Errata for ASM Exam MFE/3F Study Manual (Ninth Edition) Sorted by Date
1
Errata and updates for ASM Exam MFE/3F (Ninth Edition) sorted
by date
Note the corrections to Practice Exam 6:9 (page 613) and 10:18. None of the answer choices is
correct for Practice Exam 10:15.
[3/3/2013]
On page 840, in the solution to question 74, on the last two lines, replace the expression 27.65724e −0.08 =
25.53 with 27.65724/1.024 = 25.55 .
[1/4/2013]
On page 243, in the solution to exercise 11.7, on the last line, change +0.00536e 0.03/4 to −0.00536e 0.03/4
[11/1/2012]
On page 715, the solution to question 11 has multiple typos involving the 45’s and 50’s. The correct solution is
We use put-call parity to calculate the value of a 1-year put.
P (50, 45, 1) = C (50, 45, 1) + 45e −0.1 − 50e −0.1 = 3.00
The value of the chooser option, denoted by V , by formula (??), is (note that (r − δ)(T − t ) = 0)
V = C (50, 45, 4) + e −δ(T −t ) P (50, 45, 1)
so we have 12 = C (50, 45, 4) + e −0.3 (3.00) from which it follows that C (50, 45, 4) = 12 − 3e −0.3 =
9.78 . (E)
As indicated in Subsection 14.4.1, you could derive equation (14.9) using put-call parity; the maximum of P (S , 45, 3) and C (S , 45, 3) at time 1 is
C (S , 45, 3) + max 0, P (S , 45, 3) − C (S , 45, 3) = C (S , 45, 3) + max 0, 45e −0.3 − S e −0.3
= C (S , 45, 3) + e −0.3 max 0, 45 − S )
which becomes C (S , 45, 4) + e −0.3 P (S , 45, 1) when discounted to time 0.
[10/29/2012]On
page 223, in the solution to exercise 10.18, on the third line, change “volatility of the put” to
“elasticity of the put”. On the eighth line, delete −1 from the right hand side.
[10/9/2012]
On page 463, in the solution to exercise 22.10, on the second line, change a to c .
[10/5/2012]
On page 7, on the third line of the paragraph beginning “Butterfly spreads”, change K 1 to K 3 . On
the fourth line of the paragraph, change K 3 to K 1 .
[10/2/2012]
On page 321, on the first line of part 2 of the answer to Example 14D, change −0.26406 to −0.26372.
[10/2/2012]
On page 347, in the solution to exercise 14.31, on the last line, change 65.50 + to 65.50 = .
[9/24/2012]
On page 547, in the solution to exercise 26.2, on the displayed line, remove the minus sign before
1000N e −0.05 .
[8/30/2012]
On page 294, in the answer to Example 13I, on the second displayed line, change −0.87816 to
−0.77124. On the third displayed line. change P (40, to P (40.5,.
[8/23/2012]
On page 111, in line with the corrected solution to Example 5A, change γ = 0.59136 in Figure 5.1
to γ = 0.22643. Also, 2 lines above Quiz 5-1, an equals sign should be inserted before −0.149302.
[8/23/2012]
On page 138, in the solution to exercise 6.14, the heading of the third column of the table should
be ln(St /St −1 ).
Updated 3/3/2013
2
[8/23/2012]
[8/14/2012]
Errata for ASM Exam MFE/3F Study Manual (Ninth Edition) Sorted by Date
On page 202, on the fourth line of Subsection 10.1.6, change 0.01 to 100.
p
p
On page 178, on the fourth displayed line of the page, change t to T .
[8/8/2012]
On page 782, in the solution to question 5, on the first displayed line, delete “C(50,60,3)+” on the
left hand side.
[8/4/2012]
On page 379, in the third paragraph from the bottom in point 1, delete the first “Given that X (t ) =
k ,” and capitalize the “t” immediately after that comma.
[8/4/2012]
On page 543, in exercise 26.22, on the last displayed line, add “dt” after the large right parenthesis.
[8/4/2012]
On page 825, in the solution to question 37, 4 lines from the end, change −0.01 to 0.01.
[7/24/2012]
On page 435, in the solution to exercise 20.1, on the fourth line, change (ii) to (iii). On the seventh
line, change (iii) to (iv).
[7/15/2012]
On page 449, in exercise 21.11(iii), change S (0) to W (0).
[7/14/2012]
On page 150, on the second line from the end of the page, “is the stock” should be “if the stock”.
[7/9/2012]
On page 414, on the first line, change d 1 to d 2 . On the second line, change d 2 to d 1 .
[6/17/2012]
On page 112, replace the fourth through eighth lines with
At the u node, the replicating portfolio cannot be used, so the calculation is the same as before,
and γ = 0.59136.
[6/17/2012]
[4/25/2012]
On page 144, on the second line of the paragraph beginning with “1.”, change 125/100 to 125/100−
1.
∂P
∂ P /∂ t
On page 531, 2 lines above Example 26F, change
to
.
∂t
P (r, t , T )
[4/21/2012]
On pages 837–838, in the solution to question 69, 8 lines from the bottom of page 837, change
76.9 to 76.8 and change 43.1 to 43.2 twice. 4 lines from the bottom of the page, change 43.1 to
43.2 and 16.8401 to 16.8692. In Figure B.8 on page 838, change 43.1 (third column, lowest node)
to 43.2.
[4/15/2012]
On pages 110–111, in the answer to Example 5A, the calculation of γ at the upper node is incorrect
since the replicating portfolio cannot be used at a node for which early exercise is optimal. Here
is the corrected solution:
α = 0.15 and δ = 0.10, while h , the period of the binomial tree, is 1/4 of a year. The probability of
an up movement is
p=
e (α−δ)h − d e 0.05(0.25) − 0.8 1.012578 − 0.8
=
=
= 0.425157
u −d
1.3 − 0.8
0.5
We calculate ∆ and B at the d node and at the initial node. This calculation is no different from
the ones we did in previous lessons; the same formulas are used. We will use the stock and option
values we already calculated. The option values could be recalculated using C t = max(∆t St +
Bt ,St − 53).
1.08
−0.025
= 0.05064
∆d = e
54.08 − 33.28
−0.0075 −0.8(1.08)
Bd = e
= −1.71509
0.5
−0.025 14.6 − 0.39158
∆0 = e
= 0.53299
67.6 − 41.6
Updated 3/3/2013
Errata for ASM Exam MFE/3F Study Manual (Ninth Edition) Sorted by Date
B0 = e
−0.0075
3
(1.3)(0.39158) − (0.8)(14.6)
= −22.17495
0.5
Now we calculate the return on the option. At the d node,
0.05064(41.6) 0.0375 −1.71509 0.0075
e
+
e
0.39158
0.39158
= 1.172604
e γ(0.25) =
γ = 4 ln 1.172604 = 0.63691
At the initial node,
0.53299(52) 0.0375 −22.17495 0.0075
e
+
e
5.54027
5.54027
= 1.161024
e γ(0.25) =
γ = 4 ln 1.161024 = 0.59721
We cannot use the replicating portfolio at the u node, since the value of the option, the early
exercise value, is higher than indicated by the replicating portfolio. Therefore we must use equation (5.2) with the early-exercise value of C to back out γ:
C = e −γh p C u + (1 − p )Cd
14.6 = e −0.25γ 0.425157(34.88) + (1 − 0.425157)(1.08)
14.6
= 0.944965
e −0.25γ =
15.45031
γ = −4 ln 0.944965 = 0.22643
The results are shown in Figure (5.1).
[4/3/2012]
On page 418, in exercise 19.9, add the following line after (ii):
(iii) The price of the stock follows the Black-Scholes framework.
[4/1/2012]
On page 443, in Example 21D(i), on the displayed line, change the dS (t ) on the right to dt . In the
answer, on both displayed lines, change E to E∗ , since these are risk-neutral expected values.
[4/1/2012]
On page 716, in the solution to question 15, on the line below the first 3 displayed lines, change
0.0159 to 0.016065. Two lines lower, change $pounds640,000 to £640,000.
[4/1/2012]
On page 725, in the solution to question 9, on the first displayed line, change − 0.5a (a − 1)σ2 to
+ 0.5a (a − 1)σ2 .
[3/21/2012]
On page 462, in the solution to exercise 22.8, on the first displayed line, in the exponent of the
numerator of the second fraction, change 0.5(4)(3) to 0.5(3)(2).
[3/19/2012]
On page 522, on the third line from the bottom, change B (t ) to B (T ).
[3/8/2012]
On page 124, in the solution to exercise 5.13, 4 lines from the end, change “one year” to “three
months”.
[2/29/2012]
On page 464, in the solution to exercise 22.14, on the third displayed line, remove the negative
sign in −0.154375.
[2/26/2012]
On page 200, on the first displayed line, the signs should be reversed:
dP dC
=
− δS e −δ(T −t ) + r K e −r (T −t )
dt
dt
Updated 3/3/2013
4
Errata for ASM Exam MFE/3F Study Manual (Ninth Edition) Sorted by Date
[2/24/2012]
On page 549, in the solution to exercise 26.13, on the first line, change B (0, 3) to B (0, T ).
On page 417, in exercise 19.6, change (ii) to “ Var ln S (t )/S (0) = 0.01t .”
[2/21/2012]
On page 256, in Example 12G(i), add “%.” after 26.
[2/21/2012]
On page 258, on the fourth line, add “%.” after 10.
[2/21/2012]
On page 261, in the introductory box for exercises 12.8 and 12.9, in (i), add “%.” after 4.
[2/21/2012]
On page 264, in exercise 12.22(iv), add “%.” after 5.
[1/25/2012]
On page 420, in the solution to exercise 19.7, the expression for Vt on the second line should have
S (t )0.5 instead of S (t ), so
Vt = 0.055S (t )0.5 e 0.055t
[2/26/2012]
Similarly, on the fourth line, change the term before the equals sign to 0.055S (t )0.5 e 0.055t .
d2 Z (t )
d2 X (t )
to
.
dt 2
dZ (t )2
[1/17/2012]
On page 403, on the second line of the answer to Example 18F, change
[1/15/2012]
On page 397, in the solution to exercise 17.9, on the fifth line, change “then Z 2 ” to “then Z 3 ”. A
more accurate version of the sentence is
. . . then Z 3 is a Brownian motion with variance equal to the sum of the variances of 0.24Z 1 ‘ and
0.1Z 2 . . .
[1/13/2012]
On page 93, in exercise 4.27 on the second line, change the upper-case in futures to lower-case.
[12/1/2011]
On page 54, on the last line of the page, change “borrow” to “lend”.
[11/29/2011]On
page 271, in the solution to exercise 12.11, on the fifth line, delete the first “is”. Put a negative
sign before N (−d 1 ). On the sixth line, delete one of the negative signs in the exponent of e −r .
[11/15/2011]On
page 789, on the first line of the solution to question 28, change “put” to “call”.
[11/10/2011]On
page 678, the solution to question 15 is incorrect. The correct solution is
The prepaid forward price of currency, as indicated in Table 1.2, is
x t e −r f (T −t )
Here, for dollars in terms of euros, x t = 1/1.50 and dollars are the foreign currency so r f = 0.04.
Also, T − t = 2. We conclude that the prepaid forward price is 100e −0.04(2) /1.50 = 61.54 .
[11/9/2011]
On page 472, on the 7th displayed line of the page, there should be a dt at the end of the line, so
that the line looks like this:
‚Z t
Œ ‚
Œ
Z t
−λt
−λt
−λt
λs
−λt
λs
dX (t ) = −λX (0)e
+ αλe
dt + e
d
σe dZ (s ) − λe
σe dZ (s ) dt
0
0
[11/9/2011]
On page 486, on the last line of the warning box, change “year n” to “year k ”.
[11/5/2011]
On page 363, in the exercise 15.1(v), the word after “risk-free” should be “interest”.
[11/5/2011]
On pages 773–774, in the solution to question 15, the payoffs should be discounted at 0.02. The
multiplication by e −0.02 may be postponed to the end, however, since multiplying the five payoffs
by e −0.02 will multiply the standard deviation by e −0.02 . Therefore, replace the last phrase of the
solution, “then take the square root. . . ” with “then take the square root and multiply by e −0.02 to
Updated 3/3/2013
Errata for ASM Exam MFE/3F Study Manual (Ninth Edition) Sorted by Date
5
p
get the standard deviation of the call option price, e −0.02 0.000020272 = 0.0044 . None of the
five answer options are correct.
[11/4/2011]
On page 613, in question 9(iv), the right side of the equation should be e 0.2952t .
[11/4/2011]
On page 727, in the solution to question 15, the column St /St −1 is incorrect, except that 1.0025 is
correct. The five entries in that column should be 1.0025, 1.0948, 0.9180, 0.9429, 1.0579.
[11/3/2011]
On page 135, in the solution to exercise 6.3, on the last line, change > to <.
[11/3/2011]
On page 220, in the solution to exercise 10.6, the final answer is missing a negative sign and should
be −0.52757.
[11/2/2011]
On page 156, in the solution to exercise 7.2, on the first line, change “lognormal” to “normal” in
two places.
[11/1/2011]
On page 704, in the solution to question 6, 3 lines from the bottom of the page, change the 0.09531
in the denominator to 0.125.
page 464, in the solution to exercise 22.15, 2 lines from the bottom of the page, change the r
in the exponent to α.
[10/30/2011]On
[10/26/2011]On page 546, on the last line of exercise 26.38, delete the phrase “, using a negative sign to indicate
a sale”, and delete the negative signs in the five choices.
[10/26/2011]On page 555, in the solution to exercise 26.38, on the third displayed line, delete the negative sign
before 1.64065. On the fifth displayed line, put a negative sign before 0.74177. On the next line,
delete the negative sign before 1.9247. On the last line, replace “sell” with “buy”.
[10/26/2011]On
page 656, question 18 is defective. In (iii), change 0.07 to 0.05. Divide all the answer choices
by 10, so that they are 0.01, 0.015, 0.02, 0.025, and 0.03.
[10/26/2011]On
page 774, correct the solution to question 18 (in accordance with the revised question) as
follows:
• On the fourth displayed line, change 0.07 to 0.05.
• The last two lines should read:
−0.05σ2 − 0.01 + 0.02 = 0
σ2 = 0.02
[10/25/2011]On
(C)
page 492, in exercise 24.20, in the graph, replace “Month 5” with “Month 6”.
[10/22/2011]On page 510, in the solution to exercise 25.3, on the second to last line, put a negative sign in front
of 0.10433: N (−0.10433).
[10/17/2011]On
page 412, four lines below equation (19.1), change (r − δ)C to (r − δC )C .
[10/10/2011]On
page 838, the answer key for question 69 should be (C) rather than (A).
[10/9/2011]
On page 414, on the third line in the S a paragraph, add an a before r − δ:
0.5a (a − 1)σ2S a + a (r − δ)S a = r S a
[10/9/2011]
On page 454, 5 lines above Quiz 22-1, add dt at the end of the line.
[10/5/2011]
On page 390, on the fifth line, the paragraph should start “The time-t value of a geometric . . . ”
Add a hyphen after “time”, delete “nbd”, and move t after the hyphen.
Updated 3/3/2013
6
Errata for ASM Exam MFE/3F Study Manual (Ninth Edition) Sorted by Date
[10/2/2011]
On page 145, two lines after the answer to Example 7B, change µ = 0.14 to µ = 0.15. On the
second line of the paragraph beginning “You will notice”, change e 0.14 to e 0.15 and change 46.01
2
to 46.47. Change 46.01 to 46.47 on the next line as well. On that
line, change 40e 0.14−0.3 = 42.05 to
2
2
2
40e 0.15−0.3 = 42.47. On the fourth line, change 40 e 0.14+0.5(0.3 ) = 48.13 to 40 e 0.15+0.5(0.3 ) = 48.61.
On page 146, in the caption for Figure 7.1, change µ = 0.14 to µ = 0.15.
[10/2/2011]
On page 694, the answer key for question 5 should be (D). Correct the answer key on page 692 as
well.
[10/2/2011]
On page 707, the answer key for question 19 should be (B). Correct the answer key on page 703
as well.
[9/27/2011]
On page 168, on the first line of Table 8.2, change xi to Si .
[9/27/2011]
On page 169, change the first sentence of exercise 8.3 to
A stock’s price follows a lognormal model.
[9/27/2011]
On page 217, in exercise 10.19, replace (vii) with
The risk premium is positive.
[9/27/2011]
On page 223, in the solution to exercise 10.19, on the last line, replace “where we used . . . since
the risk-free rate is nonnegative” with “We used −0.62 since using 0.62 results in an r greater than
0.19, making the risk premium negative.”
[9/27/2011]
On page 273, in the solution to exercise 23, replace the first two expressions in the displayed line
with
∆d u − ∆d d
Γd =
Sd u − Sd d
[9/27/2011]
On page 391, on the second displayed line of the answer to Example 17A, the first expression
should be
S (t )
Pr ln
> ln 1.05
S (0)
[9/27/2011]
On page 499, in the solution to exercise 24.20, on the second to last line, replace 0.965523 with
0.983570. On the last line, replace 0.965523 with 0.983570 and replace the final answer 0.9681
with 0.9758.
[9/27/2011]
On page 515, on the third displayed line of Section 26.1, the one ending with (*), change P (t , t , T )
to P (r, t , T ). Also, put a 0.5 factor in front of (T − t )2 .
[9/27/2011]
On page 516, put a 0.5 factor before the expression under the brace with ¬.
[9/27/2011]
On page 516, in the table of the answer to Example 26A, on the second line under the heading,
change −2.608047 to −2.608074.
[9/27/2011]
On page 530, on the third line of Subsection 26.3.2, change “rats” to “rates”.
[9/27/2011]
On page 693, the answer key for question 3 should be (A) Correct the answer key on page 692 as
well.
[9/7/2011]
On page 261, in exercise 12.6(vi), add “%.” at the end of the line.
[9/7/2011]
On page 405, in exercise 18.9, on the third line from the end, change T − t to 1 − t .
[9/7/2011]
On page 408, the solution to exercise 18.9 has several errors. The correct solution is
Updated 3/3/2013
Errata for ASM Exam MFE/3F Study Manual (Ninth Edition) Sorted by Date
7
The Itô process for X (t ) is
Since Y (t ) = Ft P,1
dX (t )
= (r − r f )dt + σ dZ (t ) = (0.03 − 0.08)dt + 0.15 dZ (t )
X (t )
X (t ) = X (t )e −0.08(1−t ) , by Itô’s lemma, we have
dY = e −0.08(1−t ) dX (t ) + 0.08Y dt
= e −0.08(1−t ) −0.05X (t ) dt + 0.15 dZ (t ) + 0.08Y dt
= −0.05Y dt + 0.15Y dZ (t ) + 0.08Y dt = 0.03Y dt + 0.15 dZ (t )
so µ t , Y (t ) = 0.03 .
[8/30/2011]
On page 6, third line, change ’s to seller’s.
[8/27/2011]
On page 387, the solution to exercise 16.7 is incorrect. The correct solution is
Let X (t ) be the exchange rate, and Y (t ) = ln X (t ). Logging the expression we’re given,
Y (t ) = Y (0) + 0.005t + 0.1Z (t )
so Y (5) is a normal random variable with mean ln X (0) + 0.005(5) = ln 0.9 + 0.025 and variance
(0.12 )(5) = 0.05. The probability that X (t ) is less than 1, or Y (t ) less than 0, is
0 − (ln 0.9 + 0.025)
N
= N (0.35938) = 0.64035
p
0.05
[8/26/2011]
On page 454, 2 lines above Quiz 22-1, replace Y at the end with dt and put a dt after the second
summand, so that the line reads:
dY
aS
=
(α − δ)dt + σ dZ (t ) + 0.5a (a − 1)σ2 dt − a (r − δ) + 0.5a (a − 1)σ2 dt
Y
S
[8/23/2011]
On page 388, the solution to Quiz 16-3 is incorrect. The correct solution is
ln X (t )/X (0) = 0.05t + 0.3Z (t ) is an arithmetic Brownian motion. By memoryless properties of
Brownian motion, the distribution of ln X (2.5)/30 is normal with mean 0.05(0.5) = 0.025 and
variance (0.32 )(0.5) = 0.045. The probability of 30 ≤ X (t ) ≤ 33 is
ln 33/30 − 0.025
ln 30/30 − 0.025
Pr 30 ≤ X (t ) ≤ 33 = N
−N
p
p
0.045
0.045
= N (0.33145) − N (−0.11785)
= 0.62985 − 0.45309 = 0.17676
[8/20/2011]
On page 268, in the box before question 12.39, (iii) and (iv) are cut off. (iii) should finish “5% per
annum” and (iv) should finish “20% per annum”.
[8/20/2011]
On page 278, in the solution to question 12.39, if 5-place rounding of the normal distribution
function is used, then N (d 1 ) = 0.53206 and the final answer is 46,794 shares. The solution to
question 12.40 with 5-place rounding is as follows:
In this question, they didn’t want you to include the changes of prices of the stock in the cost;
they ask for the cost of the hedge, not the cost of the instrument that is being hedged.
Updated 3/3/2013
8
Errata for ASM Exam MFE/3F Study Manual (Ninth Edition) Sorted by Date
The values of d 1 that are provided are rounded to 2 decimal places. We will use them, but we will
calculate the normal distribution to 5 decimal places.
N (−0.10) = 0.46017, and N (−0.05) = 0.48006. Initially we buy 46,794 shares. After 1 week, we
need 46,017 shares so we sell 46, 017 − 46, 794 = 777 shares. After 2 weeks we need 48,006 shares
so we buy 48,006−46,017 = 1989 shares. Each week’s purchase or sale is at the week’s stock price.
These purchases are then accumulated at interest for 2 weeks, 1 week, or 0 weeks. The following
table summarizes the calculation of the cost of the hedge:
Total
Shares
46,794
46,017
48,006
Shares
Purchased
46,794
−777
1,989
Stock
Price
Interest
Factor
49.16
49.33
49.09
1.001925
1.000962
1
Accumulated
Cost
2,304,821
−38,366
97,640
2,364,095
The interest factors in this table were computed as e 0.05(2)/52 = 1.001925 and e 0.05/52 = 1.000962.
The final column is the product of shares purchased, stock price, and interest factor. The accumulated cost of the hedge is 2,364,095 .
[8/19/2011]
On page 442, on the first displayed line in the answer to Example 21C, change 0.3 dZ (t ) to 0.2 dZ (t )
in two places.
[8/19/2011]
On page 443, in Example 21D(ii), change S (0) = 10 to S (0) = 40.
[8/17/2011]
On page 43, in the enumerated list at the bottom of the page, item 1, change S − K 1 to S − K 2 .
[8/17/2011]
On page 294, on the second line of the page, change 45.5 to 45 and change 4.5923 to 4.5968. On
the eighth line, change 4.5923 to 4.5968.
[8/13/2011]
On page 214, in exercise 10.6(ii), change the dividend yield from 0.05 to 0.06.
[8/5/2011]
On page 135, the solution to exercise 6.4 is incorrect. The correct solution is
The gain in exercising is the gain in dividends on the stock, or S (1 − e −0.06 ) = 0.058235S . The loss
is the loss in interest on the strike price, 50(1 − e −0.04 ) = 1.96053, plus the loss of the implicit put.
Calculate the gain and loss starting at 64 and working down:
Stock price
Dividend gain
Interest and put loss
64
63
62
64(0.058235) = 3.72707
63(0.058235) = 3.66883
62(0.058235) = 3.61060
1.96053 + 1.6 = 3.56053
1.96053 + 1.7 = 3.66053
1.96053 + 1.8 = 3.76053
When the stock price is 62, it is not optimal to exercise, since the loss is greater than the gain.
We don’t know what the put’s price is when the stock price is between 62 and 63, but it is worth
at least 1.7. So the gain is definitely larger than the loss when 0.058235S > 1.96053 + 1.7, or S =
3.66053/0.058235 = 62.858. The lowest price for which it may be optimal to exercise the option
is 62.858 .
[7/22/2011]
On page xi, on the first line of the second paragraph under “The normal distribution table”, add
“use” after “you may”.
[7/22/2011]
On page xii, replace the first line with
http://www.beanactuary.org/exams/preliminary/register/Regpdf/MFE3F_Table.pdf
Updated 3/3/2013
Errata for ASM Exam MFE/3F Study Manual (Ninth Edition) Sorted by Date
9
[7/5/2011]
On page 60, in exercise 3.5, delete the period at the end of the first line and add “having a period
of 6 months. Also on the second-to-last line, after “‘stock”, add “expiring in 6 months”.
[5/24/2011]
On page 629, in question 28, replace the first sentence with
Let S (t ) be the time-t value of a stock index, and Q (t ) the time-t value of an annuity contract.
The annuity’s contract value grows at the same rate as the value of the stock index, except that a
continuously compounded 1% management fee is assessed. More precisely,
S (t + dt ) − 0.01S (t )dt
Q (t + dt ) = Q (t )
S (t )
[5/22/2011]
On page 556, in the solution to exercise 26.39, on the second line, the exponent is based on the
formula in McDonald, but McDonald’s formula is erroneous; there should be a negative sign before 0.5σφ(52 ). This has no effect on the solution since φ = 0. Since McDonald has not corrected
this error, it is unlikely you would be expected to know the correct formula.
Updated 3/3/2013