Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Financial Mathematics
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions


Not looking for a job? Tell us about your ideal job,
and we'll only contact you when it opens up.
https://www.dwsimpson.com/register


Financial Mathematics Old FM Forum

Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 09-27-2006, 02:54 PM
Tom's Avatar
Tom Tom is offline
Actuarial Outpost Administrator
Contact me: Send me a PM
or email me
tom.troceen@dwsimpson.com
CAS SOA COPA
 
Join Date: Jan 1987
Location: Sitting in front of a red button w/ your name on it
College: FSU ActSci Alumni
Favorite beer: Root
Posts: 11,511
Blog Entries: 7
Post Done with the exam? Share your Exam 2/FM study notes here!

You can post your notes online using the upload button after clicking post reply, or you can always email them to me at tom(at)actuarialoutpost.com. If that isn't easy enough, just PM me here and I can send you my fax number or we can work something else out!


Any questions about what/how to post, can be answered here!

Thanks!

=====================
\\\\\\\ please read ///////
=====================


All posts in this thread that do not have notes attached will be deleted!

Members who donate notes* will be added to a user group much like the site supporters. This group will have added privileges such as a larger avatar and a custom user title other than 'member.'

Please note that some notes may be out of date, contain information that may no longer be tested, or not cover all required information for your exam. Please check your exam syllabus for a list of required study topics for your exam, before using these notes.

Notes that have been donated have not been checked for accuracy! If you do find an error in any of the notes, please feel free to point them out to me (or the original poster) via PM and I can edit the post where they were uploaded to call the error to everyone's attention.

Please only post notes that you own or have permission to post. Please respect otherís intellectual property and only post notes that meet our copyright policy.

Thanks again,

Tom



*a respectable amount


=====================
/////// please read \\\\\\\
=====================
__________________
Questions? Contact me at tom@actuarialoutpost.com or send me a PM here.
Reply With Quote
  #2  
Old 09-27-2006, 03:17 PM
MyKenk's Avatar
MyKenk MyKenk is offline
Note Contributor
CAS AAA
 
Join Date: Nov 2005
Location: twitter.com/mykenk
College: Drake '06
Posts: 8,595
Default

Attached find my notes for the Kellison book. Focusing on MY weak spots, there's very little in the way of formula development, i tried to make it theory heavy:
Attached Images
File Type: pdf Kellison Reading Notes.pdf (229.1 KB, 28839 views)
__________________
Reply With Quote
  #3  
Old 10-04-2006, 04:10 PM
tbug's Avatar
tbug tbug is offline
Note Contributor
SOA
 
Join Date: Jul 2006
Studying for G&H Core
Favorite beer: Yuengling
Posts: 10,826
Default wow!

Thank you so much for posting these notes! I've been using them 1) to look up formulas I've forgotten when I'm studying at work (since my books are at home) and 2) to get specific information that differs from Broverman (such as GICs), since I don't have the Kellison book. You rock
Reply With Quote
  #4  
Old 10-08-2006, 07:09 PM
no driver's Avatar
no driver no driver is offline
Note Contributor
SOA
 
Join Date: Jan 2006
Studying for nothing!
Posts: 2,352
Default FM Formulas

NEW PRINTABLE VERSION!
Scroll down to the bottom for a PDF that prints nicely. I will leave the original post up here so that folks can use it as a quick reference.

no driver
11/12/2006

Introduction:
Since ASM does not have a formula summary, I decided to compile one to use as I started working on old test questions. In the interest of other actuarial students, I thought I would share the results.

A few notes:
  1. This set of formulas is mostly derived from the 3rd edition of the ASM manual for Exam FM/2. As a reference, it does not attempt to recreate the methods presented in the ASM manual and skips many of the necessary techniques for using these formulas to solve certain types of problems. In particular you will notice that there are no formulas from chapters 2 and 8, and very little from chapter 5.
  2. Since the syllabus for the exam will change after the November 2006 sitting, this compilation will not be complete for exams given in 2007 and beyond, but it can probably be used as a starting point for future exam takers.
  3. I may have misstated some of the explanations of the formulas either through lack of understanding or inadequate keyboard/Tex skills. Please let me know if you find errors in this document and I will attempt to correct them. Also note that some formulas have no explanation, and are intended to show identities and useful relationships between terms that have been defined previously.
  4. This summary is meant as a reference. You donít need to memorize all of these formulas to do well on the exam. In fact, most of them can be easily derived from one another. As you work problems, some of these formulas will become second nature. For some of the problems where these formulas may work, you may prefer working from first principles or an intermediate derivation. Mykenk has suggested that you only need to know five formulas for the 2006 exam: Arithmetically increasing & decreasing annuity, geometrically increasing annuity, principle repaid at time t, and the price of a bond. As you learn the material you will figure out what works for you.

no driver 10/08/2006

Chapter 1:
Basics:
: accumulation function. Measures the amount in a fund with an investment of 1 at time 0 at the end of year .

: amount of growth in year .

: rate of growth in year , also known as the effective rate of interest in year .

: any accumulation function can be multiplied by a constant (usually the principal amount invested) to obtain a result specific to the amount invested.

Common Accumulation Functions:
: simple interest.

: variable interest.

: compound interest.

Present Value and Discounting:
: amount you must invest at time 0 to get 1 at time .

: effective rate of discount in year .

Some Useful Relationships:






Nominal Interest and Discount:
and are the symbols for nominal rates of interest compounded m-thly.









Force of Interest:
: definition of force of interest.



If the Force of Interest is Constant:






Chapter 3:
Annuities:
: PV of an annuity-immediate.

: PV of an annuity-due.



: AV of an annuity-immediate (on the date of the last deposit).

: AV of an annuity-due (one period after the date of the last deposit).





Perpetuities:
: PV of a perpetuity-immediate.

: PV of a perpetuity-due.



Chapter 4:
m-thly Annuities & Perpetuities:
: PV of an n-year annuity-immediate of 1 per year payable in m-thly installments.

: PV of an n-year annuity-due of 1 per year payable in m-thly installments.

: AV of an n-year annuity-immediate of 1 per year payable in m-thly installments.

: AV of an n-year annuity-due of 1 per year payable in m-thly installments.

: PV of a perpetuity-immediate of 1 per year payable in m-thly installments.

: PV of a perpetuity-due of 1 per year payable in m-thly installments.



Continuous Annuities:
Since ,

: PV of an annuity (immediate or due) of 1 per year paid continuously.

Payments in Arithmetic Progression:
In general, the PV of a series of payments, where the first payment is and each additional payment increases by can be represented by:


Similarly:


: AV of a series of payments, where the first payment is and each additional payment increases by .



: PV of an annuity-immediate with first payment 1 and each additional payment increasing by 1; substitute for in denominator to get due form.

: AV of an annuity-immediate with first payment 1 and each additional payment increasing by 1; substitute for in denominator to get due form.

: PV of an annuity-immediate with first payment and each additional payment decreasing by 1; substitute for in denominator to get due form.

: AV of an annuity-immediate with first payment and each additional payment decreasing by 1; substitute for in denominator to get due form.

: PV of a perpetuity-immediate with first payment 1 and each additional payment increasing by 1.

: PV of a perpetuity-due with first payment 1 and each additional payment increasing by 1.



Additional Useful Results:
: PV of a perpetuity-immediate with first payment and each additional payment increasing by .

: PV of an annuity-immediate with m-thly payments of in the first year and each additional year increasing until there are m-thly payments of in the nth year.

May God Have Mercy on Your Soul:
: PV of an annuity-immediate with payments of at the end of the first mth of the first year, at the end of the second mth of the first year, and each additional payment increasing until there is a payment of at the end of the last mth of the nth year.

: PV of an annuity with continuous payments that are continuously increasing. Annual rate of payment is at time .

: PV of an annuity with a continuously variable rate of payments and a constant interest rate.

: PV of an annuity with a continuously variable rate of payment and a continuously variable rate of interest.

Payments in Geometric Progression:
: PV of an annuity-immediate with an initial payment of 1 and each additional payment increasing by a factor of .

Chapter 5:
Definitions:
: payment at time . A negative value is an investment and a positive value is a return.

: PV of a cash flow at interest rate .

Chapter 6:
General Definitions:
: payment made at the end of year , split into the interest and the principle repaid .

: interest paid at the end of year .

: principle repaid at the end of year .

: balance remaining at the end of year , just after payment is made.

On a Loan Being Paid with Level Payments:
: interest paid at the end of year on a loan of .

: principle repaid at the end of year on a loan of .

: balance remaining at the end of year on a loan of , just after payment is made.

For a loan of , level payments of will pay off the loan in years. In this case, multiply , , and by , ie etc.

Sinking Funds:

: total yearly payment with the sinking fund method, where is the interest paid to the lender and is the deposit into the sinking fund that will accumulate to in years. is the interest rate for the loan and is the interest rate that the sinking fund earns.



Chapter 7:
Definitions:
: Price paid for a bond.

: Par/face value of a bond.

: Redemption value of a bond.

: coupon rate for a bond.

: modified coupon rate.

: yield rate on a bond.

: PV of .

: number of coupon payments.

: base amount of a bond.



Determination of Bond Prices:
: price paid for a bond to yield .

: Premium/Discount formula for the price of a bond.

: premium paid for a bond if .

: discount paid for a bond if .

Bond Amortization:
When a bond is purchased at a premium or discount the difference between the price paid and the redemption value can be amortized over the remaining term of the bond. Using the terms from chapter 6:
: coupon payment.

: interest earned from the coupon payment.

: adjustment amount for amortization of premium ("write down") or

: adjustment amount for accumulation of discount ("write up").

: book value of bond after adjustment from the most recent coupon paid.

Price Between Coupon Dates:
For a bond sold at time after the coupon payment at time and before the coupon payment at time :
: "flat price" of the bond, ie the money that actually exchanges hands on the sale of the bond.

: "market price" of the bond, ie the price quoted in a financial newspaper.

Approximations of Yield Rates on a Bond:
: Bond Salesman's Method.

Price of Other Securities:
: price of a perpetual bond or preferred stock.

: theoretical price of a stock that is expected to return a dividend of with each subsequent dividend increasing by , .

Chapter 9:
Recognition of Inflation:
: real rate of interest, where is the effective rate of interest and is the rate of inflation.

Method of Equated Time and (Macauley) Duration:
: method of equated time.

: (Macauley) duration.

Volatility and Modified Duration:
: PV of a cash flow at interest rate .

: volatility/modified duration.

: alternate definition of (Macauley) duration.

Convexity and (Redington) Immunization:
convexity

To achieve Redington immunization we want:



Download this formula summary:
Prints nicer than this post too.
Attached Images
File Type: pdf FM Formulas 2.01.pdf (110.6 KB, 20038 views)

Last edited by no driver; 11-14-2006 at 03:02 PM..
Reply With Quote
  #5  
Old 10-13-2006, 07:02 PM
ebony's Avatar
ebony ebony is offline
Member
SOA
 
Join Date: Mar 2006
Studying for CSP - GH
Favorite beer: +Hb!l pnq
Posts: 985
Default

Sweet No Driver. Your awesome for this!
Reply With Quote
  #6  
Old 10-13-2006, 07:35 PM
MyKenk's Avatar
MyKenk MyKenk is offline
Note Contributor
CAS AAA
 
Join Date: Nov 2005
Location: twitter.com/mykenk
College: Drake '06
Posts: 8,595
Default

That's a lot of formulas... I'm gonna stick to memorizing the 6 or 7 that I plan to memorize... but very impressive, none-the-less! You have the time to put this together... you're probably ready.
__________________
Reply With Quote
  #7  
Old 10-19-2006, 09:50 PM
hao_sarah hao_sarah is offline
 
Join Date: Aug 2006
Posts: 4
Default

Thank you for sharing.
Reply With Quote
  #8  
Old 10-28-2006, 07:17 PM
beck beck is offline
Member
 
Join Date: Oct 2006
Posts: 349
Default

thx for this nice and long summary, no driver... amazingly i recognize and remember most of those formulas, doing tons of questinos really do help : D
Reply With Quote
  #9  
Old 10-28-2006, 07:18 PM
Buzz Lightyear's Avatar
Buzz Lightyear Buzz Lightyear is offline
Notes Contributor
CAS
 
Join Date: Aug 2006
Favorite beer: Excuse me, I think the word you're searching for is "alcoholic malt beverage".
Posts: 337
Default Using the BAII Plus workbook to calculate duration and convexity

The following is an outline of how the BA II plus calculator workbook can be used to calculate the Macaully Duration, Modified Duration and Convexity of a bond for short duration bonds quite easily. I will use the question below to help illustrate: -

Quote:
A 2-year bond has an annual coupon rate of 10% and makes semiannual coupon payments. At the end of the 2 years, the bond's par value of $100 is repaid. The yield on the bond is 10% compounded semiannually.

Calculate the convexity of the bond.
First create a table like the screenshot below.




The following letters are assigned for calculations: -
m = coupon frequency/year
r = annual effective interest rate
Calculating the price
  • Enter the original coupon and redemption value data into the fields of the CF worksheet on your calculator.
  • Press the NPV key, enter the interest rate (i.e. 5% for this question), and CPT NPV.
    In this question it is obviously 100 as the coupon rate and the yield rate are equal.
  • Save this value into the memory.
Calculating the Mac Duration
  • Return to CF.
  • Change C values to "Cash Flow * t" values.
  • CPT new NPV (call NPV'), and save to different memory.
Quote:
D(MAC) = (1/m)*(NPV'/NPV)
For example D(MAC) = 1/2 * 372.3/100 = 1.86

Modified Duration
Quote:
D(MOD) = D(MAC)/(1+r)
Calculating the Convexity
  • Return to CF.
  • Change C values to "Cash Flow * t^2" values.
  • CPT new NPV (call NPV''), and save to different memory.
Quote:
Convexity = (1/(1+r)^2) * [(1/m^2) * (NPV''/NPV) + D(MAC)]
For example Convexity = (1/(1.05)^4) * [1/4 * (1443.9/100) + 1.86] = 4.50

Credit: Credit where credit is due. I learned this method using Yufeng Guo's awesome manual for FM.
Attached Images
 
__________________
Spoiler:

Pure Nerd
52 % Nerd, 0% Geek, 0% Dork

Last edited by Buzz Lightyear; 10-28-2006 at 07:22 PM..
Reply With Quote
  #10  
Old 10-28-2006, 11:21 PM
hokensuri hokensuri is offline
Member
 
Join Date: May 2006
Posts: 106
Default

Have you tried the question below using the formula shown above?

http://www.math.ilstu.edu/krzysio/KO-FM-Exercise4.pdf
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


All times are GMT -4. The time now is 10:47 PM.


Powered by vBulletin®
Copyright ©2000 - 2018, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.43658 seconds with 10 queries