Jan 14

FRM 2008 Early Bird - Episode #1

by David Harper, CFA, FRM, CIPM

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Contents

  • About the Early Bird
  • Learning Objectives
  • Video tutorial
  • Practice Questions (4)

About the Early Bird

Hello! You are receiving this email because you are interested in the Early Bird 2008 FRM candidate preparation. If that is not true and/or you do not wish to receive "early bird" assistance, please click here to unsubscribe

The Early Bird preparation is a new service this year, provided by the Bionic Turtle. Several customers asked for help in getting an early start on the FRM. In particular for 'quant.' This Early Bird preparation is our answer and will focus on quantitative methods. If you have questions, the best thing to do is to post them on the forum located here. Why? Primarily because somebody else probably has a similar question and there are no dumb questions. If we share on the forum, everybody benefits!

Here is how the early bird prep works. We send you an weekly email on Monday with (i) a learning objective(s), (ii) a link to a brief tutorial to view, and (iii) a link to practice question(s) that relate to the learning objective. You will be tempted to skip the practice question (after all, November is eleven months away!). I ask that you try to get into the habit of doing a few practice questions immediately! If the questions are good, there is simply no better way to gain a deeper understanding of the material.

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Learning Objectives (ideas to ponder)

  • Greek notation
  • Random variables
  • Functions of random variables
  • Brief introduction to matrices

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Video Tutorial

The 55-minute video tutorial is located here (with a table of contents).

If you are a paid member, you can also access this in the member section (where you will also find the downloadable slides, if you would like to view those. As well as an ipod format file.)

About the Practice Questions

I crafted (or selected) practice questions that I think will help you best prepare. Occasionally, the practice questions will be difficult and/or refer to topics that we have not yet addressed. Please do not get frustrated; try and see these questions merely as a means to learn the material. For example, consider the first practice question:

  • Gives you practice on a probability question
  • But it is compound in three parts: the first part is easier than the third part. You may not be able to answer the third part. No matter, just view that part as a "muscle stretch."
  • It introduces definitions you may or may not know (credit default basket swap) and a key concept yet to be discussed (default correlation). Don't worry about that. I am just trying to applied questions whenever possible.

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Four Practice Questions

Here are this week's practice questions. These four questions relate to the first tutorial:

Question #1

A credit default swap basket contains 10 bonds. The probability of default (PD) for each bond is 5% and the probability of default for each bond is independent of other defaults (i.e., default correlations are zero). What is the probability that (i) no bonds default, (ii) at least one bond defaults, and (iii) exactly one bond defaults?

Question #2

Let an expected credit loss (EL) equal the product of the probability of default (PD) and the loss given default (LGD). Specifically, EL = (PD)(LGD). Let's assume (unrealistically) that PD and LGD are both discrete random variables. PD is a random variable with four outcomes: {1%, 2%, 3%, or 4%} and LGD is a random variable with four outcomes: {20%, 30%, 40%, 50%). In both cases, each outcome is equally likely; i.e., both are characterized by a discrete uniform distribution. For example, there is a 25% chance that PD is 1%, a 25% chance that PD is 2%, and so on.

(i) What is the standard deviation of the probability of default (PD), as an independent, discrete random variable?
(ii) What is the expected loss (EL) if PD and LGD are independent?
(iii) Assume that PD and LGD are perfectly correlated; e.g., if PD is 1%, then LGD is 20%, if PD is 2%, then LGD is 30%, and so on. What is the expected loss (EL) under this scenario of perfect correlation?

Question #3

If an investment grows at 8% per year continuously compounded, (i) how many years until the investment doubles from (X) to (2X). (note that we do not need to know the size of investment X). (ii) if an investment compounds continuously at 8% in the first year and 6% in the second year, what is the implied annualized growth rate, for the two year period, on an continuously compounded basis (continuously compound annual growth rate, CCAGR)?

Question #4

Consider a three-asset portfolio consisting of three stocks called A, B, and C. The stocks are weighted, respectively, 20%, 30% and 50% (weight A = 20%, weight B = 30%, and weight C = 50%). The volatility (standard deviation) of returns for all three assets is 20%. The covariances are as follows: COVAR(A,B) = 0.09 = 9%, COVAR(A,C) = 0.16 = 16%, COVAR(B,C) = 0.01 = 1%. Using matrix math, calculate the three-asset portfolio variance.

Answers to practice questions

That's all for this week. I hope this is helpful and I will see you next week!

David Harper, CFA, FRM, CIPM
Founder
www.bionicturtle.com

Comments

  1. Telon 15 Jan 2008

    Hi David,
    Could you kindly clarify why the 0.09 in the covariance matrix whilst the covariance (A, B) = 0.9

    Thanks.

    Telon

  2. David Harper, CFA, FRM, CIPM 15 Jan 2008

    Hi Telon,

    My mistake. Apologies. The question (now corrected) should say COVAR (A,B) = 0.09. Thanks for spotting that…

    David

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