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Thomas Berry-Stölzle
Hendrik Kläver
Shen Qiu
Terry College of Business
University of Georgia
Should Life Insurance CompaniesInvest in Hedge Funds?
Financial support from the AXA Colonia-Studienstiftung im Stifterverband für die Deutsche Wissenschaft is gratefully
acknowledged.
T. Berry-Stölzle University of Georgia
1. Introduction
Agenda
2. Model
3. Simulation Results
4. Implications for Asset Management
5. Summary
T. Berry-Stölzle University of Georgia
The assets under management in the hedge fund industry rose from approximately $50 billion in 1990 to approximately $1 trillion by the end of 2004.
Hedge funds provide actively managed portfolios in publicly traded assets.
Hedge funds are free from the regulatory controls stipulated by the Investmant Company Act of 1940.
Free choice in the type of securities for investment as well as the type of positions. e.g., investment in derivatives, sell short or take on leveraged positions.
Potential to generate risk return profiles different from traditional asset classes.
1. Introduction
T. Berry-Stölzle University of Georgia
Since January 1, 2004 hedge funds can be established in Germany.
In September 2004, the German Insurance Authority (BaFin) included hedge funds in the list of permitted investments for German life insurance companies.
Now, insurers can invest up to 5% of the reserves in hedge funds, using the opening clause 10%.
Insurers can file an application with the BaFin to increase the maximum hedge fund holding by another 5%.
Insurers are not allowed to invest more than 35% of the reserves in „risky“ assets.
Situation in Germany
T. Berry-Stölzle University of Georgia
Should life insurers invest in hedge funds?
How much should they invest in hedge funds?
How does an insurance company’s liability structure affect investments in hedge funds?
Research Questions
T. Berry-Stölzle University of Georgia
Idea: Kling, Richter, and Ruß (2007) model the standard German life insurance product with all its guarantees. We extend their model on the asset side with 3 correlated AR(1) GARCH(1,1) processes.
Calibrate model to DAX, REXP, and hedge funds indices
Analyze optimal asset allocation under various parameter settings applying Monte Carlo Simulations.
Method
T. Berry-Stölzle University of Georgia
2. Model
Balance Sheet Perspective:
Assets Liabilities
With: market value of assets
policy reserve / book value of liabilities
hidden reserves (+capital)
tA tL
tR
tAtA
tA
tL
tR
T. Berry-Stölzle University of Georgia
Three Assets: Stock, Bond, Hedge Fund
Each follows an AR(1) GARCH(1,1) process
Processes are correlated
Special case of Engle and Kroner (1995)
Limitation: Only one set of GARCH parameters for all three processes.
Assets
T. Berry-Stölzle University of Georgia
Insurance Contract:
Single-premium term-fix insurance (no charges)
Premium P is payed at t=0, benefit is payed at t=T
No mortality effects
Regulatory and Legal Requirements:
Minimum interest rate guarantee for whole policy period
Cliquet-style guarantee!
At least = 90% of asset returns have to be credited to the policyholders’ accounts (based on book values !)
Liabilities
T. Berry-Stölzle University of Georgia
Asset Valuation:
Hidden reserves: market value of assets exceeds book value
Insurers can reduce reserves immediately.
Increase of reserves subject to constraints (parameter y = 50%)
Profit Participation:
Usually German insurers credit a smoothed rate of interest to policyholders‘ accounts.
Management decision rule:
Credit target rate of interest z>g to policyholders, as long as the reserve quota stays within [a,b].
Management Interaction
/t tR L
T. Berry-Stölzle University of Georgia
Model:
with asset allocation = const.
Calculate efficient frontier
Short sales are not allowed
Choose portfolio from the efficient set
Optimal Asset Allocation
, ,( )
shortfall probabilityf asset allocation asset scenarios others
portfolioreturn
T. Berry-Stölzle University of Georgia
Data:
Monthly returns of CISDM hedge fund strategy indices from the Center for International Securities and Derivatives Markets
Stock and bond index data from Datastream
01/1992 – 12/2005
Deviations from Estimated Parameter Values:
Set expected bond return to 5% instead of 6.8%
Subtract 3% from expected hedge fund returns to correct for biases in hedge fund database
Model Calibration
T. Berry-Stölzle University of Georgia
Base Case
Parameters:
x = 0.2 reserve quota
g = 0.0275 min. interest r.
z = 0.05 target interest r.
= 0.03 dividends
= 0.9 min. participation
y = 0.5 hidden reserves
10.000 independent
Monte Carlo simulations
3. Simulation Results
Shortfall Probability in %
Ex
pe
cte
d R
etu
rn i
n %
T. Berry-Stölzle University of Georgia
Interest Rate Guarantees
Shortfall Probability in %
Ex
pe
cte
d R
etu
rn i
n %
Parameters:
g = 0.04
vs.
g = 0.0275
T. Berry-Stölzle University of Georgia
Shortfall Probability in %
Ex
pe
cte
d R
etu
rn i
n %
Initial Reserve Quota
Parameters:
x = 0.1
vs.
x = 0.2
T. Berry-Stölzle University of Georgia
Shortfall Probability in %
Ex
pe
cte
d R
etu
rn i
n %
Restrictions in Asset Valuation
Parameters:
y = 0.95
vs.
y = 0.5
T. Berry-Stölzle University of Georgia
Model results:
Life insurers with cliquet-style guarantees should not hold volatile asset portfolios.
Diversification is beneficial, and hedge funds help.
Insurers with higher guarantees or lower surplus / financial reserves should hold more hedge funds.
But
Model only considers correlations, but dependence in extrem market situations is probably different.
Hedge fund returns in database are from a time period where there were only few of them.
4. Asset Management
T. Berry-Stölzle University of Georgia
ad hoc Recommendation for Insurers:
Limits of hedge fund positions should be determined by stress tests. These limits will probably be binding in any optimization
Insurers should monitor hedge fund returns closely.
Conclusion for Regulators:
Financially weak insurers have incentives to invest a lot in hedge funds (go-for-broke behavior).
Asset Management (II)
T. Berry-Stölzle University of Georgia
We extend the Kling, Richter, and Ruß (2007) model of a German life insurance company on the asset side with 3 correlated AR(1) GARCH(1,1) processes.
Calibrate model to real world data.
Analyze optimal asset allocation under various parameter settings applying Monte Carlo Simulations.
Hedge funds offer an effective instrument for portfolio diversification
5. Summary