SOA Course FM
CAS Exam 2
Flashcards
Summer 2012
Important formulas
Key lists
Crucial concepts
CONTENTS
Contents
Page
How to use these flashcards
3
Background topics
4
Financial mathematics chapters:
1.
Interest rates and factors
6
2.
Level annuity factors
10
3.
Varying annuity factors
14
4.
Non-annual time periods
22
5.
Project appraisal and loans
32
6.
Bond & stock valuation
38
7.
Duration, convexity & immunization
46
8.
The term structure of interest rates
52
9.
Introduction to derivatives
54
10.
Forwards and options
60
11.
Derivative strategies
76
12.
Risk management
90
13.
Forwards and futures
94
14.
Swaps
104
Page 2
© BPP Professional Education: 2012 exams
HOW TO USE THESE FLASHCARDS
These flashcards are designed to help you memorize important formulas
efficiently in your preparation for the Course FM exam. It is extremely
important for a mathematically intensive, multiple choice exam that you
thoroughly understand important formulas and how to apply them under
stressful exam conditions. Once you have this mastered, you will have a
competitive advantage over most of the other students taking the exam
that will provide a level of confidence that should result in a passing
score.
The left hand-sides of important formulas are presented on evennumbered pages, while the complete formulas are presented on oddnumbered pages. This format is designed to quickly improve your
memorization of the important formulas. We suggest using a blank sheet
of paper to conceal the complete formulas on the odd pages as you look at
the incomplete formulas on the even pages. As you work your way
through the incomplete formulas on the even pages, you can gradually
reveal the complete formulas by shifting the blank sheet of paper down
the even-numbered pages.
For a multiple choice exam, memorization of lists is not as important as
being able to recognize items within a list when they are presented.
Course FM / Exam 2 is not an essay exam, so you will not be asked to
recite a memorized list, but you will be asked about whether or not an
item in a list is appropriate in the context of the question.
We have designed these flashcards so that they can be carried
conveniently and read frequently in the final run-up to the exam. Check
each section when you feel confident with the material covered.
Each person has a different approach to learning. While we have tried to
be reasonably complete with the flashcards, some students may prefer to
derive some of the formulas while others may prefer to memorize them
all. These flashcards cannot possibly cover everything that will ever
appear on the Course FM exam since they would become too unwieldy
and ultimately less useful for the student. So we hope that you will
personalize these flashcards by adding your own formulas, comments,
and notes to help you pass the exam.
Good luck with your studying.
© BPP Professional Education: 2012 exams
Page 3
BACKGROUND TOPICS
Quadratic equation
ax 2  bx  c  0
x
Geometric series
a  1  r  r 2    r n1  


Linear interpolation
a d


x e 
 b f 
solve for x
Timing of cash flows


End of year x =
Beginning of year x =
Percentage change
% 
Page 4
© BPP Professional Education: 2012 exams
BACKGROUND TOPICS
Quadratic equation
ax 2  bx  c  0
x
b  b 2  4 ac
2a
Geometric series
 1  rn 
a  1  r  r 2    r n1   a 



 1  r 
Linear interpolation
a d 


x e 
 b f 
ab d f

xb e f
solve for x
Timing of cash flows


End of year x = time x years
Beginning of year x = time (x – 1) years
Percentage change
% 
new  old
old
© BPP Professional Education: 2012 exams
Page 5
FINANCIAL MATHEMATICS
Call option payoffs
Long call option payoff =
Short call option payoff =
Payoff diagrams for a call option
The graphs of the payoffs from a call option are:
Moneyness of a call option
A call option is in the money at time t if _______________
A call option is at the money at time t if _______________
A call option is out of the money at time t if ____________
Page 68
© BPP Professional Education: 2012 exams
FINANCIAL MATHEMATICS
Call option payoffs
Long call option payoff  max(0, ST  K )
Short call option payoff   max(0, ST  K )
Payoff diagrams for a call option
The graphs of the payoffs from a call option are:
Short call option
Long call option
Payoff
upon
expiration
0
K
0
K
ST
Moneyness of a call option
A call option is in the money at time t if St  K .
A call option is at the money at time t if St  K .
A call option is out of the money at time t if St  K .
© BPP Professional Education: 2012 exams
Page 69
FINANCIAL MATHEMATICS
Collared stock
A
collared
stock
position
is
created
by
___________________________________________________
Purchased straddle
A purchased straddle position is created by
___________________________________________________
Written straddle
A
written
straddle
position
is
created
by
___________________________________________________
Purchased strangle
A purchased strangle position is created by
___________________________________________________
Written strangle
A
written
strangle
position
is
created
by
___________________________________________________
Page 86
© BPP Professional Education: 2012 exams
FINANCIAL MATHEMATICS
Collared stock
A collared stock position is created by owning the stock,
buying a lower strike put and selling a higher strike call.
Purchased (long) straddle
A purchased straddle position is created by buying a call
option and a buying put option with the same strike price
and time to expiration.
Written (short) straddle
A written straddle position is created by selling a call
option and selling a put option with the same strike price
and time to expiration.
Purchased (long) strangle
A purchased strangle position is created by buying a call
option and buying a put option with a lower strike price
than that of the call but with the same time to expiration.
Written (short) strangle
A written strangle position is created by selling a call
option and selling a put option with a lower strike price
than that of the call but with the same time to expiration.
© BPP Professional Education: 2012 exams
Page 87
FINANCIAL MATHEMATICS
Computing the fixed swap rate for an interest rate swap
The fixed swap rate can be computed by equating
___________________________________________________
Deferred swaps
A deferred start swap is ______________________________
Amortizing swaps
An amortizing swap is _______________________________
Accreting swaps
An accreting swap is _______________________________
Page 108
© BPP Professional Education: 2012 exams
FINANCIAL MATHEMATICS
Computing the fixed swap rate for an interest rate swap
The fixed swap rate can be computed by equating the
present value of the payments made by the fixed rate
payer to the present value of the payments made by the
variable rate payer.
R
n
n
i1 P  0, ti   i1 P  0, ti   r0 ti1 , ti 
Deferred swaps
A deferred start swap is a swap in which the fixed swap
rate is determined today and the swap payment dates
occur at later times.
Amortizing swaps
An amortizing swap is a swap in which the notional
principal decreases over time.
Accreting swaps
An accreting swap is a swap in which the notional
principal increases over time.
Again, we can calculate the fixed swap rate for a swap
with a varying principal amount by equating the PV of the
payments made by the fixed rate payer to the present
value of the cashflows made by the variable rate payer.
R
n
n
i1 Qti  P  0, ti   i1 Qti  P  0, ti   r0 ti1 , ti 
© BPP Professional Education: 2012 exams
Page 109