SOA真题November2001Course8V

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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
Morning Session