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Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk

  • * Corresponding author: Xun Li

    * Corresponding author: Xun Li

This research is partially supported by the National Natural Science Foundation of China (Nos. 71871071, 72071051, 71471045), the Innovative Research Group Project of National Natural Science Foundation of China (No. 71721001), the Natural Science Foundation of Guangdong Province of China (Nos. 2018B030311004, 2017A030313399), and Research Grants Council of Hong Kong under grants 15213218 and 15215319

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  • This paper investigates a multi-period asset allocation problem for a defined contribution (DC) pension fund facing stochastic inflation under the Markowitz mean-variance criterion. The stochastic inflation rate is described by a discrete-time version of the Ornstein-Uhlenbeck process. To the best of our knowledge, the literature along the line of dynamic portfolio selection under inflation is dominated by continuous-time models. This paper is the first work to investigate the problem in a discrete-time setting. Using the techniques of state variable transformation, matrix theory, and dynamic programming, we derive the analytical expressions for the efficient investment strategy and the efficient frontier. Moreover, our model's exceptional cases are discussed, indicating that our theoretical results are consistent with the existing literature. Finally, the results established are tested through empirical studies based on Australia's data, where there is a typical DC pension system. The impacts of inflation, investment horizon, estimation error, and superannuation guarantee rate on the efficient frontier are illustrated.

    Mathematics Subject Classification: Primary: 90C26; Secondary: 91B28, 49N15.


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  • Figure 1.  Efficient frontier with various time horizons

    Figure 2.  Inflation Vs non-inflation

    Figure 3.  Efficient frontier's sensitivity to the variation of $ \phi $

    Figure 4.  Impact of SG rate on efficient frontier

    Figure 5.  Impact of the ratio $ a $ on efficient frontier

    Table 1.  Salary growth rate

    Date Total earnings ($ fanxiexian_myfh $) Growth rate
    May-2012 1053.20 N/A
    Nov-2012 1081.30 1.0267
    May-2013 1105.00 1.0219
    Nov-2013 1114.20 1.0083
    May-2014 1123.00 1.0079
    Nov-2014 1128.70 1.0051
    May-2015 1136.90 1.0073
    Nov-2015 1145.70 1.0077
    May-2016 1160.90 1.0133
    Nov-2016 1163.50 1.0022
    $ q_k $(half yearly) N/A 1.0112
    $ q_k $(quarterly) N/A 1.0056
     | Show Table
    DownLoad: CSV

    Table 2.  Log-inflation rate

    $ \hat{\bar{I}} $ $ \hat{\sigma} $ $ \hat{\phi} $ Confidence interval for $ \hat{\phi} $ (95$ \% $)
    0.54$ \% $ 0.45$ \% $ 0.5709 (0.4731, 0.6687)
     | Show Table
    DownLoad: CSV

    Table 3.  TN yield

    Year Weighted Average Issue Yield ($ \% $)
    2009 3.1537
    2010 4.4971
    2011 4.5861
    2012 3.4670
    2013 2.6450
    2014 2.5127
    2015 2.0541
    2016 1.8134
    2017 1.5807
    $ r_k^0 $(annually) 2.9233
    $ r_k^0 $(quarterly) 0.7229
     | Show Table
    DownLoad: CSV
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