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(Last updated 1/27/17)
[1/27/17] Note to students sitting for the June 2017 or later exam: The 11th and earlier editions of this manual are no longer suitable for these exams. A 12th edition that covers the new syllabus was published in January 2017.
[10/29/14] Note on changes in Learning Objectives and Text References:
Changes were made in the Learning Objectives and Text References for the October 2013 and December 2014 exams. The following terms were eliminated from the syllabus: (1) investment year allocation methods; (2) effective duration; (3) convertible bonds and mandatorily convertible bonds; (4) paylater strategies. Also, the term current value was added to the Learning Objectives. The effects of these changes on ASMs FM/2 manual are shown below under the items dated 10/29/14. ((There are also a couple of corrections of typos dated 10/29/14 which are unrelated to the above changes.)
[7/17/11] Important note on immunization! Students have reported that
there have been a surprising number of questions on immunization
(including the topics of duration and convexity) on recent exams. The
5 practice exams in this manual contain very, very few questions on
these topics. We suggest that you thoroughly review Sections 9c to 9n
before you take the exam.
[5/21/13] Page 21, Q. 5. Answer choice (B) should be 1414.
[4/28/10] Page 21, Q. 7. This problem should actually appear at the end of Sections 1a(vi) to 1a(ix).
[5/21/13] Page 26. The Note at the end should refer to (1 + i)2n.
[5/21/13] Page 37, solution to Q. 6. Note that there is actually no need to explicitly calculate i/2. From
1000(1 + i/2)28 = 1,980, we have (1 + i/2)10 = 1.9810/28, X = 1000(1 + i/2)10 = 1000(1.9810/28) =
1,276.
[3/25/12] Page 53, solution to Q. 1. Add the following note after the solution: Some students interpret:
His account is credited with interest at a nominal rate of i convertible semiannually to mean that
Bruces account earns interest only at the end of each 6-month period. Therefore, they reason
that after 7.25 years, Bruce has only 100(1 + i/2)14 in his account. However, it is very important
to note that in Exam FM/2, an account is always assumed to grow with interest continuously, no
matter how the interest rate is stated (e.g., as an annual effective rate, as a nominal rate
compounded m-thly, as a force of interest, etc.). If there is an exception to this assumption, it
should be clearly stated in the question.
[10/29/14] Page 67, solution to Q. 8. Add the following note at the beginning of the solution:
Note: Occasionally, you may see the term current value, as in this question. This simply means
the value of a series of payments on a specified date, some of which are made before that date
and some after that date. Thus, current value is the sum of the AV and PV of the payments on
the specified date.
[5/21/13] Page 82, diagram in the middle of the page. 3% applies to a period of of a year. (The arrows
make it appear as if 3% applies to of a period, which is of a year.)
[7/17/11] Page 113, solution to Q. 7, 2nd line. R = 150.80 (based on the number of decimal places used),
not 150.08. The solution is based on the correct value.
[8/13/10] Page 129, solutions to Q. 7. On the last line, the denominator should be 1 - .751315. The answer
is based on the correct denominator.
[1/22/10] Page 130, solution to Q. 18, first line. On the right-hand side of the equation, the term of the
annuity should be 20, not 10. The correct term is used in the solution.
[1/22/10] Page 203, items (2)(b) and (2)(c). There should be a Q in front of the second term of the AV.
[8/13/10] Page 215, solution to Q. 11. The way the question is worded, the correct answer is (A), not (B).
As noted in the solution, the account balance at the end of the 8th year is $46,921.66. Just after
the 17th full scholarship of $5,000 is awarded, the account balance is equal to (46,921.66)(1.08)17
- 5,000(s angle 17) at 8% = $4,859.86. According to the question, if there is less than $5,000 in
the account at the end of any year, the remaining amount ($4,859.86) is immediately awarded as
a smaller scholarship. Thus, only 17 full scholarships of $5,000 are awarded. Note that the
account balance of $4,859.86 at the end of the 17th year would have grown to $5,248.65 at the
end of the 18th year at 8%. This would have permitted an 18th full scholarship to have been
awarded, but this would not follow the requirements of the question.
[10/29/14] Page 254, 3rd paragraph under the caption Yield Rate or Internal Rate of Return (IRR), 4th
sentence. Should be the present value of the returns of 500 and 800 decrease.
[8/7/13] Page 280. Investment year allocation methods are no longer included in the syllabus. Read
only the first 6 paragraphs of Section 5f and ignore the rest of this section (including the questions
at the end of the section).
[3/25/12] Page 389, solution to Q. 9, last line. 1,088.27 should be 1,099.84.
[7/17/11] Page 294, first line under b. Using the TVM registers. 4,329.48 should be 4,329.38.
[6/25/12] Page 415, solution to Q. 2, 1st line. The reference should be to Section 8(b), not Section 7(g).
[5/21/14] Pages 427-431. Since the 9th edition of this manual was published, the FM/2 exam committee
has adopted standard terminology for forward rates for exam purposes. (As noted on page 430
under Trap Alert! Warning on Terminology for Forward Rates!, the various Suggested
Textbooks use many different ways of describing the same forward rate. Thus, its a good move
on the part of the exam committee to finally specify standard terminology.)
This is how a forward rate is defined in Notation and terminology used for Exam FM/2
(available on HYPERLINK "http://www.BeAnActuary.org" www.BeAnActuary.org):
Forward rate: An m-year spot rate that comes into effect t years in the future will be
referred to as the m-year forward rate, deferred t years or as the m-year forward
rate, starting in t years.
Lets take an example. Suppose we are told that the 3-year forward rate, deferred 2 years, is
6% (or that the 3-year forward rate, starting in 2 years, is 6%). What this means is that we
could make an investment 2 years from now that would earn 6% per annum over the next 3
years (i.e., over the period from time 2 to time 5. Thus, if we were to invest, say, $10,500 at
time 2, we would have an accumulated value of 10,500(1.06)3 at time 5.
Lets take another example. How would you explain the following forward rate? The 2-year
forward rate, deferred 3 years is 4% (or the 2-year forward rate, starting in 3 years is 4%). This
means that we could make an investment 3 years from now that would earn 4% per annum over
the next 2 years, i.e., over the period from time 3 to time 5.
On pages 427 and subsequent in the manual, naturally we dont use the official terminology for
forward rates, since the 9th edition was published before this terminology was adopted. Now
that the exam committee has spoken, you should expect to see the new terminology on future
exams.
Very often, you will deal with forward rates that are in effect for only one year (i.e., forward rates
for which the m in the definition of a forward rate is equal to 1). For example, if 5% is the
one-year forward rate deferred 5 years, it means that we could make an investment at time 5 that
would earn 5% over the one-year period running from time 5 to time 6. (Note that this is the
same forward rate described in the third paragraph under Forward Rates on page 427, which
does not use the official terminology.)
You should learn how to determine forward rates from spot rates by reading pages 427-429 and
doing examples 6, 7 and 8 on pages 429-430. Although the official terminology is not used on
these pages, you should not have a problem understanding the concepts.
Keep in mind that you may have to modify questions on forward rates in the ASM manual in
terms of the official terminology. For example, see question 2 on page 433. The question asks
you to Calculate the one-year forward rate for year 2 (i.e., the one-year effective rate during year
2). While this is pretty clear, it would have been worded as follows using the official
terminology: Calculate the one-year forward rate, deferred one year. (or Calculate the one-
year forward rate, starting in one year.).
[7/17/11] Page 442, 8 lines from the bottom. Add the following sentence to the parenthesis: In fact,
in Notation and terminology used for Exam FM/Exam 2, which you can find on
HYPERLINK "http://www.BeAnActuary.org" www.BeAnActuary.org, the SOA/CAS says that, unless otherwise stated, duration means
Macaulay duration.
[7/17/11] Page 444, solution to (c), 3rd line. The reference to footnote 2 should be to footnote 3.
[5/21/13] Page 448, solution to Example 1. The 2nd sentence should refer to Example 2, not Example 3.
[7/17/11] Page 456, footnote 5. Insert the following sentence just after the 2nd sentence of the footnote:
In fact, in Notation and terminology used for Exam FM/Exam 2, which you can find on
HYPERLINK "http://www.BeAnActuary.org" www.BeAnActuary.org, the SOA/CAS says that, unless otherwise stated, convexity means
modified convexity.
[1/22/10] Page 463, just above the middle of the page, sentence beginning But the first condition .
This sentence should read But the second condition of Redington immunization is that PA =
PL .
[10/29/14] Page 468. Ignore Section 9n, since effective duration is no longer on the syllabus.
[4/23/09] Page 469, solution to Example 1. The coefficient of (a angle 3) in the formulas for both P(.045)
and P(.055) should be 5, not 3. The numerical results shown are correct.
[7/17/11] Pages 482-483, What about interest? Note that the question of interest on the proceeds of a
short sale is still not covered by the Study Notes. However, in a reply to an email sent by a
student in 2010, the Education Staff noted that new exam questions will be based on McDonald,
which assumes that this interest is paid. A number of questions on the 5 practice exams in this
manual are based on the no-interest assumption. See the errata list below for pages 654 and
subsequent.
[1/22/10] Page 493, first sentence. Add which does not pay dividends to the end of this sentence.
[1/22/10] Page 496, footnote 1. Revise the first sentence to read: We are going to assume that the forward
price for a non-dividend-paying stock is determined as the current spot price of $100
accumulated with interest at the risk-free rate.
[7/17/11] Page 497, Fig. 11.2 and page 499, Fig. 11.3. The line showing the payoff on the long forward
should intersect the y axis at -104, not -100.
[8/7/13] Page 507, 6th line. Note that Bermudian is also spelled Bermudan.
[1/22/10] Page 520, Section 13c, 3rd sentence beginning For this reason . Delete For this reason and
insert If we own the underlying asset. Also, in the Conclusion two sentences later, add in
the underlying asset at the end of the sentence.
[4/23/09] Page 523, item (1)(a). Should say in which the short position is obligated to sell, not buy.
[1/22/10] Page 530, last column of the table (Position). Add in Underlying Asset to the heading.
[1/22/10] Page 531, 2nd line. In the parentheses, add at expiration. 3rd line. Add in the underlying
asset at the end of the paragraph.
[1/22/10] Page 531, 7th line. In the parentheses, add at expiration. At the end of the next sentence, add
in the underlying asset.
[1/22/10] Page 531, Section 14c, 2nd line. Add at expiration just after spot price.
[1/22/10] Page 532, table at the top of the page. In the first column, the position shown in parentheses is
with respect to the underlying asset.
[1/22/10] Pages 532-533, solution to Example 1. The positions shown in parentheses in (I), II), (III) and
(IV) are with respect to the underlying asset.
[1/22/10] Page 533, first table. In the first column, the position shown in parentheses is with respect to
the underlying asset.
[1/22/10] Page 534, Section 14e, 3rd, 4th and 5th paragraphs. Replace these paragraphs by the following
three paragraphs:
Suppose we have a short position in an asset (for example, we sell the asset short). We would
lose money if the price of the asset increases. If we buy a call, its insurance against price
increases, since the payoff under the long call increases as the price of the underlying asset
increases. Thus, we can say that the strategy behind a long call (when we have a short position
in the underlying asset) is insurance against a high price.
A written call is like selling insurance against a high price.
As we saw in Section 13c, a long put is insurance against a decrease in the price of the
underlying asset. Thus, we can say that the strategy behind a long put (when we have a long
position in the underlying asset, such as when we own it) is insurance against a low price.
[4/23/09] Page 535, footnote (a) under the table at the top. Should say as discussed in Section 13a, not
as just discussed.
[1/22/10] Page 537, first bullet (Taxes), 4th line. Delete spot price at the time of exercise and replace by
strike price.
[1/22/10] Page 547, 1st paragraph. Add the following sentence to the end of the paragraph: We will
assume that the underlying asset does not pay dividends. 4th paragraph, 2nd line. Replace
Section 14d by Section 13a.
[1/22/10] Page 559. Just before Q.1, insert the statement: Assume that any stocks in the following
questions do not pay dividends.
[4/23/09] Page 560, Q. 13. Assume that interest is credited on the proceeds of the short sale.
[10/29/14] Page 561, solution to Q. 3. The Note should refer to Sections 15a, 15b and 15c, not 6a,
6b and 6c.
[1/22/10] Page 561, Solution to Q. 2. Add the following note after the solution:
In Section 16b, we will cover a very important principle in option pricing known as
put-call parity. You will find that using this principle, it is possible to determine X (the
premium for a 48-strike call) directly:
Put-call parity: Call(K, T) Put(K, T) = S0 PV(K)
Call(48, 1 year) 4.18 = 48 - (1.066-1)(48)
Call(48, 1 year) = 48 45.03 + 4.18 = 7.15 (rounding difference)
Put-call parity could also be used to solve several other problems in this set.
[1/22/10] Page 577, Q. 1, 1st line. After forward contract, insert with a non-dividend-paying stock as
the underlying asset and. Also, delete the sentence beginning The risk-free rate , since this
information is not required.
[1/22/10] Page 579, solution to Q. 1. Replace the solution by the following:
The combination of a long call and a short put with a strike price of K creates a synthetic
forward with a forward price of K. The premium for this off-market forward is equal to the
net premium for the long call and short put. Thus in this problem we have:
32.98 X = 18.18
X = 14.80
[1/22/10] Page 579, solution to Q. 4. In the note to the solution, delete borrowing money (with no market
risk involved and repaying and replace by lending money at the risk-free interest rate and
receiving a payment of.
[1/22/10] Page 586, item B near the top of the graph. It should say after-tax profit at a price of $130 =
$32.50, not a price of $110.
[7/17/11] Page 588-589, table at the bottom of 588 to the top of 589. The first 4 entries in the column
headed Profit on 100-110 Collar should end in .30, not .26 or .36. The next 3 entries in this
column should end in .70, not .74. All of the entries in the Combined Profit column should end
in .30, not .26.
[10/29/14] Page 590. Ignore the material under the caption Paylater, since this is no longer included in
the syllabus.
[4/28/10] Page 593, Q. 3. The problem should have made it clear that X and Y represent the highest and
lowest profit, respectively, if the puts are purchased.
[1/22/10] Page 619, 5th line of paragraph beginning Note that the broker . Add with an outside party
just after forward or futures contract.
[1/22/10] Page 619, item 1 of the table just below the middle of the page (Arrangement #4). Delete the
last sentence beginning (Brokers short forward ) and replace by (Brokers short position
in the forward contract with the buyer is offset by brokers long position in another forward
contract with an outside party.)
[7/17/11] Page 622, the line just before Section 19d. The result of the calculation is $7.55, not $7.51.
[1/22/10] Page 632, solution to Q. 8. The symbol f2 as used in this solution represents the annual effective
interest rate for the 2-year period from t = 1 to t = 3. (This is not how f2 was defined in the text
of the manual.)
[10/29/14] Pages 635 and subsequent (Practice Exams). Because the topic of investment year allocation
methods is no longer on the syllabus, ignore the following questions in the Practice Exams:
PE #1, Q. 22; PE #2, Q. 20; PE #3, Q. 8; PE #5, Q. 30.
[7/17/11] Page 637. We suggest that you do Practice Exams 4 and 5 first, since most students think they
are easier than Practice Exams 1 to 3.
[4/28/10] Page 648, solution to Q. 20, last 2 lines. 1035.45 should be 1030.45. The final answer of 10.36
is correct.
[7/17/11] Page 654, Q.11, page 670, Q.7, page 686, Q. 23 and page 700, Q. 27. All of these questions
should say that you should assume that no interest is paid to the short-seller on the proceeds of
the short sale. Note that if this is not stated, you should assume that this interest is paid. (See
pages 482-483, What about interest?)
[4/23/09] Page 658, 1st line. 2007 should be 2008.
[1/22/10] Page 680, solution to Q. 29. On the 3rd line, a division bar was omitted from the 2nd term on the
left-hand side of the equation, which should read: 51.21/(1 + x)2. On the 4th line, the factor
(1.09) should be (1.29). The result for 1 + x is correct.
[7/17/11] Page 681, solution to Q. 34, 3rd equation. The number in the angle-bracket should be 282
(= 360 78), not 360. The result is based on the correct value.
[4/28/10] Page 685, Q. 15. The put options in this problem are priced incorrectly, since the premiums
should increase as the strike price increases. The solution is based on the premiums as shown.
[4/23/09] Page 687, Q. 33. The first bullet should read Kc = Kp 20.
[7/17/11] Page 699, Q. 19. The question should ask for the non-zero value of X.
[4/28/10] Page 699, Q. 20. The question should make it clear that the production cost of 17.50 is incurred
at the time of sale, i.e., one year from now.
[7/17/11] Page 700, Q. 23. The question should make it clear that the bond was originally purchased to
yield a minimum of 8%. Also, it should say that the bond matures at par in 30 years.
[8/13/10] Page 705, solution to Q. 17. On the last line, P should be equal to 122,215.3. The answer is still
(D).
[7/17/11] Page 706, solution to Q. 23. To find the price at which the bond was originally purchased to
yield a minimum of 8%, we must find the lowest price for all possible redemption dates. The
price assuming maturity at par in 30 years, as shown in the solution, is $943.711. If we assume
that the bond is called at $1,050 at the end of 6 to 29 years, the price would be greater than
$943.711. (This can be seen by looking at the premium/discount formula for the price, or by
a couple of trial calculations.) Thus, the original price was $943.711, as shown in the solution.
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