A Savings Plan With Targeted Contributions

• DOI: http://doi.org/10.1111/j.1539-6975.2012.01485.x
• Author: Iqbal Owadally,Steven Haberman,Denise Gómez Hernández
• Published date: 01 December 2013
• Date: 01 December 2013

© The Journal of Risk and Insurance, 2013, Vol. 80, No. 4, 975–1000

DOI: 10.1111/j.1539-6975.2012.01485.x

975

ASAV I N G S PLAN WITH TARGETED CONTRIBUTIONS

Iqbal Owadally

Steven Haberman

Denise G´

omez Hern´

andez

ABSTRACT

We consider a simple savings problem where contributions are made to a

fund and invested to meet a future liability. The conventional approach is

to estimate future investment return and calculate a fixed contribution to be

paid regularly by the saver. We propose a flexible plan where contributions

are systematically adjusted and targeted. We show by means of stochastic

simulations that this plan has a reduced risk of a shortfall and is relatively

insensitive to errors in the planner’s estimate of future returns. Sensitivity

analyses in terms of parameter values, stochastic return models and invest-

ment horizons are also performed.

INTRODUCTION

We consider a simple savings problemwhere an individual puts aside funds in order

to meet a certain liability at a given date in the future. The individual may contribute

to a medium-term investment and savings vehicle, for example, to meet school or

college fees for his children in 5 years time. Another example is where the individual

wishes to purchase property. He may save for, say 5 years, and then withdraw some

or all of his investment and use it as a deposit or down payment as part of a home

loan. A longer-term example is a retirement or pension fund, where the individual

saves out of labor income to provide a lump sum at retirement. This may then be

used to buy an annuity.

In most problems of this kind, a financial planner or adviser will assist the individual

to determine how much he should save and invest every month (say), depending on

his household finances. Two relateddecisions must be made: how much the monthly

contribution will be and where the savings will be invested. In this article, we do not

consider the second decision, that is, asset allocation, although we discuss this briefly

later. We assume instead that the individual saves in a variable-rate bank account or

in a low-risk mutual fund.

Iqbal Owadally and Steven Haberman are at Cass Business School, City University, London,

UK. Denise G´

omez Hern´

andez is with Universidad Aut´

onoma de Quer´

etaro, Mexico. The

authors can be contacted via e-mail: M.I.Owadally@city.ac.uk, S.Haberman@city.ac.uk, and

denise.gomez@uaq.mx. The authors would like to thank two anonymous referees who made

very valuable suggestions and helped improve this article.

976 THE JOURNAL OF RISK AND INSURANCE

A very risk-averse investor could save in a term-deposit bank account or in a zero-

coupon bond, yielding a fixed interest rate. However, it could be thata medium-term

fixed-income investment like this is unavailable or pays unattractive rates. A less risk-

averse investor, such as a young worker aspiring to home ownership, may instead

wish to invest in a stock market fund to try and achieve the largest possible future

down payment as part of a home loan. If his stock market investment performs poorly

after 5 years, this may mean that a smaller home loan, or a more expensive loan with

a higher debt-to-equity ratio, will be available to him. On the other hand, a worker

who is close to retirement age is usually advised to invest in less risky, bond-like,

assets so as to secure a comfortable retirement.

In standard economic theory, this savings problem can be cast as a

consumption–investment problem, with consumption (or saving) and asset alloca-

tion as decision variables, and with a utility or loss function as an objective criterion

that is optimized dynamically. Even though idealized assumptions may be made,

this approach can lead to decision rules that are simple to implement and that can

be used to benchmark performance. In practice, however, financial planners do not

employ stochastic dynamic optimization to provide retail advice to individual savers.

They will suggest instead that the individual sets aside a given amount every month,

or possibly a fixed percentage of income, and will also offer suggestions regarding

asset allocation. Dynamic optimization is not used regularly by financial planners at a

retail level because of the complications caused by real-world features such as taxes,

transaction costs, and investment charges, because of imperfect knowledge about

asset return distributions, and because it is difficult to capture individuals’ varying

financial circumstances and requirements.

One example is in the deterministic lifestyling strategies commonly employed in

target-date funds and in pension planning (Shiller, 2005; Blake, Cairns, and Dowd,

2001). Advisers typically suggest a fixed monthly contribution based on a range of as-

sumed investment rates of return (Employee Benefits Security Administration, 2006).

Another example is work-related savings vehicles, such as an employer-sponsored

pension plan, where a fixed proportion of salary is determined (McGill et al., 2004).

The new Florida public sector pension plan described by Lachance, Mitchell, and

Smetters (2003) requires that individuals save a uniform 9 percent of pay. The Actu-

arial Foundation and WISER (2004) suggest a rule of thumb of saving 15 percent of

pay toward retirement.

Our approach in this article is to try to improve upon the conventional fixed-

contribution approach. We suggest a flexible targeted-contribution savings plan that

has variable contributions that depend on current and historic investment perfor-

mance. We investigate whether this new plan performs robustly, in terms of meeting

an investment target at a given horizon, under a wide range of investment conditions.

We show, by means of simulations, that this plan is less risky than the conventional

fixed-contribution plan. Our proposed savings plan is based on a method used in

industrial process control (e.g., Box and Luce˜

no, 1995). The method has also been

proposed in the econophysics literature (Gandolfi, Sabatini, and Rossolini, 2007) and

is applied in the pensions literature to defined benefit pension funding with determin-

istic economic scenarios (Owadally, 2003). The innovation in this article is to apply

this method to a savings problem with a simple stochastic investment environment.