Scholes value of the following options. Show your calculations:
a. A call with X=40, S = 50, σ = 0.40, Rf = 0.01, T= 0.5
The BS call value is C = $11.690
With the table provided, a value of 11.78 is also reasonable. Both rounding d1 and d2 and interpolating N(d1)
and N(d2) are acceptable ways of use of the table.
b. A call with X=60, S = 50, σ = 0.45, Rf = 0.015, T= 1.5
The BS call value is C = $7.943
With the table provided, a value of 8.12 is also reasonable.
2. Assume you have a put option contract (consisting of 100 options) on T-Mobile. This stock currently trades at
$31.80, has a volatility of 0.44, and a strike price of $25. Assume the risk-free rate is 0.75% annually.
a. Calculate the delta of this option.
d1 = 0.7838, N(d1) = 0.7823, delta is N(d1) - 1 = - 0.2177
b. Calculate how many contracts we need to create a delta-neutral hedge for a portfolio consisting of 400 stocks.
delta of the portfolio: +400. delta of 1 option: -0.2177, of one option contract: -21.77.
delta neutrality therefore needs 400/21.77 = 18.39 contracts.
rounding is not required.
c. Assume the share price moves to $35.20. Calculate the change in the option value based on delta and gamma.
The formula for gamma is:
1 2
e d
S0 2 T
This should be calculated based on the old price, S0 = 31.80. In that case, we have d1 = 0.7838, S0 = 31.80 and
gamma = [ 1/(31.8*0.44*√2π*1) ]e-0.307 = 0.0209
then the price change is delta * (35.2-31.8) + 1/2 * gamma * (35.2-31.8)2 = -0.2177 * 3.4 + 0.5*0.0209*3.42 =
-0.7402+0.1208= -0.619
d. Calculate the change in the option value based on the Black-Scholes model before and after the price change
(assume all other inputs stay the same).
d1 = 0,7838 ; d2 = 0,3438 ; N(d1) = 0,7834 ; N(d2) = 0,6345 ; put = 2,18
NB: doesn’t have to be through the put-call parity, of course, even though that was the idea.
this becomes: 1,0147 ; 0,5747 ; 0,8449 ; 0,7173 with a put value of 1,56
drop = 0.62
i
