16. (4 points) You are building a model for forecasting equity real estate values in portfolio
asset projections, given economic scenario inputs.
(a) List and justify the items you will need in order to build a robust model for equity
real estate values.
(b) Describe a method for determining the optimal level of equity real estate in your
company’s various portfolios.
COURSE 8: Fall 2003 - 13 - GO ON TO NEXT PAGE
Investment
Afternoon Session
17. (8 points) You are the Chief Risk Officer of Pusillanimous Re that provides annual
catastrophe reinsurance to the marketplace. You invest the asset portfolio in cash and
three zero-coupon bonds, each with 1-year time to maturity. You are given the following
information:
Reinsurance exposure: Excess cost layer between 100 million and 350 million of 1 billion
total earthquake exposure.
Cash Bond A Bond B Bond C
Market Value (millions) 2.0 2.2 2.0 1.8
Face Value (millions) 2.0 2.4 2.4 2.4
Expected default loss (%) 0 5 not given 15
Expected recovery rate (%) 100 not given 30 45
Historical default rate (%) 0 1 2 4
You are concerned about the default risk of your asset portfolio and the magnitude of
your liability exposure.
(a) Describe how you would calculate the 1-year default probability of Bond B using
(i) bond market prices, and
(ii) equity prices of the bond issuer.
(b) Calculate the 1-year expected default loss of Bond B implied by bond market
prices.
(c) Explain the reasons for the differences typically observed between the default
probabilities derived using historical default data and those derived from the bond
market prices.
(d) Compare and contrast the use of add-up credit default swaps (CDS) and first-todefault
CDS for management of the default risk in the asset portfolio.
(e) Describe how a first-to-default basket CDS on the asset portfolio can be valued
using a Gaussian copula approach.
(f) Explain how CAT bonds work and how they can be used to manage the option
structure of your liability risk exposure.
COURSE 8: Fall 2003 - 14 - GO ON TO NEXT PAGE
Investment
Afternoon Session
18. (4 points) The financial results at your insurance company over the past year have been
dismal. Your new CFO has asked you to determine the reasons behind this. She has
recently read about transfer pricing for banks, and is interested in applying this concept to
your company.
Total returns for your company:
Duration Credit Rating Return
Assets 10 A 5.70%
Liabilities 7 AAA (claims paying) 6.20%
Total return of generic assets over the past year:
Credit Rating
Duration A AA AAA
5 6.00% 6.50% 7.50%
6 5.90% 6.40% 7.40%
7 5.80% 6.30% 7.30%
8 5.70% 6.20% 7.20%
9 5.60% 6.10% 7.10%
10 5.50% 6.00% 7.00%
Your CFO wants to see the returns attributed to the following four sources:
1) Liability performance
2) Asset performance due to interest rate risk
3) Asset performance due to credit risk
4) Asset performance due to selection of individual securities
(a) Construct the appropriate benchmark portfolios from the generic assets provided.
(b) Attribute your company’s performance to the four sources described above, using
the benchmarks constructed in (a).
(c) Describe the considerations in benchmark selection when applying transfer
pricing to an insurance company.
COURSE 8: Fall 2003 - 15 - GO ON TO NEXT PAGE
Investment
Afternoon Session
19. (5 points) The current value of the assets and liabilities are respectively A0 and L0 . The
liability in five years is designated L5 . Senior management is concerned that the asset
portfolio could drop in value below the liability value in five years.
One method to model the asset returns would be using a multivariate normal model
and modified Cholesky decomposition with the following assumptions:
m 0.12, 0.06, 0.085equities, fixed income, real estate
covariance matrix =
0.04 0.003 0.014
0.003 0.0025 0.0015
0.014 0.0015 0.01
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(a) Evaluate potential problems in using this method to model the asset returns.
(b) Explain and evaluate the use of an option-based portfolio hedging strategy for a
portfolio of assets, A0 , and liabilities, L0 , where A0 > L0 , using
(i) a put, and
(ii) a call.
(c) Demonstrate that the strategies in (b) for the put and call options are equivalent,
assuming that cash flows are reinvested.
(d) Explain and evaluate the use of dynamic hedging by replicating the put option
using a risky portfolio and a duration-matched Treasury portfolio.
COURSE 8: Fall 2003 - 16 - GO ON TO NEXT PAGE
Investment
Afternoon Session

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