Tail Risks Across Investment Funds

Jerchern Lin

doi:10.18778/2391-6478.S1.2024.05

Authors

Jerchern Lin University of Illinois at Chicago https://orcid.org/0000-0002-2281-7068

DOI:

https://doi.org/10.18778/2391-6478.S1.2024.05

Keywords:

Tail Risk, Systematic Risk, Idiosyncratic Risk, Coskewness, Cokurtosis, Copula, Tail Dependence, ETFs, Closed-end Funds, Mutual Funds, Hedge Funds, Compensation

Abstract

The purpose of the article. Managed portfolios are subject to tail risks, which can be either index level (systematic) or fund-specific. Examples of fund-specific extreme events include those due to big bets or fraud. This paper studies the two components in relation to compensation structure in managed portfolios.

Methodology. A novel methodology is developed to decompose return skewness and kurtosis into various systematic and idiosyncratic components and applied it to the returns of different fund types to assess the significance of these sources. In addition, a simple model generates fund-specific tail risk and its asymmetric dependence on the market, and makes predictions for where such risks should be concentrated. The model predicts that systematic tail risks increase with an increased weight on systematic returns in compensation and idiosyncratic tail risks increase with the degree of convexity in contracts.

Results of the research. The model predictions are supported with empirical results. Hedge funds are subject to higher idiosyncratic tail risks and Exchange Traded Funds exhibit higher systematic tail risks. In skewness and kurtosis decompositions, the results indicate that coskewness is an important source for fund skewness, but fund kurtosis is driven by cokurtosis, as well as volatility comovement and residual kurtosis, with the importance of these components varying across fund types. Investors are subject to different sources of skewness and fat tail risks through delegated investments. Volatility based tail risk hedging is not effective for all fund styles and types.

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References

Aas, K. and Haff, I. H. (2006). The Generalized Hyperbolic Skew Student’s t-Distribution, Journal of Financial Econometrics, 4, pp. 275-309. DOI: https://doi.org/10.1093/jjfinec/nbj006

Ackermann, C., McEnally, R., Ravenscraft, D. (1999). The performance of hedge funds: Risk, return, and incentives, Journal of Finance, 54, pp. 833-874. DOI: https://doi.org/10.1111/0022-1082.00129

Agarwal, V. and Naik, N. Y. (2004). Risks and portfolio decisions involving hedge funds, Review of Financial Studies, 17, pp. 63-98. DOI: https://doi.org/10.1093/rfs/hhg044

Aggarwal, R. and Jorion, P. (2010). The performance of emerging hedge funds and managers, Journal of Financial Economics. DOI: https://doi.org/10.1016/j.jfineco.2009.12.010

Ang, A. and Chen, J. (2002). Asymmetric correlations of equity portfolios, Journal of Financial Economics, 63, pp. 443-494. DOI: https://doi.org/10.1016/S0304-405X(02)00068-5

Ang, A., Hodrick, R.J., Xing, Y. and Zhang, X. (2006). The cross-section of volatility and expected returns, Journal of Finance, 51, pp. 259-299. DOI: https://doi.org/10.1111/j.1540-6261.2006.00836.x

Ang, A., Hodrick, R.J., Xing, Y. and Zhang, X. (2009). High idiosyncratic volatility and low returns: International and further U.S. evidence, Journal of Financial Economics, 91, pp. 1-23. DOI: https://doi.org/10.1016/j.jfineco.2007.12.005

Aragon, G. O. (2007). Share restrictions and asset pricing: Evidence from the hedge fund industry, Journal of Financial Economics, 83, pp. 33-58. DOI: https://doi.org/10.1016/j.jfineco.2005.11.001

Asness, C., Krail, R. and Liew, J. (2001). Do hedge funds hedge? The Journal of Portfolio Management, 28, pp. 6-19. DOI: https://doi.org/10.3905/jpm.2001.319819

Barberis, N. and Huang, M. (2008). Stocks as lotteries: The implications of probability weighting for security prices, American Economic Review, 98, pp. 2066-2100. DOI: https://doi.org/10.1257/aer.98.5.2066

Bekaert, G. and Wu, G. (2000), Asymmetric volatility and risk in equity markets, Review of Financial Studies, 13, pp. 1–42. DOI: https://doi.org/10.1093/rfs/13.1.1

Blake, D. and Timmerman, A. (1998). The birth and death processes of mutual funds, European Finance Review, 2, pp. 57-77. DOI: https://doi.org/10.1023/A:1009729630606

Boguth, O. (2010). Stochastic idiosyncratic volatility, portfolio constraints, and the cross-section of stock returns, Working paper, University of British Columbia.

Boyer, B., Mitton, T., and Vorkink, K. (2010). Expected Idiosyncratic Skewness, Review of Financial Studies, 23, pp. 170-202. DOI: https://doi.org/10.1093/rfs/hhp041

Brennan, M.J. (1993). Agency and asset pricing, Working paper, University of California at Los Angeles.

Brown, S. J., and Goetzmann, W. N. (1995). Performance persistence, Journal of Finance, 50, pp. 679-698. DOI: https://doi.org/10.1111/j.1540-6261.1995.tb04800.x

Brown, S. J.,. Goetzmann, W. N., Ibbotson, R. G. (1999). Offshore hedge funds: Survival and performance, Journal of Business, 72, pp. 91-117. DOI: https://doi.org/10.1086/209603

Brown, K. C., Harlow, W. V. and Starks, L. T. (1996). Of tournaments and temptations: An analysis of managerial incentives in the mutual fund industry, Journal of Finance, 51, pp. 85-110. DOI: https://doi.org/10.1111/j.1540-6261.1996.tb05203.x

Busse, J. A. (1999). Volatility timing in mutual funds: Evidence from daily returns, Review of Financial Studies, 12, pp. 1009-1041. DOI: https://doi.org/10.1093/rfs/12.5.1009

Carhart, M. M. (1997). On persistence in mutual fund performance, Journal of Finance, 52, pp. 57-82. DOI: https://doi.org/10.1111/j.1540-6261.1997.tb03808.x

Chabi-Yo, F. (2009). Explaining the idiosyncratic volatility puzzle using stochastic discount factors, Journal of Banking and Finance.

Chabi-Yo, F. and Yang, J. (2009). Default risk, idiosyncratic coskewness and equity returns, Working paper, Ohio State University. DOI: https://doi.org/10.2139/ssrn.1572661

Cherkes, M., Sagi, J., and Stanton, R. (2009). A liquidity-based theory of closed-end funds, Review of Financial Studies, 22, pp. 257-297. DOI: https://doi.org/10.1093/rfs/hhn028

Chevalier, J. and Ellison, G. (1997). Risk taking by mutual funds as a response to incentives, Journal of Political Economy, 105, pp. 1167-1200. DOI: https://doi.org/10.1086/516389

Cvitanić, J., Polimenis, V., and Zapatero F. (2008). Optimal portfolio allocation with higher moments, Annals of Finance, 4, pp. 1-28. DOI: https://doi.org/10.1007/s10436-007-0071-5

Daal, E. and Yu, J.-S. (2007). Daily asset return movements and value-at-risk under alternative classes of model speciﬁcations, Working paper, Florida Institute of Technology.

Daniel, G., Sornette, D. and Wohrmann, P. (2009). Look-ahead benchmark bias in portfolio performance evaluation, Journal of Portfolio Management, 36, pp. 121-130. DOI: https://doi.org/10.3905/JPM.2009.36.1.121

Dittmar, R. F. (2002). Nonlinear pricing kernels, kurtosis preference, and evidence from the cross section of equity returns, Journal of Finance, 57, pp. 369-403. DOI: https://doi.org/10.1111/1540-6261.00425

Dokov, S., Stoyanov, S. V., and Rachev, S. T. (2007). Computing VaR and AVaR of skewed-t distribution, Working paper, University of California Santa Barbara.

Elton, E. J., Gruber, M. J. and. Blake, C. R. (2003). Incentive fees and mutual funds, Journal of Finance, 58, pp. 779-804. DOI: https://doi.org/10.1111/1540-6261.00545

Engle, R. and Mistry, A. (2007). Priced risk and asymmetric volatility in the cross-section of skewness, Working paper, New York University.

Evans, R. B. (2010). Mutual fund incubation, Journal of Finance. DOI: https://doi.org/10.1111/j.1540-6261.2010.01579.x

Fama, E. F., (1965). The behavior of stock-market prices, Journal of Business, 38, pp. 34-105. DOI: https://doi.org/10.1086/294743

Frey, R.,. McNeil, A. J. and. Nyfeler, M. A. (2001). Copulas and credit models, RISK, pp. 111-113.

Fung, W. and Hsieh D. A. (1997). Empirical characteristics of dynamic trading strategies: The case of hedge funds, Review of Financial Studies, 10, pp. 275-302. DOI: https://doi.org/10.1093/rfs/10.2.275

Fung, W. and Hsieh, D.A. (2001). The risk in hedge fund strategies: Theory and evidence from trend followers, Review of Financial Studies, 14, pp. 313-341. DOI: https://doi.org/10.1093/rfs/14.2.313

Getmansky, M., Lo, A. W., and Makarov, I. (2004). An econometric model of serial correlation and illiquidity in hedge fund returns, Journal of Financial Economics, 74, pp. 529-609. DOI: https://doi.org/10.1016/j.jfineco.2004.04.001

Goetzmann, W., Ingersoll, J., Spiegel, M., and Welch, I. (2007). Portfolio performance manipulation and manipulation-proof performance measures, Review of Financial Studies, 20, pp. 1503-1546. DOI: https://doi.org/10.1093/rfs/hhm025

Grinblatt, M. and Titman S. (1994). A study of monthly mutual fund returns and performance evaluation techniques, Journal of Financial and Quantitative Analysis, 29, pp. 419-444. DOI: https://doi.org/10.2307/2331338

Hamao, Y., Masulis, R. W. and Ng, V. (1990). Correlations in price changes and volatility across international stock markets, Review of Financial Studies, 3, pp. 281-307. DOI: https://doi.org/10.1093/rfs/3.2.281

Hansen, L. P. (1982). Large sample properties of the generalized method of moments estimators, Econometrica ,50, pp. 1029-1054. DOI: https://doi.org/10.2307/1912775

Hansen, B. E., (1994). Autoregressive conditional density estimation, International Economic Review, 35, pp. 705-730. DOI: https://doi.org/10.2307/2527081

Harvey, C. R., Liechty, M., Liechty, J., and Müller, P. (2010). Portfolio selection with higher moments, Quantitative Finance, 10, pp. 469-485. DOI: https://doi.org/10.1080/14697681003756877

Harvey, C. R., and Siddique, A. (1999). Autoregressive conditional skewness, Journal of Financial and Quantitative Analysis, 34, pp. 465-487. DOI: https://doi.org/10.2307/2676230

Harvey, C. R., and Siddique, A. (2000). Conditional skewness in asset pricing tests, Journal of Finance, 55, pp. 1263-1295. DOI: https://doi.org/10.1111/0022-1082.00247

Hemmer, T., Kim, O. and Verrecchia, R. E. (2000). Introducing convexity in to optimal compensation contracts, Journal of Accounting and Economics, 28, pp. 307-327. DOI: https://doi.org/10.1016/S0165-4101(00)00008-2

Holmstrom, B. (1979). Moral hazard and observability, Bell Journal of Economics, 10, pp. 74-91. DOI: https://doi.org/10.2307/3003320

Hunter, D., Kandel, E., Kandel, S. and Wermers, R. (2010). Endogenous benchmarks, Working paper, University of Maryland. DOI: https://doi.org/10.2139/ssrn.1364505

Jagannathan, R., Malakhov, A. and Novikov, D. (2010). Do hot hands exist among hedge fund managers?. An empirical evaluation, Journal of Finance, 65, pp. 217-255. DOI: https://doi.org/10.1111/j.1540-6261.2009.01528.x

Jondeau, E. and Rockinger, M. (2003). Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements, Journal of Economic Dynamics and Control, 27, pp. 1699-1737. DOI: https://doi.org/10.1016/S0165-1889(02)00079-9

Kan, R. and Zhou, G (1999). A Critique of the Stochastic Discount Factor Methodology. Journal of Finance, 54, pp. 1221-1248. DOI: https://doi.org/10.1111/0022-1082.00145

Kane, A. (1982). Skewness preference and portfolio choice, Journal of Financial and Quantitative Analysis, 17, pp. 15-25. DOI: https://doi.org/10.2307/2330926

Kempf, A., and Ruenzi, S. (2008). Tournaments in mutual-fund families, Review of Financial Studies, 21, pp. 1013-1036. DOI: https://doi.org/10.1093/rfs/hhm057

Kim, M. S. (2010). Changes in Mutual Fund Flows and Managerial Incentives, Working paper, University of New South Wales. DOI: https://doi.org/10.2139/ssrn.1517572

Kraus, A. and. Litzenberger, R. H. (1976). Skewness preference and the valuation of risk assets, Journal of Finance, 31, pp. 1085-1100. DOI: https://doi.org/10.1111/j.1540-6261.1976.tb01961.x

Lee, C. M. C., Shleifer, A., Thaler, R. H. (1991), Investor sentiment and the closed-end fund puzzle, Journal of Finance, 46, pp. 75-109. DOI: https://doi.org/10.1111/j.1540-6261.1991.tb03746.x

Leland, H. E. (1999). Beyond mean-variance: Risk and performance measurement in a nonsymmetrical world, Financial Analysts Journal, pp. 27-36. DOI: https://doi.org/10.2469/faj.v55.n1.2239

Lo, A. W. (2002). The statistics of Sharpe ratios, Financial Analysts Journal, 58, pp. 36-50. DOI: https://doi.org/10.2469/faj.v58.n4.2453

Longin, F., and Solnik, B. (2001). Extreme correlation of international equity markets, Journal of Finance, 56, pp. 649-676. DOI: https://doi.org/10.1111/0022-1082.00340

Mandelbrot, B. (1963). The variation of certain speculative prices, Journal of Business,36, pp. 394-419. DOI: https://doi.org/10.1086/294632

McNeil, A. J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management: Concepts, Techniques and Tools, Princeton University Press.

Merton, R. C., and Henriksson, R. D. (1981). On market timing and investment performance II: Statistical procedures for evaluating forecasting skills, Journal of Business, 54, pp. 513-534. DOI: https://doi.org/10.1086/296144

Mitton, T. and Vorkink, K. (2007). Equilibrium under diversification and the preference for skewness, Review of Financial Studies, 20, pp. 1255-1288. DOI: https://doi.org/10.1093/revfin/hhm011

Moreno, D. and Rodríguez, R. (2009). The value of coskewness in mutual fund performance evaluation, Journal of Banking and Finance, 33, pp, 1664-1676. DOI: https://doi.org/10.1016/j.jbankfin.2009.03.015

Murphy, K. J. (1999). Executive Compensation, Handbook of Labor Economics, Vol. III, Orley Ashenfelter and David Card, editors. North Holland.

Patton, A. J. (2004). On the out-of-sample importance of skewness and asymmetric dependence for asset allocation, Journal of Financial Econometrics, 2(1), pp. 130-168. DOI: https://doi.org/10.1093/jjfinec/nbh006

Pontiff, J. (1997). Excess volatility and closed-end funds, American Economic Review, 87, pp. 155-169.

Ramakrishnan, R. T. S., and Thakor, A. V. (1984). The valuation of assets under moral hazard, Journal of Finance, 39, pp. 229-238. DOI: https://doi.org/10.1111/j.1540-6261.1984.tb03870.x

Samuelson, P. A. (1970). The fundamental approximation theorem of portfolio analysis in terms of means, variances and higher moments. The Review of Economic Studies, 37, pp. 537-542. DOI: https://doi.org/10.2307/2296483

Simonson, D. (1972). The speculative behavior of mutual funds, Journal of Finance, 27, pp. 381-391. DOI: https://doi.org/10.1111/j.1540-6261.1972.tb00967.x

Sirri, E. R., and Tufano, P. (1998), Costly search and mutual fund ﬂows, Journal of Finance, 53, pp. 1589-1622. DOI: https://doi.org/10.1111/0022-1082.00066

Starks, L. T. (1987). Performance incentive fees: An agency theoretic approach, Journal of Financial and Quantitative Analysis, 22, pp. 17-32. DOI: https://doi.org/10.2307/2330867

Susmel, R. and Engle, R. F. (1994). Hourly volatility spillovers between international equity markets, Journal of International Money and Finance, 13, pp. 3-25. DOI: https://doi.org/10.1016/0261-5606(94)90021-3

Swaminathan, B. (1996). Time-varying expected small ﬁrm returns and closed-end fund discounts, Review of Financial Studies, 9, pp. 845-887. DOI: https://doi.org/10.1093/rfs/9.3.845

Taleb, N. N. (2004). Bleed or blowup: what does empirical psychology tell us about the preference for negative skewness?, Journal of Behavioral Finance, 5. DOI: https://doi.org/10.1207/s15427579jpfm0501_1

Ter Horst, J. R. and Verbeek, M. (2007). Fund liquidation, self-selection, and look-ahead bias in the hedge fund industry, Review of Finance, 11, pp. 605-632. DOI: https://doi.org/10.1093/rof/rfm012

Theodossiou, P. (1998). Financial data and the skewed generalized T distribution, Management Science , 44, pp. 1650-1661. DOI: https://doi.org/10.1287/mnsc.44.12.1650

Thompson, R. (1978). The information content of discounts and premiums on closed-end fund shares, Journal of Financial Economics, 6, pp. 151-186. DOI: https://doi.org/10.1016/0304-405X(78)90028-4

Titman, S., and Tiu, C. (2010). Do the best hedge funds hedge?, Review of Studies, 24, pp. 123-168. DOI: https://doi.org/10.1093/rfs/hhq105

Treynor, J. and Mazuy, K. (1966). Can mutual funds outguess the market?, Harvard Business Review, 44, pp. 131-136.

(www1) https://www.hfr.com/ [Accessed: 08.06.2009].

(www2) https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html [Accessed: 08.06.2009].

(www3) https://people.duke.edu/~dah7/DataLibrary/TF-FAC.xls [Accessed: 08.06.2009].