COURSE 6
MORNING SESSION
SECTION A – WRITTEN ANSWER
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
**BEGINNING OF COURSE 6**
MORNING SESSION
1. (5 points) You are given the following information:
Stock
Price at Beginning
of Period
Price at End of
Period
Number of Shares
Outstanding
I 10 15 100
II 9 10 125
III 15 15 200
(a) Describe and compare:
(i) Price-weighted index
(ii) Market-value-weighted index
(iii) Equally-weighted index
(b) Calculate the percentage change over the period for:
(i) Price-weighted index
(ii) Market-value-weighted index
(iii) Equally-weighted index
(c) Calculate the end of period price for Stock III that results in an equivalent
percentage increase in the price-weighted index and the market-value-weighted
index.
Show all work.
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MORNING SESSION
2. (6 points) An investor has the following securities available for investment:
Expected Annual Return Standard Deviation of Annual Return
Stock I 9% 13%
Stock II 12% 20%
T-bills 5% 0%
The covariance between the two risky assets is 0.93%.
Construct the optimal portfolio using the three available assets, assuming:
(i) an investor’s degree of risk aversion is 4
(ii) an investor’s degree of risk aversion is 2
Show all work.
3. (10 points) You are given the following information:
•all options have nine months to expiry
•all options have a strike price of 49
•current stock price is 50
•volatility is 30%
•risk-free rate is 5% per annum
Using the binomial option pricing model and a three-month step, calculate the cost of
(i) a European put;
(ii) an American put;
(iii) a European call.
Show all work.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
4. (5 points)
(a) Describe the obligations of the trustee of a pension fund.
(b) Describe the key considerations in selecting an appropriate pension funding
method.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
5. (6 points) You are given the following financial data for Company ABC:
•capital and surplus: 800,000
•total company assets:
Bond Book Value C1 Factor
AAA 2,000,000 0.3%
BB 5,000,000 4%
B 3,000,000 12%
•other required capital components:
Risk Base Required Capital Factor
C2 150,000,000 0.1%
C3 4,000,000 1%
C4 500,000 2%
•required capital components for whole life block:
Risk Base Required Capital Factor
C1 8,000,000 6%
C2 100,000,000 0.1%
C3 3,000,000 1%
C4 400,000 2%
•ceding allowance for a reinsurance treaty is 3% of assets transferred
•C1 required capital factor for assets ceded to reinsurer is 0.5%
•required capital formula: C 4 C22 C1 C3 2 b g
•Risk Based Capital ratio = Available capital ¸Required capital
(a) Describe the weaknesses of using the required capital formula when comparing
two companies that have healthy Risk Based Capital ratios.
(b) Evaluate the impact on required capital if you entered into a 50% coinsurance
agreement for the whole life business.
(c) Evaluate the impact on required capital of upgrading all assets to a minimum
rating of BB.
(d) Recommend which capital management action the company should use.
Show all work.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
6. (5 points) You are given the following information about three stocks in a multiple stock
universe using the single-index model:
Beta Mean Excess Return Standard Deviation
Stock I 1.25 12% 40%
Stock II 0.75 5% 25%
Stock III 1.75 12% 40%
Market 1.00 8% 20%
The risk-free rate is 6% per year.
(a) Explain why the single-index model is an effective tool for portfolio optimization.
(b) Determine the value of the items in the input list required for the development of
a Markowitz efficient frontier.
(c) Calculate the expected return and standard deviation for a portfolio consisting of
equal proportions of Stock I, Stock II, and Stock III.
Show all work.
7. (8 points) You are given the following information for company XYZ:
•it only sells deferred annuities with rates guaranteed to age 65
•its target market is young professionals under the age of 30
•policy surrenders are paid at the greater of book value and market value
•products are credited with new money interest rates, which are currently at
historical lows
•currently the liabilities are supported by fixed income securities
XYZ is considering investing up to 50% of assets supporting the liabilities in equity
investments.
XYZ has implemented an annual process to monitor duration mismatch between assets
and liabilities.
Analyze XYZ’s interest rate risk management practices and, if appropriate, recommend
changes to current practices to help minimize this risk.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
COURSE 6
MORNING SESSION
SECTION B – MULTIPLE CHOICE
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
1. You are given the following characteristics of a zero-coupon bond:
•term to maturity: 5 years
•yield: 8% on a semi-annual basis
Calculate the original-issue discount.
(A) 31.9%
(B) 32.4%
(C) 46.3%
(D) 53.7%
(E) 67.6%
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
2. You are given the following information about a trading day on the New York Stock
Exchange (NYSE):
•advances: 2,000
•declines: 1,500
•advancing volume: 300,000
•declining volume: 600,000
Calculate the trin statistic and indicate if the NYSE is considered bearish or bullish for
that given day.
(A) 0.38, bearish
(B) 0.38, bullish
(C) 2.00, bullish
(D) 2.67, bearish
(E) 2.67, bullish
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
3. You are given the following information as of January 1, 2002:
•stock price: 67
•call option price: 2
•call option strike price: 72
•call option expiry: January 1, 2003
•rate of return on a one-year T-bill: 4% annual effective
Stock Price on
January 1, 2003
Probability
76 0.60
64 0.40
Calculate the risk premium for the call option.
(A) 0.05
(B) 0.16
(C) 0.32
(D) 0.40
(E) 0.46
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
4. You are given the following information for a portfolio consisting of three stocks:
Weight Wi b g Beta bi b g Standard Deviation s i b g
Stock I 20% 1.2 11%
Stock II 40% 0.9 14%
Stock III 40% 1.0 20%
The standard deviation of the deviation of the common factor from its expected value
s F b g is 15%.
Using a single factor arbitrage pricing model, calculate the nonsystematic risk standard
deviation for this portfolio.
(A) 10.0%
(B) 15.0%
(C) 15.8%
(D) 16.2%
(E) 18.0%
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
5. You are given the following information for a 15-year callable bond:
•annual coupon rate: 9% payable semi-annually
•price: 95.32
•effective duration: 3.17
•convexity measure (C): (67.31)
C
V V V
V y
2
2
0
0
2 bg
Calculate the price of the bond after a 50 basis point increase in interest rates.
(A) 93.65
(B) 93.97
(C) 95.32
(D) 96.67
(E) 96.99
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
6. You are given the following information with respect to a single-period securities model:
S P
S
0 10 10
1
11 33 0
11 0 0
11 0 22
b g
b g
L
N
MMM
O
Q
PPP
Determine the value of P which makes the model arbitrage-free.
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
7-16. Each of questions 7 through 16 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).
7. X. Asian call options I. Payoffs depend on the average price
of the underlying asset during the
life of the option.
Y. Lookback call options II. Guarantees the purchase of the asset
at the lowest price during the life of
the option.
III. Can use averages for the exercise
price.
8. X. Cliquet option I. Guaranteed exchange-rate contracts.
Y. Quanto option II. A series of standard call options that
pays the annual increase in the
underlying assets.
III. The strike resets at the beginning of
each year.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
9. X. Interest rate corridor I. The purchase of a cap at one strike
rate and the sale of a floor at a lower
strike rate.
Y. Interest rate collar II. The purchase of a cap at one strike
rate and the sale of another cap at a
higher strike rate.
III. Sometimes described as swapping
into a bond.
10. X. Zero-coupon convertible bond I. Sacrifice yield
Y. Putable convertible bond II. Greater credit risk
III. Lower premium
11. X. Modified duration I. Allows for changing cash flows as
interest rates change.
Y. Effective duration II. Does not allow for changing cash
flows as interest rates change.
III. Not an appropriate measure for
callable bonds.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
7-16. Each of questions 7 through 16 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).
12. X. Decreasing yield rates I. Increases the effective maturity of a
callable bond.
Y. Higher coupon rate II. Increases the effective maturity of a
putable bond.
III. Increases the effective duration of a
non-callable bond.
13. X. Prepayment risk modeling I. The principles of arbitrage cannot be
relied on to ensure that the valuation
will be correct.
Y. Low-discrepancy method II. Arc tangent functions are commonly
used.
III. Takes into account path
dependencies in the cash flows.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
14. X. Parallel shift interest rate
generators
I. Based on lognormal or Markov
chain processes.
Y. Non-parallel shift interest rate
generators
II. Used for New York 7 scenarios.
III. Works well with classical
immunization theory.
15. X. Contingent immunization I. Reduces the risk associated with
nonparallel shifts of a sloped yield
curve.
Y. Combination matching II. Liquidity needs are provided for in
the initial cash flow matched period.
III. A blend of active management with
immunization.
16. X. Risk Based Capital planning I. Reduce outstanding short-term debt.
Y. Liquidity planning II. Portfolio diversification.
III. Public perception management.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
17-25. These questions consist of an assertion in the left-hand column and a reason in the righthand
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.
17. ASSERTION
Commercial mortgage-backed
securities have higher
prepayment risks than residential
mortgage-backed securities.
BECAUSE
REASON
Commercial mortgage-backed
securities are often balloon loans.
18. ASSERTION
A portfolio consisting of
negatively correlated assets offers
better risk-return opportunities
than individual component
securities on their own.
BECAUSE
REASON
The standard deviation of a
portfolio is less than the weighted
average of the standard deviations
of its component securities.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
19. ASSERTION
Under CAPM, the standard
deviation of the return of a
security is the critical element in
calculating the price of that
security.
BECAUSE
REASON
Under CAPM, all investors are
assumed to be rational meanvariance
optimizers.
20. ASSERTION
For a callable bond, the
difference between effective and
modified durations decreases as
interest rates increase.
BECAUSE
REASON
The probability of a callable bond
being called decreases as interest
rates increase.
21. ASSERTION
Convertible bonds offer upside
equity potential with downside
protection.
BECAUSE
REASON
Convertible bonds have a lower
yield relative to non-convertible
bonds.
22. ASSERTION
Generally, a valuation model
with two or more factors is
implemented by simulation.
BECAUSE
REASON
Simulation permits the inclusion
of path dependency in the cash
flows of the instrument.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
17-25. These questions consist of an assertion in the left-hand column and a reason in the righthand
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.
23. ASSERTION
Option exposures can be
managed by matching expected
asset and liability cash flows.
BECAUSE
REASON
The asset and liability cash flow
matching technique determines a
dollar value for the interest rate
exposures that exist.
24. ASSERTION
Option-based portfolio insurance
strategies are time variant.
BECAUSE
REASON
With respect to option-based
portfolio insurance strategies, the
optimal mix of risky and riskless
positions depends on the time left
before the horizon is reached.
25. ASSERTION
The Multiple Asset Performance
strategy is equivalent to
purchasing an option that allows
the buyer to choose the asset to
call or buy at a guaranteed price.
BECAUSE
REASON
A Multiple Asset Performance
option valuation-based approach
does not require asset return
forecasts.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
26. You are given the following information with respect to a callable bond:
•par amount: 1,000
•term to maturity: 3 years
•annual coupon rate: 6% payable annually
•value of embedded call option: 20
Term Annual Spot Interest Rates
1 7%
2 8%
3 9%
Calculate the value of the bond.
(A) 906
(B) 926
(C) 930
(D) 950
(E) 1,000
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
27. You are given the following information with respect to a non-callable bond:
•par amount: 1,000
•term to maturity: 4 years
•annual coupon rate: 8% payable annually
1-Year Annual Forward Interest Rates
Time
Scenario X Scenario Y
0 7% 7%
1 7% 6%
2 8% 7%
3 10% 5%
Each interest rate scenario has an equal probability of occurring.
Calculate the value of the bond.
(A) 1,000.00
(B) 1,018.40
(C) 1,022.80
(D) 1,030.39
(E) 1,031.07
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
28. You are given the following information with respect to a multiplicative binomial
branching model:
•the short rate one year from now will be either:
r r gamma t
u
t ´1 b1 g , or
r r gamma t
d
t ¸1 b1 g , with equal probability
•volatility: 20%
•current short term interest rate: 6%
•notional amount of a 2-year interest rate collar: 100
Calculate the value of a 2-year interest rate collar with strike levels of 5% and 8%.
(A) 0.141
(B) 0.187
(C) 0.328
(D) 0.348
(E) 0.368
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
MORNING SESSION
29. You are given the following information:
•expected market return: 12%
•standard deviation of market return: 10%
•risk-free rate: 4%
•utility function of the investor: U E R
R
M M
( ) M
s( )2
5
Calculate the optimal percentage the investor would invest in the market.
(A) 10%
(B) 20%
(C) 30%
(D) 40%
(E) 50%
COURSE 6: MAY 2002 m END OF EXAMINATION
MORNING SESSION
30. You are given the following information:
•immunization target: 9.0%
•minimum return acceptable to the fund sponsor: 6.0%
•worst case return for an actively managed portfolio: 2.5%
Calculate the minimum proportion of the initial portfolio (X) that should be actively
managed.
(A) X 40%
(B) 40% X 45%
(C) 45% X 50%
(D) 50% X 55%
(E) 55% X 60%
**END OF COURSE 6**
MORNING SESSION
COURSE 6
AFTERNOON SESSION
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
AFTERNOON SESSION
**BEGINNING OF COURSE 6**
AFTERNOON SESSION
Beginning with question 8
8. (4 points) Describe the risks associated with investing in fixed income securities.
9. (5 points) You are given the following information:
Projected Cash Flows
Duration
Year 1 Year 2 Year 3 Year 4 Year 5
Liabilities 4.2 210 69 445 180 1980
Assets 4.3 194 254 41 200 2200
Universe of available assets for investment:
•90-day T-bills
•2-year bonds with annual coupons of 5%
•3-year bonds with annual coupons of 6%
•5-year bonds with annual coupons of 10%
Determine the necessary asset transactions to cash flow match the projected liability cash
flows.
Show all work.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
AFTERNOON SESSION
10. (8 points) The Chief Financial Officer (CFO) of a large corporation is considering
offering an innovative “collared floater” with the following features:
•value at issue: par
•par amount: 10 million
•term to maturity: 5 years
•coupon: semi-annual payment and reset, 6-month LIBOR + 0.50%
•minimum coupon: 7.5%
•maximum coupon: 12.5%
The CFO intends to use derivative instuments to convert this collared floater into
synthetic fixed-rate funding. The following quotes for five-year, semi-annual settlement
interest rate swaps, caps and floors on 6-month LIBOR are obtained from a market maker
in derivative products:
Bid Ask
Swaps for LIBOR 8.65% 8.75%
Interest Rate Cap at 12.0% 0.65% 0.75%
Interest Rate Cap at 12.5% 0.50% 0.60%
Interest Rate Cap at 13.0% 0.35% 0.45%
Interest Rate Floor at 7.0% 0.80% 0.90%
Interest Rate Floor at 7.5% 0.95% 1.05%
Interest Rate Floor at 8.0% 1.10% 1.20%
(a) Determine the specific combination of transactions which result in a synthetic
fixed rate of funding.
(b) Explain why this combination works.
(c) Calculate the effective (all-in) interest cost for this synthetic fixed-rate funding.
(d) Identify the situations when credit risk is a concern to the corporation in this
transaction.
Show all work.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
AFTERNOON SESSION
11. (6 points)
(a) Define a floating-rate security and describe its features.
(b) Describe the yield spread measures used to evaluate floating-rate securities.
(c) Describe the factors affecting the price of floating-rate securities.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
AFTERNOON SESSION
12. (8 points) ABC Financial is considering two opportunities for capital investment for the
upcoming fiscal year:
•a deposit-taking business earning a guaranteed return of 10% per year
•a life insurance business earning one of two possible returns:
20%, or -20% per year.
ABC is also considering a one-year reinsurance agreement that would eliminate any loss
on its life insurance business. The single premium would be paid at the beginning of the
fiscal year.
(a) Compare the features of the reinsurance contract and an option contract.
(b) Calculate the reinsurance premium for the year by applying risk-neutral valuation
to solve for the replicating trading strategy for the reinsurance contract.
(c) Assume that the life insurance business now has a third possible outcome of
catastrophic loss, where all of the capital investment in the life insurance business
is lost.
You are given the following:
•The unit Arrow-Debreu e1 b g price is its upper bound price less
1
12
•S b1g1
0 0
0
1
10
11
5
4
5
4
3
2
1
2
L
N
MMM
O
Q
PPP Calculate the new reinsurance premium using risk-neutral valuation.
(d) Explain how your reinsurance premium calculations would be affected if the
deposit taking business earned a guaranteed return of 20% per year.
Show all work.
COURSE 6: MAY 2002 GO ON TO NEXT PAGE
AFTERNOON SESSION
13. (4 points) You are an investment actuary managing the pension assets of a small
Canadian company.
(a) Describe the key considerations in setting the Statement of Investment Policies.
(b) Describe possible investment vehicles.
COURSE 6: MAY 2002 EEE END OF EXAMINATION
AFTERNOON SESSION
14. (5 points) You are given the following securities:
60-day T-bill: face amount: 1,000
150-day T-bill: face amount: 1,000
Stock of ABC Corporation:
current price: 25
dividend rate: 6%, payable continuously
The amount of dividend payment is constant, regardless
of changes in stock price.
European call option on the ABC stock:
current price: 1
strike price: 30
time to exercise date: 60 days
d1 0.7
European put option on the ABC stock:
current price: 6
strike price: 30
time to exercise date: 60 days
Futures contract: underlying security: 90-day T-bill
time to delivery date: 60 days
face amount: 1,000
current price: 984
Cumulative normal distribution:
Z 1.4 0.7 0 0.7 1.4
N(Z) 0.0808 0.242 0.5 0.758 0.9192
Calculate the current market price of the 150-day T-bill.
Show all work.
**END OF COURSE 6**
Course 6
May 2002
Multiple-Choice Answer Key
1 B 26 A
2 D 27 E
3 C 28 C
4 A 29 B
5 A 30 C
6 A 31
7 E 32
8 B 33
9 D 34
10 B 35
11 B 36
12 B 37
13 A 38
14 B 39
15 C 40
16 D 41
17 D 42
18 A 43
19 D 44
20 A 45
21 B 46
22 B 47
23 E 48
24 A 49
25 B 50 |
