5. (3 points) LifeCo is concerned about the mismatch of its assets and liabilities at the total
company level.
(a) Calculate the modified duration of surplus excluding separate accounts.
(b) Estimate the change in interest rates that would reduce total company surplus to
zero.
(c) Calculate the modified duration of liabilities needed to immunize surplus.
(d) Criticize the manner in which the interest rate risk exposure is quantified in (b)
and (c).
6. (5 points) LifeCo’s ALM committee manages the investment needs and risk exposures
of several business segments with very different characteristics.
(a) Explain how the target asset duration should be changed to address any imbalance
between benefit duration and renewal premium duration for each of LifeCo’s
product lines.
(b) Describe the constraints on asset sales that must be considered when rebalancing
asset segments.
7. (3 points)
(a) Explain the two basic properties of utility functions as described by Gerber and
Pafumi.
(b) Explain the principle of equivalent utility.
COURSE 8: Fall 2003 -6- GO ON TO NEXT PAGE
Investment
Morning Session
8. (4 points) You are given the following information for zero-coupon bonds:
Maturity Interest Rate
1-year 4%
2-year 5%
3-year 6%
(a) Construct two sample portfolios of equal value, each using zero-coupon bonds at
all three maturities, such that the portfolio durations are the same.
(b) Approximate the impact on the value of the two portfolios of a 1% increase in
zero-coupon interest rates at every maturity using the portfolios’ modified
duration.
(c) Approximate the impact on the value of the two portfolios of a 1% increase in the
1-year zero-coupon rate and no change in the 2 and 3-year zero-coupon rates
using the portfolios’ modified duration.
(d) Evaluate the validity of the approximations in (b) and (c).
9. (4 points) You maintain a model that determines the 1-month 95% confidence value at
risk (VAR) of your company’s guaranteed minimum accumulation benefit (GMAB)
portfolio.
(a) Describe the key limitations of the VAR methodology.
(b) Describe methods that can be used to test and address these limitations.
COURSE 8: Fall 2003 -7- GO ON TO NEXT PAGE
Investment
Morning Session
10. (5 points) A large Canadian life insurer, CanCo, is about to purchase a mid-sized U.S.
insurer, TargetCo. Assume:
(1) TargetCo will continue all of its existing lines of business.
(2) TargetCo will reinvest profits in its U.S. operations.
(3) TargetCo’s Corporate functions will be performed in CanCo’s Canadian office.
(4) TargetCo’s Sales and Marketing and other lines of business functions will
continue to operate in the U.S.
The post-acquisition strategic plan assumes:
CanCo TargetCo
Pro forma Cash Flow Summary
Operational Expenses – Sales and Marketing CAD 200 USD 50
Operational Expenses – Corporate and Other CAD 300 CAD 75
Policy Benefits and Other Expenses CAD 100 USD 20
Premium and Investment Income CAD 700 USD 150
Balance Sheet (at date of acquisition)
Assets CAD 11,000 USD 2,500
Liabilities CAD 9,000 USD 2,000
Surplus CAD 2,000 USD 500
Exchange Rate
1 USD = 1.5 CAD volatility = 4%
Risk-Free Interest Rate
Canada: 4%
US: 3%
(a) Describe the financial and economic impacts that foreign exchange rate risk could
have
(i) in general, on a multinational company, and
(ii) specifically, on CanCo and TargetCo following this acquisition.
COURSE 8: Fall 2003 -8- GO ON TO NEXT PAGE
Investment
Morning Session

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