| SOA真题May2005ExamC |
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Course 6: Spring 2005 - 1 - GO ON TO NEXT PAGE
Morning Session
COURSE 6
MORNING SESSION
SECTION A – WRITTEN ANSWER
Course 6: Spring 2005 - 2 - GO ON TO NEXT PAGE
Morning Session
**BEGINNING OF EXAMINATION**
MORNING SESSION
1. (5 points) Your company is evaluating active and quasi-passive investment strategies for
bond portfolio management.
(a) Define each quasi-passive indexation approach.
(b) Describe the advantages and disadvantages of each quasi-passive indexation
approach.
(c) Explain the reasons your company would consider an active investment strategy.
(d) Describe the sector and security strategies that an active investment manager
would use to select individual bonds.
2. (7 points) Your company is offering a 15-year term-certain immediate annuity with
payments linked to the CPI. Policyholders can withdraw funds on demand at market
values.
The universe of available investments consists of the following:
%26#8226; Short-term T-bills
%26#8226; Real return public bonds
%26#8226; Corporate bonds
%26#8226; Real estate
(a) Outline the advantages and disadvantages of each investment for backing this
annuity.
(b) Recommend an investment strategy using the investments available.
(c) Describe the major components of an accumulated cash flow scenario-based
model.
(d) Outline the major components of the investment policy statement for this product.
Course 6: Spring 2005 - 3 - GO ON TO NEXT PAGE
Morning Session
3. (5 points) You are given the following information:
Bond Term Effective Duration Effective Convexity
A 5 3.1 -41.7
B 5 4.5 23.4
C 5 4.2 21.3
D 5 2.7 64.5
The option and price characteristics of Bonds A, B, C and D are as follows:
%26#8226; one bond is option-free with a current price above par
%26#8226; one bond is option-free with a current price below par
%26#8226; one bond is callable, priced at par
%26#8226; one bond is putable, priced at par
(a) Determine the option and price characteristics corresponding to each of Bonds A,
B, C and D. Explain your answer.
(b) Assess the limitations of duration as an interest rate risk measure.
(c) Define convexity. Compare effective convexity and modified convexity.
(d) Calculate the approximate percentage price change for Bonds A and B assuming a
decrease in yield of 0.50%.
Show all work.
Course 6: Spring 2005 - 4 - GO ON TO NEXT PAGE
Morning Session
4. (10 points) You are given the following with respect to treasury securities as of today,
May 13, 2005:
Security Years to Maturity
Annual Coupon Rate
Paid Semi-annually Yield-to-maturity
A 0.5 0% 3.0%
B 1.0 0% 3.2%
C 1.5 6% 3.5%
D 2.0 5% 3.6%
(a) Calculate the spot rate for each maturity date.
(b) Explain how arbitrage profits could be made from coupon stripping.
(c) Calculate the one-year forward rate, one year from today.
(d) With respect to the pure expectations theory
(i) Describe the theory
(ii) Describe the interpretations of the theory that have been put forth by
economists
(iii) Explain the shortcomings of the theory
(e) With respect to other theories of term structure of interest rates:
(i) Briefly describe each theory
(ii) Using each theory, compare the one-year spot on May 13, 2006, with the
one-year forward rate calculated in (c)
Show all work.
Course 6: Spring 2005 - 5 - GO ON TO NEXT PAGE
Morning Session
5. (5 points) You are given the following information with respect to Stock XYZ:
%26#8226; price: 50
%26#8226; variance: 4%
%26#8226; dividend rate: 0%
The risk-free rate compounded continuously is 6%.
You are also given the following selected values from the Standard Normal Cumulative
Distribution Function:
Z N(Z) Z N(Z) Z N(Z)
.01 0.5040 .11 0.5438 .21 0.5832
.02 0.5080 .12 0.5478 .22 0.5871
.03 0.5120 .13 0.5517 .23 0.5910
.04 0.5160 .14 0.5557 .24 0.5948
.05 0.5199 .15 0.5596 .25 0.5987
.06 0.5239 .16 0.5636 .26 0.6026
.07 0.5279 .17 0.5675 .27 0.6064
.08 0.5319 .18 0.5714 .28 0.6103
.09 0.5359 .19 0.5753 .29 0.6141
.10 0.5398 .20 0.5793 .30 0.6179
(a) List the assumptions required for put-call parity.
(b) Use the Black-Scholes formula to calculate the price of a one-year European call
option on Stock XYZ with a strike price of 52.
(c) Calculate the price of a one-year European put option on Stock XYZ with a strike
price of 52.
Show all work.
Course 6: Spring 2005 - 6 - GO ON TO NEXT PAGE
Morning Session
6. (6 points) You are given the following with respect to a portfolio of bonds:
Bond
Annual
Coupon Par
Market
Value
Option
Features
Years to
Maturity
A 4.50% 100 100 none 2
B 6.00% 100
callable in one
year at 101 2
You are given the following with respect to a binomial lattice:
%26#8226; rL : 4%
%26#8226; σ : 15%
%26#8226; time interval between nodes: 1 year
(a) Calculate the one-year spot rate.
(b) Calculate the two-year spot rate.
(c) Calculate the one-year implied forward rate.
(d) Calculate the value of the option in Bond B.
Show all work.
7. (4 points) Outline the risks faced by a U.S. investor in purchasing a 10-year privatelyplaced
U.S. corporate callable bond.
Course 6: Spring 2005 - 7 - GO ON TO NEXT PAGE
Morning Session
COURSE 6
MORNING SESSION
SECTION B – MULTIPLE CHOICE
Course 6: Spring 2005 - 8 - GO ON TO NEXT PAGE
Morning Session
1-5. Each of questions 1 through 5 consists of two lists. In the list at the left are two items,
lettered X and Y. In the list at the right are three items, numbered I, II and III. ONE of
the lettered items is related in some way to EXACTLY TWO of the numbered items.
Indicate the related items using the following answer code:
Lettered Item
Is Related to Numbered Items
(A)
X
I and II only
(B)
X
II and III only
(C)
Y
I and II only
(D)
Y
I and III only
(E)
The correct answer is not given by (A), (B), (C) or (D).
1. X. Yield-to-maturity return method I. Requires an explicit reinvestment
rate assumption
Y. Total return method II. Is commonly used for pricing and
trading
III. Ignores the capital gain or loss from
security sales
2. X. Effective duration matching I. Very expensive to implement
Y. Cash flow matching II. Only works for small changes in
interest rates
III. Accounts for options embedded in
the assets and liabilities
Course 6: Spring 2005 - 9 - GO ON TO NEXT PAGE
Morning Session
3. X. Tracking error of 68 basis points I. Assuming a normal distribution, there
is a 68% probability that the portfolio
return over the next year will be
within one standard deviation of the
annualized benchmark return
Y. Portfolio β of 68% II. The portfolio has less volatility than
the benchmark
III. Expect a 68 basis point increase in the
portfolio return if there is a 100 basis
point increase in the benchmark return
4. X. Planned amortization classes I. Priced at tighter spreads to the
Treasury curve than sequential-pay
bonds
Y. Accretion-directed classes II. Redirect principal only
III. Complete protection against
extension of average life if interest
rates rise
5. X. Increase in volatility I. Decreases the value of a putable
bond
Y. Decrease in volatility II. Increases the value of a call option
III. For a given price, increases the
option-adjusted spread for a putable
bond
Course 6: Spring 2005 - 10 - GO ON TO NEXT PAGE
Morning Session
6-10. Questions 6 through 10 consist of an assertion in the left-hand column and a reason in the
right-hand column. Code your answer to each question by blackening space:
(A) If both the assertion and the reason are true statements, and the reason is a correct
explanation of the assertion.
(B) If both the assertion and the reason are true statements, but the reason is NOT a
correct explanation of the assertion.
(C) If the assertion is a true statement, but the reason is a false statement.
(D) If the assertion is a false statement, but the reason is a true statement.
(E) If both the assertion and the reason are false statements.
6.
ASSERTION
Returns on the S%26amp;P 500 stock
index are not affected by stock
splits.
BECAUSE
REASON
Returns on market-value-weighted
indices are based on holding
investments in proportion to their
market values.
7.
ASSERTION
The extended Vasicek model is
able to provide an exact fit to the
current term structure of interest
rates.
BECAUSE
REASON
The drift term in the extended
Vasicek model is time-independent.
Course 6: Spring 2005 - 11 - GO ON TO NEXT PAGE
Morning Session
8.
ASSERTION
Firm-wide stress tests are
reviewed frequently but changed
infrequently.
BECAUSE
REASON
Stress tests may be usefully
applied to markets in which
illiquid conditions produce asset
price jumps and impede securities
trading during times of stress.
9.
ASSERTION
The FHA experience method is
rarely used as a prepayment
model.
BECAUSE
REASON
The FHA experience method does
not reflect the effect of age on prepayments.
10.
ASSERTION
If a risk-free asset is available,
only aggressive investors will be
affected by a restriction on
borrowing.
BECAUSE
REASON
A borrowing restriction drives
aggressive investors to portfolios
on the efficient frontier of risky
assets.
Course 6: Spring 2005 - 12 - GO ON TO NEXT PAGE
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