Optimal retirement planning with a focus on single and joint life annuities

Abstract

We optimize the asset allocation, consumption and bequest decisions of a couple with an uncertain lifetime. The asset menu consists of zero coupon bonds and pure endowments with different maturities, whole life annuities and stocks. The pure endowments pay either fixed or variable benefits, and, similarly to the whole life annuities, are contingent on either a single or a joint lifetime. We model the stock returns and the parameters for the term structure with a vector autoregressive model, thus considering time-varying investment opportunities. To find the optimal solution we use a multi-stage stochastic programming approach, which allows for including complex surrender charges on pure endowments and annuities, as well as transaction costs on stocks and bonds. Our findings indicate that despite high surrender charges, households should invest in a wide combination of life contingent products with different maturities and underlying financial risk.

Keywords:

• Annuity
• Household
• CRRA utility
• Stochastic programming

JEL Classifications:

• C61
• D91
• G11
• G22

Notes

No potential conflict of interest was reported by the authors.

1 For example, UK had compulsory annuity purchase until April 2011.

2 See, e.g. Annuity Shopper at http://www.immediateannuities.com/pdfs/as/annuity-shopper-2013-10.pdf

3 Alternatively, rather than obtaining the CRRA utility of consumption, individuals can be characterized by Epstein/Zin preferences, see, e.g. Horneff et al. (2008), have a piecewise linear utility function determining the attitude to risk and return in relation to the current financial status, liabilities and future consumption goals, see Dempster and Medova (2011), or follow a target-based approach with different penalties below and above the target (see Blake et al. 2013).

4 In the last years the European Court of Justice ruled that gender may not be used in pricing of life contingent products, and since December 2012 the unisex pricing is in force according to the European law, see e.g. http://www.thisismoney.co.uk/money/pensions/article-1713762/How-EU-gender-rule-hits-your-pension.html Nevertheless, in our model we take a more general approach, and price the products according to the individual’s gender, as it is still the case in many countries such as the US, see e.g. Annuity Shopper at http://www.immediateannuities.com/pdfs/as/annuity-shopper-2013-10.pdf.

5 In practice, annuity providers assume that individuals are dead with probability one upon age 110, thus the maturity date for the last pure endowment is set to the 109th birthday of the annuitant.

6 See financial websites for private investors, e.g. http://money.cnn.com/retirement/guide/annuities_basics.moneymag/index9.htm and http://www.fool.com/retirement/annuities/annuities02.htm.

7 Bank of England, http://www.bankofengland.co.uk/statistics/pages/yieldcurve/default.aspx

8 Given the mortality tables, see IFA (2008), the price at a given node n and time T of a whole life annuity contingent on a female’s (male’s) lifetime aged 85 upon T, and paying yearly cash-flows of £1, is equal to (£) ( (£)). Therefore, the prices at node n and time T of the whole life annuities paying £4.05 are (£) and (£), respectively. Following formula (31(31) ), the price at node n and time T of a whole life 50% J&S annuity is equal to (£).

9 To explain the replication of Y% J&S products, we have ignored the M&E charges and surrender charges.