Top

Zeitschrift für die gesamte Versicherungswissenschaft

Published in:

16-09-2016 | Abhandlung

The Illiquidity Discount of Life Insurance Investments

Authors: Ruth Kümmerle, Markus Rudolf

Published in: Zeitschrift für die gesamte Versicherungswissenschaft | Issue 3/2016

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

We incorporate an illiquid life insurance investment in the multi-period investment strategy of an investor with constant relative risk aversion and independent and identically distributed returns. In our setup, the liquid and the illiquid assets are risky and correlated and the illiquid investment cannot be rebalanced. We calculate the illiquidity discount as the difference in certainty equivalent rates of return between the optimal strategy with all assets being rebalanced in each period and the strategy with the illiquid investment. Calibrating our model to data of the German market we find a negative relationship between the level of risk aversion and the illiquidity discount when the investor does not rebalance at all. However, when the investor rebalances his liquid assets in each period to hedge against the illiquid investment the illiquidity discount becomes economically negligible.

previous article Aktuelle und zukünftige Fragen der Lebensversicherung zwischen Zivil- und Aufsichtsrecht – Information und Beratung nach der Richtlinie (EU) 2016/97 über Versicherungsvertrieb

next article Private Hochwasservorsorge und Elementarschadenversicherung

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

These results are especially due to the high positive correlation between the illiquid investment and the liquid assets. Negative correlations increase the ID and change the investor specific pattern as shown exemplarily in Appendix C.

Albrecht, P.: 30 Jahre Kapitalanlageperformance der deutschen Lebensversicherer. Working Paper. University of Mannheim, Mannheim (2010). available through: https://ub-madoc.bib.uni-mannheim.de/2980

Albrecht, P., Maurer, R., Schradin, H.R.: Die Kapitalanlageperformance der Lebensversicherer im Vergleich zur Fondsanlage unter Rendite- und Risikoaspekten. Verlag Versicherungswirtschaft, Karlsruhe (1999)

Ang, A., Papanikolaou, D., Westerfield, M.: Portfolio Choice with Illiquid Assets. Manage Sci 60(11), 2737–2761 (2014)CrossRef

BaFin: Geschäftsbericht 2001 des Bundesaufsichtsamtes für Versicherungswesen B (2003). available through: www.bafin.de

Berketi, A.K.: Insolvency risk and its impact on the policyholders’ investment choices: a mean–variance approach for participating life insurance business in UK. Insur Math Econ 25(3), 349–372 (1999)CrossRef

Brandt, M.: Portfolio Choice Problems. In: Aït-Sahalia, Y., Hansen, L.P. (eds.) Handbook of Financial Econometrics: Tools and Techniques. Elsevier, Amsterdam (2010)

Brandt, M., Santa-Clara, P.: Dynamic Portfolio Selection by Augmenting the Asset Space. J Finance 61(5), 2187–2217 (2006)CrossRef

Browne, S., Milevsky, M., Salisbury, T.: Asset Allocation and the Liquidity Premium for Illiquid Annuities. J Risk Insur 70(3), 509–526 (2003)CrossRef

Brunnermeier, M., Nagel, S.: Do Wealth Fluctuations Generate Time-Varying Risk Aversion? Micro-Evidence on Individuals’ Asset Allocation. Am Econ Rev 98(3), 713–736 (2008)CrossRef

Budhraja, V., Figueiredo, R.: How Risky Are Illiquid Investments? J Portfolio Manag 31(2), 83–93 (2005)CrossRef

BVZL: Secondary Market for Life Insurance Policies (2010). available through: http://www.bvzl.de

Cao, D., Teïletche, J.: Reconsidering asset allocation involving illiquid assets. J Asset Manag 8(4), 267–282 (2007)CrossRef

Chaffe, D.: Option Pricing as a Proxy for Discount for Lack of Marketability in Private Company Valuations. Bus Valuat 12(4), 182–188 (1993)CrossRef

Chipalkatti, N., Luft, C., Levine, L., Lummezen, M.: Estimating the Marketability Discount: A Comparison Between Bid-Ask Spreads, and Longstaff’s Upper Bound. J Appl Finance 23(1), 57–70 (2013)CrossRef

Cremers, J.-H., Kritzman, M., Page, S.: Portfolio formation with higher moments and plausible utility. Revere Street Working Paper Series, Financial Economics, vol. 272-12. (2003)

Cremers, J.-H., Kritzman, M., Page, S.: Optimal Hedge Fund Allocations. J Portfolio Manag 31(3), 70–81 (2005)CrossRef

De Roon, F., Guo, J., Horst, J.: Being Locked Up Hurts. Working Paper. Tilburg University, Tilburg (2010). available through: http://ssrn.com/abstract=1342450

DeMiguel, V., Garlappi, L., Uppal, R.: Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy? Rev Financial Stud 22(5), 1915–1953 (2009)CrossRef

Diepold, D., Dzienziol, J.: Illiquide Assets in der Portfoliooptimierung. Zeitschrift Für Betriebswirtschaft 79(10), 1143–1173 (2009)CrossRef

Garlappi, L., Skoulakis, G.: Taylor series approximations to expected utility and optimal portfolio choice. Math Fiancial Econ 5(2), 121–156 (2011)CrossRef

Gatzert, N., Holzmüller, I., Schmeiser, H.: Creating Customer Value in Participating Life Insurance. J Risk Insur 79(3), 545–670 (2012). doi:10.1111/j.1539-6975.2011.01453.xCrossRef

GDV: Die deutsche Lebensversicherung in Zahlen: Geschäftsentwicklung 1997. GDV, Berlin (1997)

GDV: Die deutsche Lebensversicherung in Zahlen 2014 (2014). available through: http://www.gdv.de

Geltner, M.: Smoothing in Appraisal-Based Returns. J Real Estate Finance Econ 4(3), 327–345 (1991)CrossRef

Getmansky, M., Lo, A., Makarov, I.: An econometric model of serial correlation and illiquidity in hedge fund returns. J financ econ 74(3), 529–609 (2004)CrossRef

Goecke, O.: Pension saving schemes with return smoothing mechanism. Insur Math Econ 53(3), 678–689 (2013)CrossRef

Hieber, P., Korn, R., Scherer, M.: Analyzing the effect of low interest rates on the surplus participation of life insurance policies with different annual interest rate guarantees. Eur Actuar J 5(1), 11–28 (2015). doi:10.1007/s13385-014-0102-3CrossRef

Hoesli, M., Liljeblom, E., Löflund, A.: The Effect of Lock-Ups on Suggested Real Estate Portfolio Weight. Int Real Estate Rev 17(1), 1–22 (2014)

Kolm, P., Tütüncü, R., Fabozzi, F.: 60 Years of portfolio optimization: Practical challenges and current trends. Eur J Oper Res 234(2), 356–371 (2014)CrossRef

Kroll, Y., Levy, H., Markowitz, H.: Mean-Variance Versus Direct Utility Maximization. J Finance 39(1), 47–61 (1984)CrossRef

Kümmerle, R., Rudolf, M.: Portfolio Optimization with Illiquid Life Insurance Investments. Working Paper. WHU – Otto Beisheim School of Management, Vallendar (2016). available through: http://ssrn.com/abstract=2501334

Levy, H., Markowitz, H.: Approximating Expected Utility by a Function of Mean and Variance. Am Econ Rev 69(3), 308–317 (1979)

Longstaff, F.: How Much Can Marketability Affect Securities Values. J Finance 50(5), 1767–1774 (1995a)CrossRef

Longstaff, F.: Placing No-Arbitrage Bounds on the Value of Nonmarketable and Thinly-Traded Securities. Adv Futur Options Res 8, 203–228 (1995b)

Longstaff, F.: Valuing Thinly-Traded Assets. Working Paper. NBER, Cambridge, Mass. (2014). available through: http://www.nber.org/papers/w20589 CrossRef

Loudon, G., Okunev, J., White, D.: Hedge Fund Risk factors and the Value at Risk of Fixed Income Trading Strategies. J Fixed Income 16(2), 46–61 (2006)CrossRef

Markowitz, H.: Mean-variance approximations to expected utility. Eur J Oper Res 234(2), 346–355 (2014)CrossRef

Merton, R.: Lifetime Portfolio Selection under Uncertainty. Rev Econ Stat 3(51), 247–257 (1969)CrossRef

Merton, R.: Optimum Consumption and Portfolio Rules in a Continuous-Time Model. J Econ Theory 3(4), 373–413 (1971)CrossRef

Mossin, J.: Optimal Multiperiod Portfolio Choices. J Bus 41(2), 215–229 (1968)CrossRef

Pulley, L.: A general mean-variance approximation to expected utility for short holding periods. J Financial Quant Analysis 16(3), 361–373 (1981)CrossRef

Samuelson, P.: Lifetime Portfolio Selection by Stochastic Dynamic Programming. Rev Econ Stat 3(51), 239–246 (1969)CrossRef

Skoulakis, G.: On the quality of Taylor approximations to expected utility. Appl Financial Econ 22(11), 863–876 (2012)CrossRef

Sun, W., Fan, A., Chen, L.-W., Schouwenaars, T., Albota, M.: Optimal Rebalancing for Institutional Portfolios. J Portfolio Manag 32(2), 33–43 (2006)CrossRef

Wolff, K.-H.: Versicherungsmathematik. Springer-Verlag, Wien, New York (1970)CrossRef

Title: The Illiquidity Discount of Life Insurance Investments
Authors: Ruth Kümmerle
Markus Rudolf
Publication date: 16-09-2016
Publisher: Springer Berlin Heidelberg
Published in: Zeitschrift für die gesamte Versicherungswissenschaft / Issue 3/2016
Print ISSN: 0044-2585
Electronic ISSN: 1865-9748
DOI: https://doi.org/10.1007/s12297-016-0343-0

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Springer Professional "Wirtschaft+Technik"

Other articles of this Issue 3/2016

Beitragsentwicklung und Verteilungseffekte der RfB in PKV-Beständen

Marktversagen auf dem geförderten Pflegezusatzversicherungsmarkt?

Aktuelle und zukünftige Fragen der Lebensversicherung zwischen Zivil- und Aufsichtsrecht – Information und Beratung nach der Richtlinie (EU) 2016/97 über Versicherungsvertrieb

Private Hochwasservorsorge und Elementarschadenversicherung

Seitz, Björn/Finkel, Bastian/Klimke, Dominik: D&O-Versicherung. Kommentar zu den AVB-AVG

Neuerscheinungen versicherungswissenschaftlicher Bücher – Ausführliche Hinweise