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The efficacy of life insurance company general account equity asset allocations: a safety-first perspective using vine copulas

Published online by Cambridge University Press:  21 January 2018

Ryan Timmer
Affiliation:
Jackson National Life Insurance Company, Lansing, MI 48951, USA
John Paul Broussard*
Affiliation:
School of Business – Camden, Rutgers, The State University of New Jersey, Camden, NJ 08102, USA Hanken School of Economics, Helsinki, Finland
G. Geoffrey Booth
Affiliation:
Eli Broad College of Business, Michigan State University, 355 Eppley Center, East Lansing, MI 48824, USA
*
*Correspondence to: John Paul Broussard, School of Business – Camden, Rutgers, The State University of New Jersey, Camden, NJ 08102, USA. Tel: +1 (856) 225-6647; E-mail: [email protected]

Abstract

We study the asset allocation decision of a life insurance company’s general account with respect to the possibility of large negative economic shocks and examine how this account is affected by policyholder investment decisions in the company’s separate account. This is accomplished using a performance metric that incorporates downside risk measured using univariate and multivariate extreme value distributions. Because of its well-known price volatility, diversification attributes, and significant weight in the combined general and separate accounts, our primary focus is the company’s equity investments. Although industry asset allocations have varied over the past two decades, we find that the actual allocations to equity in the general account are close to the allocation percentages suggested by our extreme value metrics and both are far below the maximum values indicated by the relevant regulatory bodies.

Type
Paper
Copyright
© Institute and Faculty of Actuaries 2018 

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References

Aas, K., Czado, C., Frigessi, A. & Bakken, H. (2009). Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics, 44, 182198.Google Scholar
Allen, D.E., McAleer, M. & Singh, A.K. (2014). Risk measurement and risk modelling using applications of vine copulas. Discussion Paper No. TI 14-054/III, Tinbergen Institute, Amsterdam, The Netherlands.Google Scholar
American Council of Life Insurers (ACLI) (2005, 2007, 2009, 2011, 2013, and 2014). Life Insurers Fact Book 2005. ACLI, Washington, DC.Google Scholar
Bailey, A.H. (1862). On the principles on which funds in life assurance societies should be invested. Journal of the Institute of Actuaries, 10, 142147.Google Scholar
Bawa, V.S. & Lindenberg, E.B. (1977). Capital market equilibrium in a mean-lower partial moment framework. Journal of Financial Economics, 5(2), 189200.Google Scholar
Bacon, C. (2016). How sharp is the sharpe ratio? – risk adjusted performance measures, StatPro. Available online at the address www.statpro.com [accessed 6-Dec-2016].Google Scholar
Bedford, T. & Cooke, R.M. (2001). Probability density decomposition for conditionally dependent random variables modeled by vines. Annals of Mathematics and Artificial Intelligence, 32, 245268.Google Scholar
Bedford, T. & Cooke, R.M. (2002). Vines – a new graphical model for dependent random variables. The Annals of Statistics, 30, 10311068.Google Scholar
Booth, G.G. & Broussard, J.P. (2002). The role of REITs in asset allocation. Finance (Revue de l’Association Finance de Francaise de France), 23(2), 108124.Google Scholar
Booth, G.G. & Broussard, J.P. (2016). The Sortino ratio and the generalized Pareto distribution: an application to asset allocation. In F. Longin (Ed.), Extreme Events in Finance: A Handbook of Extreme Value Theory and its Applications (pp. 443464). Wiley Interscience, Hoboken, NJ.Google Scholar
Brechmann, E.C. & Czado, C. (2013). Risk management with high-dimensional vine copulas: an analysis of the Euro Stoxx 50. Statistics & Risk Modeling, 30, 307342.Google Scholar
Brechmann, E.C. & Schepsmeier, U. (2013). Modeling dependence with C- and D-vine copulas: the R package CDVine. Journal of Statistical Software, 52(3), 127.Google Scholar
Browne, S. (1995). Optimal investment policies for a firm with a random risk process: exponential utility and minimizing the probability of ruin. Mathematics of Operations Research, 20, 937958.Google Scholar
Carmona, R. (2014). Statistical Analysis of Financial Data in R. Springer Science+Business Media, New York, NY.Google Scholar
Chiu, M.C. & Li, D. (2009). Asset-liability management under the safety-first principle. Journal of Optimization Theory and Applications, 143, 455478.Google Scholar
Clarke, K.A. (2007). A simple distribution-free test for nonnested model selection. Political Analysis, 15, 347363.Google Scholar
Consiglio, A., Cocco, F. & Zenios, S.A. (2008). Asset and liability modelling for participating policies with guarantees. European Journal of Operational Research, 186, 380404.Google Scholar
Consiglio, A., Pecorella, A. & Zenios, S.A. (2009). A conditional value-at-risk model for insurance products with a guarantee. International Journal of Risk Assessment and Management, 11, 122137.Google Scholar
Czado, C. (2010). Pair-copula constructions of multivariate copulas. In P. Jaworski, F. Durante, W. Härdle & T. Rychlik (Eds.), Copula Theory and its Applications (pp. 93109). Springer-Verlag, Berlin, Germany.Google Scholar
Czado, C., Schepsmeier, U. & Min, A. (2012). Maximum likelihood estimation of mixed C-Vines with application to exchange rates. Statistical Modelling, 12, 229255.Google Scholar
Henebry, K.L. & Diamond, J.M. (1998). Life insurance investment portfolio composition. Journal of Insurance Issues, 21(2), 183203.Google Scholar
Harlow, W.V. & Rao, R.K.S. (1989). Asset pricing in a generalized lower partial moment framework. Journal of Financial and Quantitative Analysis, 24(3), 285311.Google Scholar
Hart, O.H. (1965). Life insurance companies and the equity capital markets. Journal of Finance, 20(2), 358367.Google Scholar
Heaton, J. & Lucas, D. (2000). Portfolio choice in the presence of background risk. The Economic Journal, 110, 126.Google Scholar
Hogan, W.A. & Warren, J.M. (1974). Toward the development of an equilibrium capital market based on semivariance. Journal of Financial and Quantitative Analysis, 9(1), 111.Google Scholar
Joe, H. (1996). Families of m-variate distributions with given marginals and m(m – 1)/2 bivariate dependence parameters. In L. Rüschendorf, B. Schweizer & M.D. Taylor (Eds.), Distributions With Fixed Marginals and Related Topics (pp. 120141). Institute of Mathematical Statistics, Hayward, CA.Google Scholar
Kloss, A. & Weber, M. (2006). Portfolio choice in the presence of non-tradeable income: an experimental analysis. German Economic Review, 7(4), 427448.Google Scholar
Kurowicka, D. & Cooke, R.M. (2006). Uncertainty Analysis with High Dimensional Dependence Modelling. John Wiley & Sons, Chichester, UK.Google Scholar
Lamm-Tennant, J. (1989). Asset/liability management for the life insurer: situation analysis and strategy formulation. Journal of Risk and Insurance, 56, 501517.Google Scholar
Lintner, J. (1965). The value of risk assets and the selection of risky investments in stock portfolios and capital budgeting. Review of Economics and Statistics, 47(1), 1337.Google Scholar
Liu, C.S. & Yang, H. (2004). Optimal investment for an insurer to minimize its probability of ruin. North American Actuarial Journal, 8, 1131.Google Scholar
Longin, F. (2005). The choice of the distribution of asset returns: how extreme value theory can help? Journal of Banking & Finance, 29, 10171035.Google Scholar
Loretan, M. & Phillips, P.C.B. (1994). Testing the covariance stationarity of heavy tailed time series: an overview of theory with applications to several financial datasets. Journal of Empirical Finance, 1, 211248.Google Scholar
Markowitz, H.M. (1952). Portfolio selection. The Journal of Finance, 7, 7791.Google Scholar
Markowitz, H.M. (1959). Portfolio Selection. John Wiley & Sons, New York, NY.Google Scholar
Mossin, J. (1966). Equilibrium in a capital asset market. Econometrica, 34(4), 768783.Google Scholar
National Association of Insurance Commissioners (NAIC) (1996). Investment of Insurers Model Act (Defined Limits Version). Available online at the address www.naic.org/store/free/MDL-280.pdf [accessed 20-Apr-2017].Google Scholar
National Association of Insurance Commissioners (NAIC) (2001). Investment of Insurers Model Act (Defined Standard Version). Available online at the address www.naic.org/store/free/MDL-283.pdf [accessed 20-Apr-2017].Google Scholar
Palia, D., Qi, Y. & Wu, Y. (2014). Heterogeneous background risks and portfolio choice: evidence from micro-level data. Journal of Money, Credit and Banking, 46(8), 16871720.Google Scholar
Roy, A.D. (1952). Safety first and the holding of assets. Econometrica, 20, 431449.Google Scholar
Satchell, S.E. (2001). Lower-partial moment capital asset pricing models: a re-examination. In F.S. Sortino & S.E. Satchell (Eds.), Managing Downside Risk in Financial Markets: Theory Practice and Implementation (pp. 156168). Butterworth-Hienemann Finance, Oxford, UK.Google Scholar
Sharpe, W.F. (1964). Capital asset prices: a theory of market equilibrium under conditions of risk. Journal of Finance, 19(3), 425442.Google Scholar
Sharpe, W.F. (1966). Mutual fund performance. Journal of Business, 39(1, Part 2), 119138.Google Scholar
Sharpe, W.F. (1994). The sharpe ratio. Journal of Portfolio Management, 21(1), 4958.Google Scholar
Sklar, M. (1959). Fonctions de Répartition à n dimensions er Leurs Marges. Publications de l’Institut de Statistique de L’Université de Paris, 8, 229231.Google Scholar
Sortino, F.A. (2001). From alpha to omega. In F.A. Sortino & S.E. Satchell (Eds.), Managing Downside Risk in Financial Markets: Theory Practice and Implementation (pp. 325). Butterworth-Hienemann Finance, Oxford, UK.Google Scholar
Vuong, Q.H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57, 307333.Google Scholar
Weinsier, D.J., Cataldo, F.J., Hill, C.F. & Ross, D.L. (2002). Asset allocation for life insurers. Record of Society of Actuaries, 28(1), 124.Google Scholar