mfe mailbag sep 2011 fall 2011 - bpptraining.com mailbag (sep 2011) fall 2011.pdf · bpp q&a...

Exam MFE/3F Student mailbag

© BPP Professional Education: 2011 exams

STUDENT MAILBAG

Student questions and errata (September 23, 2011)

Contents:

Questions frequently asked by students together with answers from BPP’s team of actuarial educators

Errata for the Fall 2011 edition of the BPP Course MFE course notes.

Frequently asked questions

Q: What is the current position regarding rounding when using the normal distribution?

A: The MFE exam is now computer-based and you will have instant access to an on-screen normal distribution calculator (which is very easy to use). The exam instructions now say that you should enter 5 decimals, eg (0.12345) 0.54912N , and use the full 5 decimal answer

in your calculations.

The exams in previous sessions used a printed table of the normal distribution (*), which only allowed you to look up values based on two decimal places, eg (0.12) 0.5478N , and

the exam instructions previously said that you should round values to 2 decimal places before using the ( )N function and that you should not apply any interpolation in your

calculations.

We have assumed that while you are studying for this exam you will be using the printed table of the normal distribution. So the examples in the BPP course materials and the BPP Practice Exams assume that you will follow the convention of rounding to 2 decimals. This will also allow you to work through the published past exam questions and the SOA sample questions for this subject without encountering any discrepancies.

* You can download the normal distribution table from the SOA website or you can refer to the copy we have reproduced on the next page.

Student mailbag Exam MFE/3F


Source: http://www.soa.org/files/pdf/edu-2009-fall-mfe-table.pdf



Q: How can I tell which questions in the BPP Question & Answer Bank are based on past exam questions or sample questions from the SOA website?

A: Where the BPP questions are based on questions from these sources we have indicated this next to the question number in the Q&A Bank. We’ve also included a grid at the end of this document, which shows the exact correspondence between the BPP questions and the questions they are based on.

Q: I tried to use the formulas ( )r h hu e and ( )r h hd e in conjunction with the one-step binomial tree illustration in Example 2.1 and I got some strange answers. What is the reason for this?

A: The values for the two future stock prices, 1 60S and 1 30S , used in this example (and

some of the ones in the Question & Answer Bank, and also Question 7 from the May 2009 exam paper) have just been chosen as convenient “round” numbers to illustrate the method. They have not been derived from an underlying assumption about the volatility parameter . So you may get some inconsistent answers if you make this assumption. In fact, there are several different methods that have been proposed for calculating the factors u and d (see Section 3.5), which are based on different underlying assumptions.

Note, however, that the formula ( )

*r he d

pu d

for the risk-neutral probability will always

apply, as this is not based on an underlying volatility assumption. In fact, you can see from this formula that, in order to ensure that the risk-neutral probability is in the range 0 1p (which is required in order to prevent arbitrage), the only restriction on the one-

step binomial model is that ( )r hd e u .

Q: The solution to Question 9 from Chapter 9 of the Question & Answer Bank refers to the Central Limit Theorem, which I haven’t come across before. What is this?

A: If you take a large sample (size n ) of values from a particular distribution (not necessarily,

a normal distribution) that has a mean of and a variance of 2 , the Central Limit

Theorem says that the sample mean X will have a distribution that is approximately a

normal distribution with mean and variance 2 n .

This result can be used, in conjunction with the usual properties of the normal distribution, to assess the accuracy of results obtained using the Monte Carlo method.



Q: Can you explain more about the difference between risk-neutral probabilities and real-world probabilities? How do you calculate the real-world rate of return?

A: The risk-neutral probabilities (which are p* and 1-p* for a one-step binomial tree) are the most important ones in the theory of options. These are the ones that are used to work out the theoretical option price. If we carry out calculations based on the risk-neutral probabilities, the rate of return earned on all the assets we are interested in (cash, the underlying asset and any derivatives) equals the risk-free interest rate.

However, if you were considering actually buying an option, you would want to know what rate of return you could expect to get. How much is the value of your option likely to go up (or go down) during the period you own it? To work this out using a binomial tree, you need to know what the actual probabilities of the underlying asset price going up or down are. If there's a 90% chance of the stock price going up, a call option would give a very good return, but not if the probability was only 10%. These probabilities are usually called "real-world" probabilities and are written as p and 1-p. Of course, they are entirely subjective, because nobody can say what the actual probabilities of the stock price going up or down are!

To calculate the real-world rate of return , you need to construct an equation of value. For example, the price of the call option in Example 2.1 is 5.73. If the real-world up and down probabilities are p = 0.9 and 1-p = 0.1, we can write down the following equation:

option price discount factor expected payoff

5.73 (0.9 15 0.1 0)e 85.7%

This is an application of the equation in the box on page 48 of the text.



Errata

A. BPP Course Notes

Chapter 4 (The Black-Scholes formula), Page 89

In Example 4.5 the next-to-last value of the stockmarket index for Period 2 should be 4903, not 4902. The calculations in the solution are correct.

B. BPP Course Notes – Practice Questions (at end of chapter)

(none)

C. BPP Question & Answer Bank

Question 7.35

The ( )X t h and ( )X t in item (i) should be ( )S t h and ( )S t .

D. BPP FlashCards

(none)

E. BPP Practice Exams

Practice Exam 2, Question 22

The question should include an extra piece of information: “Any cash payments from the cash-or-nothing options are equal to the strike price.”



Sources of Q&A Bank questions

BPP Q&A Bank SOA Sample Questions May 07 Exam May 09 Exam

Q1.26 Question 9 Q1.27 Question 12 Q1.28 Sample Question 1 Q1.29 Sample Question 2 Q1.30 Sample Question 26

Q2.17 Question 1 Q2.18 Question 2 Q2.19 Question 14 Q2.20 Question 3 Q2.21 Question 7 Q2.22 Sample Question 27 Q2.23 Sample Question 39 Q2.24 Sample Question 49

Q3.25 Question 11 Q3.26 Question 1 Q3.27 Sample Question 4 Q3.28 Sample Question 5 Q3.29 Sample Question 44 Q3.30 Sample Question 45 Q3.31 Sample Question 46

Q4.28 Question 3 Q4.29 Question 5 Q4.30 Question 8 Q4.31 Question 15 Q4.32 Question 13 Q4.33 Question 17 Q4.34 Question 19 Q4.35 Sample Question 6 Q4.36 Sample Question 8 Q4.37 Sample Question 17 Q4.38 Sample Question 19 Q4.39 Sample Question 20 Q4.40 Sample Question 28 Q4.41 Sample Question 31 Q4.42 Sample Question 33



Q4.43 Sample Question 36 Q4.44 Sample Question 41

Q5.23 Question 10 Q5.24 Question 19 Q5.25 Question 8 Q5.26 Question 20 Q5.27 Sample Question 16 Q5.28 Sample Question 47 Q5.29 Sample Question 9 Q5.30 Sample Question 18 Q5.31 Sample Question 23

Q6.26 Question 4 Q6.27 Question 17 Q6.28 Question 2 Q6.29 Question 4 Q6.30 Question 16 Q6.31 Sample Question 25 Q6.32 Sample Question 42 Q6.33 Sample Question 53 Q6.34 Sample Question 56 Q6.35 Sample Question 54

Q7.27 Question 6 Q7.28 Question 12 Q7.29 Question 18 Q7.30 Question 6 Q7.31 Question 10 Q7.32 Question 11 Q7.33 Question 18 Q7.34 Sample Question 10 Q7.35 Sample Question 11 Q7.36 Sample Question 12 Q7.37 Sample Question 13 Q7.38 Sample Question 24 Q7.39 Sample Question 32 Q7.40 Sample Question 34 Q7.41 Sample Question 35 Q7.42 Sample Question 37 Q7.43 Sample Question 43 Q7.44 Sample Question 48



Q7.45 Sample Question 50 Q7.46 Sample Question 61 Q7.47 Sample Question 62 Q7.48 Sample Question 63 Q7.49 Sample Question 64

Q8.27 Question 7 Q8.28 Question 9 Q8.29 Question 13 Q8.30 Question 5 Q8.31 Question 14 Q8.32 Question 15 Q8.33 Sample Question 14 Q8.34 Sample Question 21 Q8.35 Sample Question 15 Q8.36 Sample Question 22 Q8.37 Sample Question 29 Q8.38 Sample Question 30 Q8.39 Sample Question 38

Q9.24 Sample Question 57

mfe mailbag sep 2011 fall 2011 - bpptraining.com mailbag (sep 2011) fall 2011.pdf · bpp q&a...

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