# Eighty Three Days Until Exam FM

I scheduled my exam yesterday, for exactly eighty-three days from now.  I am well over the hump with studying.  I can work exam level problems on all of the interest theory material, but I have a long way to go with derivatives markets.  So, my goal until the end of December is to keep working interest theory exam problems, filling in missing bits when I find them, while I pour over the derivatives markets material.  By January I will be taking practice tests every other day, while I review solutions on the off days.

Most recently, I am working with duration and convexity.  This is good, meaty stuff, with many different levels of understanding.  I will be doing a post on it tomorrow.  I will also be posting on how to best arrive at a correct answer on these computationally complex problems, as well as posting some computation exercises.

# The Cards

Cutting them up:

I have owned this paper cutter for 25 years.  At that time, I did not own much but the clothes on my back.  How would I have survived without a paper cutter to make little books and cards and such?

Things that I gained by making these cards:

1. A strengthened knowledge of FM fundamentals.
2. Increased fluency with LaTeX.
3. A creative project which kept me focused on the subject at hand.
4. A nice little pile of finished cards.
5. Time to think about the pluses and minuses of virtual products versus actual.

# Exam FM, Chapter 1 Flashcards

I just posted my nearly final version of the first chapter of flashcards for exam FM.  I added some questions on geometric progressions, and some on force of interest, so now there are 226 cards.  I know that there are still a few holes, but I will worry about that later.  I could probably come up with 300 cards for the first chapter very easily.  But, having put together several sets of study cards, I find that I add fewer cards for subsequent topics.  In almost any subject, the most vital information to commit permanently to memory is at the beginning.

I tried to use a sampling of the different terminologies.  For instance, I used the accumulation function $a(t)$ as well as the FV, PV terminology.  When I look at the solutions for the exam sample questions, I see both types used, so I suppose that it is possible for either to appear in an examination question.

For most formulas, I give several types of numerical examples.  It is important to see the relationships at work.  To see the animals in their native habitat.

In a later post, I will describe how to use these cards to best effect.  I do intend them as a means of permanently learning the material.

# Another Update on Exam FM Flashcards

I updated my Financial Mathematics cards again this morning. The link from a couple of days ago reflects the updates. There are now 190 cards.

The cards are in the form of a PDF file, to be printed on letter size paper (8.5 x 11 in). Many printers do not print the front and back of each page in good alignment, so I made sure not to place text too near the borders of the back of the cards.  Simply print the cards out, cut a 1cm border from around the page, then cut the cards out.  Whoops!  I have mixed inches and centimeters.  I will straighten out the unit issue on the next version, with a 1/2 inch border.

I am trying to really fill out most of the fundamentals.  This makes the cards useful not just for someone studying for the actuary exams, but also for anyone learning the basics of finance.

Let me know how the cards work for you, or if you find any errors.

# Nearly done With First Chapter of Cards

I have just updated the first chapter of my Financial Mathematics cards.  (link is on post from a couple of days ago).  The deck is up to about 160 cards.  I am looking at the exam FM syllabus, plus some books, and filling in topics.  Next week the first chapter will be finalized, and I will post a permanent link on the sidebar.

Later, I will post some advice on how these cards are intended to be used.  In essence, these cards reinforce the fundamental pieces that go into solving difficult problems.  They certainly do not replace solving tough problems, or replace learning the concepts.  Often, they may suggest new ways of solving complex problems.  I intend them to be used along with a pencil, paper, and calculator.  Setting up the solution is more important than a numerical answer, however.  The numerical cards are intended more as ways of recognizing and reinforcing the fundamental equations and relationships.

I can’t wait to finally post my Exam P cheat sheet.  LaTeX is great 🙂

I have been working hard today.  Here is a PDF of the first draft of my exam FM flashcards.  So far, they just cover “chapter 1” stuff like Interest Theory and Lump Sums.  I think that there are about 110 cards so far.  I will soon be fleshing out the missing Interest Theory topics, then I will add the Annuity cards that I have made.

I am delighted to have used LaTeX to design the cards.  They are 2 cards by 5 cards on a letter size page.  This is a standard card size, which you can buy paper for at the store.  I will add some cut marks when I figure out how.

More tomorrow.

# Update on Card Formatting

Yesterday, I posted this flash card as an example:

When I did my repetitions this morning, I realized that this card, and several similar ones that I created yesterday, are too complicated.  Cards should only test one very small item of knowledge. (Read SuperMemo 20 Rules of Formatting Knowledge)  The cards from yesterday test not only the function of the “a angle n” function, but also require a calculation with this function.  A much better card is as so:

The wording of the card now makes it obvious that I am not looking for a numeric answer.  The purpose of this card is simply to help the mind to recognize and recall a common relationship that involves the present value of the annuity immediate.

# The Annuity Symbol in LaTeX and Anki

As you know, one of my favorite creative projects is to create Anki flashcards using the LaTeX markup language.  I have written about some of the process on this blog.  Originally, I needed to install MiKTeX on my system.  Now, Anki can interpret the language when it sees it.

My recent problem has been to format the symbols for annuities.  That looks like so:

Which is read as “a angle n”, and:

Which is read as “a double dot angle n.”

It gets really annoying to write and interpret things like “a double dot angle n;”  that is where the proper symbols come in.

First, I discovered that there is an \actuarialangle command which has been recently added to the MiKTeX library.  Open the Package Manager on MiKTeX, and you may install it.  To activate it in Anki, you need to use some code, in the usepackage line in the preamble of your cards.  See below.

I also discovered the lifecon package on the web.  This contains all sorts of actuarial symbols, but you need to know how to add a package to MiKTeX directly with a .sty file.  I had a little trouble with this task.

The alternative to both of the above solutions is to add some code into the preamble of your document, that defines a new LaTeX command.  There are several versions of this floating around.  The following is what I used:

\DeclareRobustCommand{\lcroof}[1]{
\hbox{\vtop{\vbox{%
\hrule\kern 1pt\hbox{%
$\scriptstyle #1$%
\kern 1pt}}\kern1pt}%
\vrule\kern1pt}}
\DeclareRobustCommand{\angle}[1]{
_{\lcroof{#1}}}

In Anki:

1. Hit the button to add a note.
2. Hit the button to choose the note type.
3. Select “Options”
4. Cut and paste the above code into the header, just under “\usepackage{amssymb,amsmath}”
5. Now you may use the \angle command in your cards.

Here is an example:

I put things on cards that I figure I should be able to solve nearly instantaneously.  The notes on the bottom of the card are to refresh my mind, if I have forgotten.  The numerical answer is not really very important, the real thing is reading the problem, and visualizing a solution.  Real test problems, and real life problems, are much more complex than the ones I put on my cards.  But the component parts need to be solved quickly, with confidence.

I am so happy now that I have annuity symbols appearing correctly.  I think that I will go make some flashcards.

# The Importance of Meta Learning

I tend to use a variety of meta-learning techniques.  The first one is simply to monitor my daily work and progress.  I have notebooks from 30 years ago filled with my daily juggling notes, notebooks from 20 years ago full of daily banjo progress, and notebooks going back 10 years full of mathematical success and failure.  Other notebooks on my shelf document medical progress.  If I look, I could find the note from 1988 when I first was strong enough to drive a stick shift, a year after my 1987 automobile accident.

Here is a photo of what some of my notebooks look like at this very moment:

If you are curious, here is a random page from a random notebook:

December 15, 2003

New Things I’ve done in the last 5 days

1. Flown in an airplane
2. Seen the Pacific Ocean
3. Been in California
4. Seen the Bush Man
6. Rode on a cable car
7. Been in San Francisco
8. Been in Hyde Park
9. Been in the Redwood forests
11. Ate Sushi
13. Been in a telecommunications switching facility
14. Saw Alcatraz
15. Crossed the Golden Gate Bridge
16. Flown over Salt Lake City

When working on a computer, there are other simple ways to document ones progress.  Here is a picture of the current graph of my progress on the 153 SOA sample problems:

The graph goes back about 70 days, and simply shows how many of the problems I solved each day (about 15, on average).    Those problems are only part of my daily studying.

By the way, 31 days left!!

# Sorry, More Technical Stuff

Currently, I am coming to grips with the law of total variance.

In words, the variance of X equals the variance of the expected value of X, given Y, plus the expected value of the variance of X, given Y.

In symbols, Var(X) = Var(E(X|Y)) + E(Var(X|Y).

By reading the verbal definition, one can see that the logic is convoluted. Given two probability distributions, it can be tricky to see how to apply the law. Once the law is applied, there are additional tricky steps of logic involving the independence of variables.

From the SOA/CAS sample problems:

A motorist makes 3 driving errors, each independently resulting in an accident with probability 0.25.  Each accident results in a loss that is exponentially distributed with mean 0.80.  Losses are mutually independent and independent of the number of accidents.  The motorists insurer reimburses 70% of each loss.  Find the variance of the total unreimbursed loss.

The above item illustrates the technical problem that I have been having when using Spaced Repetition Software to schedule repetitions of complex material.

When I encounter a difficult item, I spend time exploring the given solution, and alternate solutions. Eventually, I move on to another item. Most likely, I am not entirely comfortable with the material, and I would like to see the same material every day for a while, to approach it with different solutions. The way that the defaults on SRS software are set up, as soon as you start rating an item anything other than the most difficult setting, the item starts getting pushed off way into the future. After a week or two weeks, I have entirely forgotten many of the finer details of the item, and it is almost as if I am starting from scratch.  For difficult material, it is beneficial to see the same items every day, or every 2nd or 3rd day.

The solution to this problem is to reset the forgetting index. In Anki, I have now set my forgetting index to 3%. This task is done by downloading the shared “Forgetting Index” plugin. In the “File” menu, select “Download Shared Plugin”, and find the forgetting index plugin.

The result is that I can now look at problems on a nearly daily basis before they start whizzing into the future. Each time I look at the problem with fresh eyes, I observe new things.

In the last week, I finally have my Spaced Repetition Software working to its utmost. I use it to schedule repetitions of difficult exam problems, and of memorization items. These are two fundamentally different tasks, so it is important to set up Anki (the software that I am now using), in two different ways.  After spending time every day for a week with the above “unreimbursed loss” problem, I look at it, and think “piece of cake.”  Now, when I encounter other law of total variance situations, I have several good comparison problems stashed away in my head.