Thomas Berry-Stölzle Hendrik Kläver Shen Qiu Terry College of Business University of Georgia Should Life Insurance Companies Invest 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 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 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)

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. 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

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 = min. interest r. z = 0.05 target interest r.  = 0.03 dividends  = 0.9 min. participation y = 0.5 hidden reserves independent Monte Carlo simulations 3. Simulation Results Shortfall Probability in % Expected Return in %

T. Berry-Stölzle University of Georgia Interest Rate Guarantees Shortfall Probability in % Expected Return in % Parameters: g = 0.04 vs. g =

T. Berry-Stölzle University of Georgia Shortfall Probability in % Expected Return in % Initial Reserve Quota Parameters: x = 0.1 vs. x = 0.2

T. Berry-Stölzle University of Georgia Shortfall Probability in % Expected Return in % 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