FSA Exam Advice from a Grader

Mary Pat Campbell

In May 2007, I was taking Exam APMV; in November 2007, I was grading Exam FET. I had always promised myself that once I had achieved FSA status, I would grade an exam at least once, to learn more about the process if nothing else. I recommend others to also make this pledge; some of the mysteries of the exams will be dispelled, and also you get to be involved in safeguarding the value of your credential.

Though the FSA exams do not seem as cut–and–dried as the multiple choice preliminary exams, there are some basic principles to follow in answering questions. The items below are my own advice and observations from taking (and passing) 8V and APMV, as well as from grading FET. They do not represent official SOA advice, though some of these points can also be found in the SOA online catalog as official recommendations.

There are two broad areas of FSA exam questions: analysis and numerical. I will deal with each of these in turn.

Answering analysis questions

Orin Kerr, a law professor who blogs at the Volokh Conspiracy, had a post on first year law exams and how to answer them.¹ Prof. Kerr categorizes the exam answers as five types, ranging from terrible to terrific, and much of what he says pertains to the types of answers graders are looking for on analysis questions. Here's the key point from Kerr:

I think the basic advice is that precision and explanations are everything. To get a top grade, a student needs to identify the relevant legal question accurately, and then articulate exactly why applying the law to the facts leads to a particular outcome. Of course, when stated that way, the advice sounds pretty general. At bottom it just means that you need to show your professor that you are an excellent lawyer. Which of course is exactly the point.

The point of the FSA exams is similar: the SOA is trying to determine who will make an excellent actuary by determining who understands the material in the course of reading. In answering analysis questions on the exams, you need to identify the relevant readings and facts, and apply them to the problem at hand.

Let's consider a hypothetical problem on an exam:

You are going to hedge some VA return–of–premium maturity guarantees with stock index options, and want to model the cost of the hedge program using Black–Scholes pricing. Describe the assumptions made in Black–Scholes pricing, how each assumption can be adjusted to be more realistic, and what effect these adjustments have on option prices.

Again, the following is my personal advice for dealing with analysis–type problems–note that this is not necessarily how the grading outlines are set up, but it was how I made sure I covered all the bases, and also make sure I did not waste time grasping for lists in my head.

First I would spit out relevant definitions, lists, or formulas; anything that is rote memorized should be spat out ASAP as that short–term memory is the most likely to decay. So for the above, I would list all the assumptions that go into Black–Scholes, without elaborating on adjustments and effects on option prices.

Then I would go down the list of assumptions, indicate how realistic each is, how one would adjust (for example, discounting for dividends), and what the likely effect the change would be on the modeled price. In writing out the assumptions list, I could have put each list item with lots of space underneath each to write in these effects, but my preferred method would be to spit out any regurgitated knowledge first, with no excess space, and then go down in a separate list, item by item.

Underneath the item–by–item list, I might put in a few more points, if some of the assumptions interact, sometimes counteracting and sometimes amplifying the effects. I could also make a little table, showing how the price for European vs. American options, put vs. call options, etc., differ in making these adjustments.

In writing these lists and explanations, I would not bother to write in complete sentences, but rather in coherent phrases. I would number the list items to make it easy for me to keep track of what I covered, and also to make it easy for the grader to follow, especially if I separate the initial list of assumptions from the subsequent list of adjustments and their effects. If I know there are five items on the list, but can only remember four, I will leave one numbered item there to remind myself that I'm missing something. But I would not spend much time trying to remember that final item, and simply move on and go back to it later, if at all.

For the name of the game is to get as many points as possible. There is a grading outline for each question, with a certain number of points granted for making a particular statement or getting a particular result; you do not need to get all the points to "max out" on a question. For the problem example I gave above, if there were five points on the list and I made only four of them, that may well be enough to max out on the grading rubric.

As well, the graders will amend the grading outline if they see acceptable answers/statements on actual papers that don't appear on their original grading outline. It is also okay to incorporate some info from sources outside the official course of reading, but it's best to keep that light, and to note it when you do it. The grading outlines are based on the official course of reading; sometimes the problems are based on a single study note, and sometimes it weaves together information crossing several different study notes. The most likely amendments to grading outlines are items omitted that came from the official course of reading. True statements that come from outside the course of reading might be added to the outline, but it's not that likely. Concentrate on getting the material from the official syllabus.

And to get the greatest number of points: answer the question as given.

You will not "lose" points for putting irrelevant stuff in–the grading outlines are additive, so you can only add up more points. However, you're just wasting time if you add in stuff that has nothing to do with the original question. The idea is to use your exam time effectively–add to your answers in a way that gives maximum marginal impact to your final score. So adding tangential points to a problem that you've pretty fully–fleshed out will be less useful than adding a few relevant points to a question you've got very little on already.

For example, suppose on the Black–Scholes example problem, I decide to take a detour to talking about variable annuity guarantees in general, after having answered the actual question. I probably should have revisited a different question if I have that much time to waste. If you've got a slam dunk on a question, you're probably not really boosting your overall score by spending time on it. Go back to a problem that you're somewhat sketchy on, if you think you can answer some more, no matter how halting. Make sure you set yourself a time limit on every question (three minutes per point), so that you make sure you get to other questions; you don't want to fail because you ran out of time writing a 10–page–thesis on a six point question.

Also, while you don't lose points for putting down irrelevant info, you will get no points for an item if you contradict it. To go back to the Black–Scholes example, if I said an adjustment increased the price of an at–the–money put option, and then said that it decreased the price of the same option, then no points would be given at all. It would be obvious to the grader that I was trying to cover all bases, and that I really didn't know the answer.

Finally, make sure that if you're asked for a recommendation, that you make a recommendation. If you're asked a yes or no question, answer yes or no. The greatest number of points is allocated to the reasoning behind a recommendation or decision, but the decision or recommendation itself is accorded a non–zero amount of points.

Answering Numerical Questions

Even if you run into trouble on a numerical problem, in terms of actually being able to solve a certain set of equations (say), you can score rather well. I ran into a lot of trouble on some numerical problems on the Fall 2006 8V exam, but my overall score ended up very good. Here is a general way to attack a numerical problem, especially one you're having trouble getting through all the way to the end, whether due to time or just running into a mental roadblock.

1. Write down any relevant formulas, no variables replaced by numbers.
2. Identify any variables that you have numbers for (time, interest rate, probabilities, etc.)
3. Describe the process you're going to use in general terms
4. Actually do the calculations. If it involves something done repeatedly, such as filling out multiple time period binomial trees, show the full work at least once, to show you know how to do one iteration.

If at any point you run into a roadblock, because you can't solve for something you need for the next step, just assume some reasonable value for the answer and explicitly state what you're doing.

I used this process when I ran into my nemesis question: #16 on Fall Exam 8V, which involves solving for a barrier option price by taking regular stock option prices and replicating the payoffs on a grid. I had gone over a similar example in Hull the very night before, but I just couldn't get the numbers to work out. I kept messing up a key calculation step, but did not realize it at the time. I realized early on I was hitting a wall and so I dropped working on the problem to deal with others before returning to it.

First, I wrote down the idea behind trying to determine a barrier option price by cobbling together "plain vanilla" options: one would get the static replication to match up to the value of the barrier option on the boundaries, to make a good approximation to the solution. Then I noted the boundaries on which I was trying to match, and what the values were along that boundary. Then I indicated that I knew I had to start at the terminal boundary (i.e., at maturity) and then work backwards, and determining previous values of various options with the table like so (and showed how the equations were set up).

And then I went back to the wall, hitting my head against it, and not getting past putting the first option in.

Although I passed that exam, I will never find out how I did on that particular question. The point is I set myself up for getting maximal points even though I couldn't actually calculate anything as I never got past the first step. The process is generally more important than the actual numerical answer.

As I mentioned above in the analysis section, grading is additive. You can get points only for what the graders see. Yes, of course you can get full points for working through the problem without showing the unaltered formulas, without showing every little step, and without explaining the process before doing it–if you do it completely correctly.

But what are the chances of that happening?

You might key a number into your calculator incorrectly, or switch a sign by accident, and then you can end up with minimal points because you didn't show the interim steps. In contrast, by explicitly outlining the process for solving the problem and showing a logical flow, you may get close to a perfect score, even if you screw up a few numbers.

Also, at this level of actuarial exam, if you have a numerical problem (at least for APMV), chances are good that it will be a multi–step problem. If you can't do one of the earliest steps, you need to be able to continue so that the only points you miss out on are from that first step. Also, it is only common courtesy to indicate to the graders that you don't know how to solve that part (or don't have enough time), so you're just going to assume the solution (such as "I assume the discount rate is 5 percent, as I can't do this step.") You will not lose extra points by making this admission, and it will save the grader the effort of trying to figure out just where you got the number from.

Remember: be nice to the graders! Do not waste their time. They have to read your complete papers, looking for any possible points, even if you decide that you're going to spend your time writing pleading notes or go on a tangential disquisition on the essence of randomness where the question asked for techniques for reducing variance in Monte Carlo simulations.

To that end, make your paper easy to follow and easy to read. I'm sure the trees will forgive you if you leave huge empty spaces between steps of your problem, or draw up your binomial tree to take up the entire page (I did that on one problem). If the grader can't see what you did, they can't give you points for what you did correctly.

To that end, as well, I encourage exam–takers to number their pages for each problem (separately). Suppose one question takes five pages; I would number in the upper right–hand corner: "Page 1/5," "Page 2/5," etc. There are a few reasons for this–courtesy to the grader is the first. Your exam papers can get out of order before the SOA sends them to the graders, so numbering will make it easier for the graders to follow the flow. More importantly to the exam–taker is that if a page is missing from your solution, numbering the pages will make this evident. Graders notify the SOA if we think papers or pages are missing, but we won't be able to tell if you don't number your pages.

Remember, these are my personal tips. In ye olden days (i.e., the 2000 exam system), you would have Courses 5 and 6 to ease you into written exams. In the new system, the FSA exams will be very different from what came before in your actuarial education.

For more information on exams, please consult the SOA Spring 2008 catalog.

¹For more on the The Volokh Conspiracy. "Bad Answers, Good answers, and Terrific Answers," please visit http://volokh.com/archives/archive_2007_02_11-2007_02_17.shtml#1168382003.