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以下则是高顿网校小编为您整理的一系列精算师考前珍贵资料，请笑纳。
COURSE 8: Investment - 1 - GO ON TO NEXT PAGE
November 2000
Morning Session
November 2000
Course 8V
Society of Actuaries
COURSE 8: Investment - 2 - GO ON TO NEXT PAGE
November 2000
Morning Session
** BEGINNING OF EXAMINATION **
MORNING SESSION
Questions 1 – 3 pertain to the Case Study.
Each question should be answered independently.
1. (10 points) The Board of Directors of LifeCo was recently given a presentation on the
paper by Robert van der Meer and Meye Smink, Strategies and Techniques for Asset-
Liability Management: An Overview. As the newly appointed Chief Risk Officer for
LifeCo, the Board has asked you to give a presentation.
(a) Categorize and describe the ALM strategies and techniques employed by LifeCo
within the framework provided by van der Meer and Smink.
(b) Assess the relative merits or return-driven versus value-driven strategies for
LifeCo.
(c) Formulate an ALM strategy for LifeCo (from the framework provided by
van der Meer and Smink) that reduces the total company exposure to interest rate
risk and provides an opportunity to increase company surplus.
(d) Evaluate your proposed strategy using the criteria set out in the paper by
van der Meer and Smink.
COURSE 8: Investment - 3 - GO ON TO NEXT PAGE
November 2000
Morning Session
Questions 1 – 3 pertain to the Case Study.
Each question should be answered independently.
2. (9 points) LifeCo management wants to segment the Group line of business for
asset/liability management purposes into:
(i) Long Term Disability (LTD), and
(ii) Other A&H.
The newly allocated balance sheet for LTD is shown below:
Present Value Modified Duration Adjusted Duration
Assets 550.9 13.5 11.00
Liabilities 532.0 8.1 5.37
Economic Value 18.9 169.47
The Relative Volatility of assets for Other A&H is the same as for LTD. The Relative
Volatility of liabilities for Other A&H is 1.
(a) Construct the new Other A&H allocated balance sheet.
(b) Assess the limitations of only using the above measures in managing interest rate
risk.
(c) Contrast the use of Adjusted Duration with the measures used by LifeCo to
manage its exposure to interest rate risk.
(d) The portfolio manager for the Group line of business argues that Franchise Value
should be considered in the liability target duration calculation. Define Franchise
Value.
(e) Explain the implications of using Franchise Value for determining target
durations.
COURSE 8: Investment - 4 - GO ON TO NEXT PAGE
November 2000
Morning Session
Questions 1 – 3 pertain to the Case Study.
Each question should be answered independently.
3. (22 points) LifeCo wants to establish a delta/gamma/vega/rho hedge on the equity
exposure of their variable annuity business, using positions in some or all of the
following assets.
Asset Price Delta Gamma Vega Rho
S&P 500 Future 0 100 0 0 0
30-year Treasury
bond future
0 0 0 0 -12,598
1-year Put 51.98 -0.34608 0.00184 3.688 -3.98
1-year Call 109.45 0.65392 0.00184 3.688 5.45
10-year Put 42.88 -0.10529 0.00029 5.761 -14.82
10-year Call 489.57 0.89472 0.00029 5.761 40.51
LifeCo’s liabilities have the following sensitivities:
Delta – 2,659.90
Gamma 1.036
Vega 1952
Rho – 101,910,000
All deltas and gammas are per unit change in the S&P 500 index.
Vegas are per 1% change in volatility
Rhos are per 1% change in interest rates
Current value of the S&P 500 is 1300
(a) (6 points) Construct a hedge position using the above assets that minimizes the
cost of the hedge without regard to the operational guidelines.
(b) (1 point)
(i) Assess whether the hedge determined in part (a) would be in violation of the
operational guidelines for use of derivatives.
(ii) Recommend any necessary changes to the guidelines.
COURSE 8: Investment - 5 - GO ON TO NEXT PAGE
November 2000
3. (Continued)
(c) (6 points)
(i) Calculate the 1-day, 99%VAR on the portfolio, before and after the hedge is
applied using delta and gamma to approximate it.
(ii) Assess the validity of these numbers.
(d) (4 points) LifeCo is worried about the liquidity of the 30-year Treasury bond
future.
(i) Analyse the effectiveness of the proposed hedges with respect to rho.
(ii) Propose alternative methods and alternative assets to improve rho exposure
coverage.
(e) (5 points) The newly appointed Chief Risk Officer is concerned about the use of
derivatives in the hedging strategy. Verify that the operational and credit risks of
managing derivatives have been adequately covered by LifeCo’s operational
guidelines for use of derivatives.
COURSE 8: Investment - 6 - GO ON TO NEXT PAGE
November 2000
Morning Session
4. (6 points) You have the following market information:
? Price of a 2-year zero coupon bond: 89
? 1-year short rate i0 b g: 7%
A new actuarial student in your company has implemented an interest rate model to price
interest rate derivatives. His model gives the following results:
Sample space i1
w1 6.0%
w 2 8.0%
(a) Describe the different types of model risk that must be considered when building
or using a model.
(b) Explain the concept of arbitrage-free in the context of an interest rate model for
pricing derivatives.
(c) Assess the validity of the proposed model given the information above.
5. (4 points)
(a) Describe how the following factors will generally impact the Option-Adjusted
Spread (OAS) of a Planned Amortization Class (PAC) for a typical PAC bond.
(i) Average life of the PAC
(ii) Premium versus discount collateral
(iii) Lockout versus no lockout
(iv) Window length
(v) Whether or not a Z-bond funds the PAC
(b) Describe the shortcomings associated with OAS in *uating mortgage-backed
securities.
(c) Describe how you would use OAS, considering the shortcomings.
COURSE 8: Investment - 7 - GO ON TO NEXT PAGE
November 2000
Afternoon Session
6. (5 points) You are given the following information on a European put option on a bond:
? Put option
? Maturity of option 1 year
? Strike price level 1000
? Underlying bond
? Cash price 1000
? Present value of bond coupon payments 100
? 1 year forward yield volatility 10%
? Modified duration 10 years
? Forward yield 7%
? Risk-free rates are flat at 5.13%
(a) Calculate the price of this option using Black’s model. Show your work.
(b) Contrast alternatives for calculating delta and gamma for this option with a stock
option.
7. (4 points)
(a) Describe the psychological factors that prevent rational investment decisionmaking.
(b) List five major anomalies which the standard paradigm of rationality fails to
explain. Give an example for each case and specify the key behavioral factors
that explain such anomalies.
** END OF EXAMININATION **
MORNING SESSION
COURSE 8: Investment - 8 - GO ON TO NEXT PAGE
November 2000
Afternoon Session
** BEGINNING OF EXAMINATION **
AFTERNOON SESSION
Beginning with question 8
8. (4 points) As a product development actuary you have been asked to research and
develop an Equity Indexed Annuity (EIA) product.
(a) Describe the basic product features of an EIA.
(b) Recommend and justify an investment strategy for the EIA product.
(c) Describe the potential risks associated with an EIA and the investment strategy
you have recommended in (b).
COURSE 8: Investment - 9 - GO ON TO NEXT PAGE
November 2000
9. (7 points) Consider a simple sequential Commercial Mortgage-Backed Securities
(CMBS) deal with the following senior/subordinated structure:
Class Rating Average Life Size
A-1 AAA 9.3 73.50
A-2 AA 10.0 5.50
A-3 A 10.0 6.00
B-1 BBB 10.0 4.75
B-2 BB 10.0 4.00
B-3 B 10.0 4.00
C Not Rated 10.0 2.25
Loan N/A 9.5 100.00
Collateral information:
Debt Service
Coverage
Ratio
(DSCR)
Loan-to-value
(LTV)
Net Operating
Income (NOI)
Volatility
Original 2.5 65% 6%
Stressed 1.2 90% 10%
? Collateral consists of 9% coupon, non-callable, 10-year balloon, commercial
mortgage loans with a 30-year amortization schedule.
? Subordinated class loss allocation: C, B-3, B-2, B-1, A-3, A-2.
(a) Describe how your Option Adjusted Spread (OAS) valuations would change by
rated class if the collateral weighted average DSCR and LTV ratios were to
change over the short term from original to stressed levels.
(b) Describe the relative impact of using the stressed NOI volatility assumption
versus the original assumption on your OAS valuations for the B classes.
COURSE 8: Investment - 10 - GO ON TO NEXT PAGE
November 2000
Afternoon Session
9. (Continued)
(c) Assume the following:
? The collateral is made up of lower quality commercial mortgage loans that
have prepayment penalties and are fully callable at par after five years without
penalty.
? The most senior class is priced at a discount.
Describe the impact of these assumptions on your OAS valuations for the most
senior class.
(d) (i) Explain the rationale for an issuer to use interest-only (IO) classes in a class
structure.
(ii) Describe the sensitivity of the OAS valuation of an IO class to default losses
and involuntary principal payments in a senior-subordinated CMBS deal.
COURSE 8: Investment - 11 - GO ON TO NEXT PAGE
November 2000
Afternoon Session
10. (7 points) You are the portfolio manager for a United Kingdom domiciled insurance
company. The portfolio currently has a U.S. asset of $300,000 with a volatility
(s) of 0.02 per day.
You have been asked to *uate an investment in a Planned Amortization Class (PAC)
tranche of a collaterized mortgage obligation, where the mortgage collateral is residential
mortgages originated in the U.S. The PAC security you are considering is $200,000 and
has an asset volatility(s) of 0.015 per day.
The two assets have a correlation factor of 30%. The change in portfolio value is
normally distributed and asset returns have a bivariate normal distribution.
(a) Describe the factors affecting mortgage prepayment modeling.
(b) Describe, in general, the risks associated with political climate risk.
(c) Describe the three distinct categories of currency hedging techniques available for
hedging this asset.
(d) Assess the benefit of diversification when adding this PAC security to the
portfolio, using a 5-day, 95% VAR. Show your work.
COURSE 8: Investment - 12 - GO ON TO NEXT PAGE
November 2000
Afternoon Session
11. (6 points) Your company has a portfolio of investment-grade bonds and mortgagebacked
securities (MBS) with an option-adjusted duration of 4 years. The portfolio
supports a closed block of single premium deferred annuities (SPDAs) with minimum
rate guarantees of 5%.
The company, using the portfolio yield method, declares the crediting interest rates
monthly. However, the V.P. of marketing strongly recommends that the credited rate be
based on current market rates.
The company's economist has forecast the following interest rates under two economic
scenarios:
Current
Environment
Recession
Scenario
Inflation
Scenario
10 Year T-Note Yield 6% 4% 8%
90 Day T-Bill Yield 5% 3% 11%
(a) Predict the effects on your company's asset portfolio and the SPDA block using
each interest rate crediting methodologies under the following:
(i) recession scenario
(ii) inflation scenario
(b) Explain why it may be disadvantageous to reposition the portfolio using outright
sales and purchases.
(c) Describe option strategies to hedge against a movement from the current
environment to:
(i) recession scenario
(ii) inflation scenario
(d) Describe the risks related to the options strategies used in (c).
COURSE 8: Investment - 13 - GO ON TO NEXT PAGE
12. (6 points) XYZ Life Insurance Company originates home equity loans to elderly
homeowners. The loan is not due for repayment until the borrower dies or moves out of
the property. The amount of the initial loan is based on the age of the borrower and the
property value. Interest and fees are accumulated until repayment. The only source of
repayment is the property.
A government institution provides insurance against the risk that the eventual repayment
amount is less than the loan balance at that time. The premium, which is added to the
loan balance, is an initial fee of 2% of the loan value and 0.5% of the outstanding loan
balance annually. The homeowner can repay in full at anytime without penalty.
The loan interest rate is reset every six months. The net rate of interest, after insurance
premium and expenses, is the rate on 6 month CD's plus 3%. Based on projected cash
flow, the company issues GICs of 1, 3 and 5-year maturities.
The following three strategies have been proposed:
(i) Issue fixed rate instead of variable rate loans.
(ii) Swap the variable interest rates for fixed interest rates.
(iii) Purchase insurance against the risk of homeowners dying earlier or later
than expected.
(a) Analyze the risks associated with the current strategy.
(b) Describe the risks associated with the three proposed strategies.
COURSE 8: Investment - 14 - STOP
November 2000
Morning Session
13. (7 points) You are given the following information about a European put option on a
non-dividend paying stock:
? Stock price 40
? Risk-free interest rate 7% (continuously compounded)
? Strike price 35
? Time to maturity 8 months
You are also given the following volatilities derived from actively-traded European call
options on the stock:
Strike Price
Time to maturity 30 35 40 45
3 months 0.290 0.225 0.180 0.150
6 months 0.280 0.230 0.230 0.160
1 year 0.275 0.236 0.221 0.180
(a) Calculate the price of this option using the Black-Scholes formula. Show your
work.
(b) Contrast the stock price distribution implied by the volatility matrix with the lognormal
distribution.
(c) Describe models of stock price behavior that are consistent with the implied
distribution.
14. (5 points) The asset portfolio of a U.S. life insurance company includes real estate
properties. The portfolio manager is currently considering adding to the portfolio an
equity investment in an office building in Atlanta. The building is fully leased at fixed
rates with 10 years remaining on its leases and subject to a mortgage equal to 50% of its
current market value. The mortgage is for 10 years, interest-only, and interest is paid
monthly at 1 month LIBOR plus a fixed spread.
(a) Evaluate the risks of this specific investment.
(b) Propose approaches to reduce the risks identified in (a).
COURSE 8: Investment - 15 - STOP
November 2000
Morning Session
15. (7 points) The debt of Company X consists of one zero coupon bond with the following
payment probabilities at maturity:
Default Risk Probabilities
Real World Risk-Neutral
No default 85% 75%
Default with 70% recovery 10% 15%
Default with 35% recovery 5% 10%
Additional information is as follows:
? Debt maturity 5 Years
? Payment due at maturity 1000
? Risk-free rate 5% (continuously compounded)
Company Z has written a European option which will pay 1000 in 5 years in exchange
for Company X’s debt.
Assume Company X and Z have equal but independent default risk.
(a) Calculate the market's expected spread for the bond over the risk-free rate. Show
your work.
(b) Determine the possible payoffs at maturity of a European option written by
Company Z which will pay 1000 in 5 years in exchange for Company X's debt.
(c) Calculate the value of this option. Show your work and state your assumptions.
COURSE 8: Investment - 16 - STOP
November 2000
Morning Session
16. (6 points) You are given the following information about two estimations of the Market
Value (MV) of the total policy liabilities of a life insurance company:
Method used Estimation
MV (Liability) $2.0 billion
MV (Asset) – MV (Equity) $1.8 billion
(a) Contrast the two methods.
(b) Explain how the uncertainty of cash flows can be reflected in the estimation of the
market value under the MV (Liability) method.
17. (5 points)
(a) Describe the following fixed income risk measures:
(i) prepayment uncertainty,
(ii) volatility risk (vega),
(iii) zero volatility spread (ZVO),
(iv) spread duration.
(b) Your company’s fixed income portfolio contains MBS, CMBS, CMO, ARM,
callable and putable corporate bonds, and ABS. Explain the impact of each of the
risk measures above on the different fixed income asset classes.
** END OF EXAMINATION **
以上则是【北美精算师】November2001Course8V——SOA历年真题系列，请耐心看题、答题与牢记章节重点。
高顿网校之励志箴言：人生一世，总有些片断当时看着无关紧要，而事实上却牵动了大局。 —— 萨克雷
