Skip to main content
SpringerLink
Log in

How can defined contribution pension plans benefit from momentum and mean reversion?

  • Original Research Paper
  • Published:
European Actuarial Journal Aims and scope Submit manuscript

Abstract

In this paper, we assess whether the stock market downturn can be an opportunity for Defined Contribution pension plan members to reinforce their risky assets exposure? In line with the framework developed by Kojein et al. (Manag Sci 55(7):1199–1213, 2009), we consider a DC plan investor, during the accumulation phase, whose aim is to maximize his terminal wealth. Within a continuous portfolio choice model, in which stock returns exhibit both momentum and mean reversion, DC plan members are allowed to invest their pension wealth into stocks as well as cash and bond assets. We derived the optimal portfolio candidate and we show how a DC plan investor can benefit from market opportunities by taking advantage of the momentum and mean reversion stock return properties. We find that long term investors such as DC plan members would benefit from a temporary increase of the share of risky assets in their portfolio in preparation of their retirement.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. Fama E (1970) distinguished three forms of market efficiency: weak efficiency, semi-strong efficiency and strong efficiency.

  2. $$ \phi^{*}(k)=\sum_{j=1}^{k-1}\left[\frac{2(k-j)}{k}\right]^{2}\delta_{j}\,\hbox {and}\,\delta_{j}=\frac{\sum^{T}_{t=j+1}\left(X_{t}-X_{t-1}-\hat{\mu}\right)^{2} \left(X_{t-j}-X_{t-j-1}-\hat{\mu}\right)^{2}}{\left[\sum^{T}_{t=j+1} \left(X_{t}-X_{t-1}-\hat{\mu}\right)^{2}\right]^{2}}. $$

  3. The \(M_{1}(k)\) or \(M_{2}(k)\) statistics are directly given by the Lo and Mackinlay variance ratio test.

  4. where \(s_{t} = 2u(x_{t},0), s_{t}(\bar{\mu}) = 2u(x_{t},\bar{\mu})\) and:

    $$ u(x_{t},q)=\left\{\begin{array}{ll} 0.5 & \hbox {if}\, x_{t} > q\\ -0.5& \hbox {otherwise}\end{array}\right.. $$

  5. Data source: Morgan Stanley Capital Investment (MSCI). The database comprises the United States, the United Kingdom, France, Germany, Spain, Hong Kong, Japan, Italy, Canada, Australia, Sweden, Norway, Belgium and Netherlands.

  6. The Jarque and Berra statistic is given by

    $$ JB_{\alpha} = \frac{t-k}{6}\left[S^{2}+\frac{1}{4}(K-3)^{2}\right] \sim \chi^{2}(2) $$
    (10)

    There exists a large number of normality tests such as the Shapiro Wilk parametric normality test (1965) or the Kolmogorov–Smirnov non-parametric one.

  7. Note that under \(H_{0}, \) the Jarque and Berra test is distributed as a \(\chi_{\alpha}^{2}\) squared distribution with 2 degrees of freedom.

  8. There exists a large panel of tests allowing the detection of heteroscedasticity in time series. In particular, there are the Breush and Pagan test (1979) and the White test (1980) which are frequently used in the literature.

  9. The test strategy is the following:

    • If TR \(> \chi^{2}_{\alpha} (q)\) then \(H_{0}\) cannot be accepted which involves the rejection of the homoscedasticity assumption.

    • If TR \(< \chi^{2}_{\alpha} (q)\) then \(H_{0}\) is not rejected thus we cannot reject the homoscedasticity assumption.

  10. Note furthermore that the proposed test presents higher power in simulations than the existing ones for models commonly employed in empirical finance.

  11. Note that the traditional Ljung Box test leads to a systematic rejection of the null hypothesis translating thus the presence of momentum in all the stock market returns considered.

  12. These outlier returns generally occur at the beginning of the week (Monday effect) or at the beginning of the year (January effect) [48]. Jegadeesh [25] identifies abnormal returns as the result of seasonal effects. Stock returns can also react to other factors such as news [43] or firm size effects [48].

  13. The risk premium (also known as the Sharpe ratio) is usually calculated as follows \(rp_{t}=\frac{\mu_{t} -r}{\sigma_{t}}\Leftrightarrow rp_{t}=\frac{\lambda_{t}}{\sigma_{t}}.\)

  14. Complete calculations are available in Chetouane [13].

  15. CRRA (Constant Relative Risk Aversion) is comprised within the HARA (Hyperbolic Absolute Risk Aversion) utility functions. Several functional forms are usually used in the literature. The most widespread utility function is \(U(X_{T})=\frac{1}{1-\gamma}X^{1-\gamma}_{T},\)where \(\frac{U^{\prime}(X_{T})}{U^{\prime\prime}(X_{T})X_{T}}=-\frac{1}{\gamma}.\)

  16. Ornstein LS, Ulhembeck GE (1930) On the Theory of Brownian Motion. Phys Rev 36:823–841.

  17. See Vasicek [45] for a complete presentation.

  18. Boulier et al. [9] suggest a way to connect the bond asset to the risk free asset and the constant K maturity zero coupon through the following linear combination \(\frac{dP( {{r}_{t}},t,\tau)}{P( {{r}_{t}},t,\tau)}=(1-\frac{a(t,\tau)}{a_{k}})\frac{dR_{t}}{R_{t}} +\frac{a(t,\tau)}{a_{k}}\frac{dP_{k}(r_{t},t)}{P_{k}(r_{t},t)}.\)

  19. It can be assumed that interest rate changes have a direct influence on stock market dynamics. Korn and Kraft [32], Munk and Sorensen [40] propose to include such interactions in the stock price dynamics.

  20. Munk and Sorensen [40] use the Cholevski decomposition to link both markets.

References

  1. Balvers RJ, Gilliland E, Wu Y (2000) Mean reversion across national stock markets and parametric contrarian investment strategies. J Finance 55(2):745–772

    Google Scholar 

  2. Balvers RJ, Wu Y (2006) Momentum and mean reversion across national equity markets. J Empir Finance 13:24–48

    Article  Google Scholar 

  3. Battocchio P, Menoncin F (2002a) Optimal portfolio strategies with stochastic wage income and inflation: the case of a defined contribution pension plan, CeRP Working Papers 19, Center for Research on Pensions and Welfare Policies, Turin

    Google Scholar 

  4. Battocchio P, Menoncin F (2002b) Optimal pension management under stochastic interest rates, wages, and inflation, Discussion Papers (IRES: Institut de Recherches Economiques et Sociales) 2002021, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES)

  5. Battocchio P, Menoncin F, Scaillet O (2003) Optimal asset allocation for pension funds under mortality risk during the accumulation and decumulation phases, THEMA Working Papers 2003-28, THEMA (Théorie Economique, Modélisation et Applications), Université de Cergy-Pontoise

  6. Belaire-Franch J, Contreras D (2004) Ranks and signs-based multiple variance ratio tests, Working paper, University of Valencia

  7. Belaire-Franch J, Opong KK (2005) Some evidence of random walk of euro Exchange rate using ranks and signs. J Banking Finance 29:1631–1643

    Article  Google Scholar 

  8. Bodie Z, Merton RC, Samuelson WF (1992) Labor supply flexibility and portfolio choice in a life-cycle model. J Econ Dyn Control 16:427–449

    Article  Google Scholar 

  9. Boulier JF, Huang SJ, Taillard G (2001) Optimal management under stochastic interest. Insur Math Econ 28:173–189

    Article  MathSciNet  MATH  Google Scholar 

  10. Brennan MlJ, Xia Y (2000) Dynamic Asset Allocation under Inflation, University of California at Los Angeles, Anderson Graduate School of Management 2893, Anderson Graduate School of Management, UCLA

  11. Cairns AJG, Blake D, Dowd K (2006) Stochastic lifestyling: Optimal dynamic asset allocation for defined contribution pension plans. J Econ Dyn Control 30(5):843–877

    Article  MathSciNet  MATH  Google Scholar 

  12. Chaudhuri K, Wu Y (2003) Random walk versus breaking trend in stock prices: Evidence from emerging markets. J Banking Finance 27(4):575–592

    Google Scholar 

  13. Chetouane M (2011) On the defined contribution strategic asset allocation. PhD dissertation, University Paris-Dauphine, LEDa-SDFi

  14. Chow KV, Denning KC (1993) A simple multiple variance ratio test. J Econ 58(3):385–401

    MathSciNet  MATH  Google Scholar 

  15. Cochrane JH (1988) How big is the random walk in GNP? J Political Econ, University of Chicago Press 96(5):893–920

    Google Scholar 

  16. De Bondt WFM, Thaler R (1985) Does the stock market overreact? J Finance. vol. 40(3):793–805

    Google Scholar 

  17. Diebold FX (1986) Testing for serial correlation in the presence of ARCH. In: Proceedings of the Business and Economic Statistics Section of the American Statistical Association, vol 1, pp 323–328

  18. Engle RF (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, Econometric Society 50(4):987–1007

    MathSciNet  MATH  Google Scholar 

  19. Escanciano JC, Lobato IN (2009) An automatic Portmanteau test for serial correlation. J Econ 1512:140–149

    Article  MathSciNet  Google Scholar 

  20. Fama EF, French KR (1988) Permanent and temporary components of stock prices. J Political Econ, University of Chicago Press 96(2):246–273

    Google Scholar 

  21. Hadri K (2000) Testing for stationarity in heterogeneous panel data. Econ J, Royal Economic Society 3(2):148–161

    MathSciNet  MATH  Google Scholar 

  22. Higgs H, Worthington AC (2003) Tests of random walks and market efficiency in Latin American stock markets: an empirical note, School of Economics and Finance Discussion Papers and Working Papers Series 157, School of economics and finance, Queensland University of Technology

  23. Im Kyung So, Pesaran MH, Shin Y (2003) Testing for unit roots in heterogeneous panels. J Econ 115(1):53–74

  24. Jarque CM, Bera AK (1980) Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Econ Lett 6(3):255–259

    Article  MathSciNet  Google Scholar 

  25. Jedageesh N (1990) Evidence of predictable behavior of security returns. J Finance 45(3):881–898

    Google Scholar 

  26. Jegadeesh N, Titman S (1995) Overreaction, delayed reaction, and contrarian profits. Rev Fin Studies, Oxford University Press for Society for Financial Studies 8(4):973–993

    Google Scholar 

  27. Jensen MC (1978) Some anomalous evidence regarding market efficiency. J Financial Econ 6(2/3):95–101

    Article  Google Scholar 

  28. Kim JH (2006) Wild bootstrapping variance ratio tests. Econ Lett 92:38–43

    Article  Google Scholar 

  29. Kim TS, Omberg E (1996) Dynamic nonmyopic portfolio behavior. Rev Fin Studies, Oxford University Press for Society for Financial Studies 9(1):141–161

    Google Scholar 

  30. Kim JH, Shamsuddin A (2008) Are Asian stock markets efficient? Evidence from new multiple variance ratio tests. J Empir Finance 15:518–532

    Article  Google Scholar 

  31. Kojein RSJ, Rodriguez JC, Sbuelz A (2009) Momentum and mean-reversion in strategic asset allocation. Manag Sci 55(7):1199–1213

    Article  Google Scholar 

  32. Korn R, Kraft H (2001) A stochastic control approach to portfolio problems with stochastic interest rates. SIAM J Control Optim 40(4):1250–1269

    Article  MathSciNet  MATH  Google Scholar 

  33. Lo AW, MacKinlay GA (1988) Stock prices do not follow a random walks: evidence from a simple specification test. Rev Financial Stud 1(1):41–66

    Article  Google Scholar 

  34. Lobato IN (2001) Testing that a dependent process is uncorrelated. J Am Stat Assoc, American Statistical Association 96:1066–1076

    Article  MathSciNet  MATH  Google Scholar 

  35. Levin A, Lin CF, Shin CSJ (2002) Unit root test in panel data: asymptotic and finite sample properties. J Econ 108:1–24

    MATH  Google Scholar 

  36. Maddala GS, Wu S (1999) A comparative study of unit root tests with panel data and a new simple test. Oxf Bull Econ Stat, Department of Economics, University of Oxford 61(0):631–652

    Google Scholar 

  37. Merton CR (1969) Lifetime portfolio selection under uncertainty: the continuous time case. Rev Econ Stat 51(3):247–257

    Article  Google Scholar 

  38. Merton CR (1971) Optimum consumption and portfolio rules in a continuous time model. J Econ Theory 3:373–413

    Article  MathSciNet  Google Scholar 

  39. Merton CR (1973) An intertemporal capital asset pricing model. Econometrica, Econometric Society 41(5):867–887

    MathSciNet  MATH  Google Scholar 

  40. Munk C, Sorensen C (2010) Dynamic asset allocation with stochastic income and interest rates. J Financial Econ 96:433-462

    Article  Google Scholar 

  41. Patro DK, Wu Y (2004) Predictability of short-horizon returns in international equity markets. J Empir Fin 11(4):553–584

    Article  Google Scholar 

  42. Poterba JM, Summers LH (1988) Mean reversion in stock prices: evidences and implications. J Fin Econ 22(1):27–59

    Article  Google Scholar 

  43. Power DM, Lonie AA, Lonie R (1991) The overreaction effect Some UK evidence. British Account Rev 23(2):149–170

    Article  Google Scholar 

  44. Tobin J (1958) Liquidity preference as behaviour towards risk. Rev Econ Studies 25(67):65–86

    Google Scholar 

  45. Vasicek O (1977) An equilibrium characterization of the term structure. J Financial Econ 5(2):177–188

    Article  Google Scholar 

  46. Watcher JA (2002) Portfolio and consumption decision under mean reverting returns: an exact solution for complete markets. J Financial Quant Anal 37(1)

  47. Wright JH (2000) Alternative variance-ratio tests using ranks and signs. J Bus Econ Stat 18(1):1–9

    Article  Google Scholar 

  48. Zarowin P (1990) Size, seasonality, and stock market overreaction. J Fin Quant Anal, Cambridge University Press 25(01):113–125

    Article  Google Scholar 

  49. Zhang A, Korn R, Ewald CO (2007) Optimal management and inflation protection for defined contribution pension plans. Blatter der DGVFM 28:239–258

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire d’Economie de Dauphine (LEDa) and Stratégie et Dynamique Financiére (SDFi), Université Paris-Dauphine, Place du Marechal Lattre de Tassigny, 75775, Paris cedex 16, France

    Mabrouk Chetouane

  2. Banque de France, 33 rue Croix des Petits de Champs, 75001, Paris, France

    Mabrouk Chetouane

Authors
  1. Mabrouk Chetouane
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mabrouk Chetouane.

Appendix

Appendix

See Tables 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.

Table 4 Descriptive statistics—monthly data
Full size table
Table 5 Descriptive statistics—daily data
Full size table
Table 6 Lo and Mackinlay variance ratio test performed on daily data
Full size table
Table 7 Lo and Mackinlay variance ratio test performed on monthly data
Full size table
Table 8 Parametric Chow and Denning test performed on daily data
Full size table
Table 9 Parametric Chow and Denning test performed on monthly data
Full size table
Table 10 Escanciano and Lobato–Modified Box–Pierce serial correlation test
Full size table
Table 11 Non-parametric Wright test: ranks test performed on daily data
Full size table
Table 12 Non-parametric Wright test: ranks test performed on monthly data
Full size table
Table 13 Non-parametric Wright test: signs test performed on daily data
Full size table
Table 14 Non-parametric Wright test: signs test performed on monthly data
Full size table

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chetouane, M. How can defined contribution pension plans benefit from momentum and mean reversion?. Eur. Actuar. J. 1 (Suppl 2), 199–231 (2011). https://doi.org/10.1007/s13385-011-0031-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13385-011-0031-3

Keywords

Search

Navigation