Optimal rules of thumb for personal finance

David Love, 27 January 2014

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Financial literacy and first-best decisions: Worlds apart?

The internet is rife with rules of thumb for personal finance: save 10% of income, withdraw 4% of assets in retirement, place 100 minus your age% in stocks, and so on. The popularity of these tips reflects a demand for simplifying complex financial problems like saving for retirement or allocating wealth across a range of assets. The simplified rules are also consistent with Herbert Simon’s vision of bounded rationality in economic decisions (1978). Given an uncertain future and the costs of gathering and processing information, Simon argued that the best one can hope for is an approximate solution to real-world decisions, or ‘satisficing’.

Satisficing, however, falls outside the assumption of unbounded rationality maintained in most research on household finance – reflecting, in part, the challenge of modelling specific forms of bounded rationality, but also a taste for explanations rooted in information, incentives, and (non-cognitive) constraints. Nevertheless, recent research on financial literacy casts doubt on the ability of many households to make well-informed financial decisions on their own. For example, Mitchell and Lusardi (2011) find that only two-thirds of Americans over the age of 50 correctly answered the following question about compound interest: “Suppose you had $100 in a savings account and the interest rate was 2% per year. After 5 years, how much do you think you would have in the account if you left the money to grow: more than $102, exactly $102, less than $102?” Another question revealed that little more than half understood that there was a benefit to diversifying investments.

Given the evidence on limited financial literacy, a natural question is whether rules of thumb might provide a low-cost substitute for more sophisticated forms of decision-making. Previous research has examined the performance of specific rules of thumb for saving (Winter et al. 2012) and, separately, portfolio allocation (Cocco et al. 2005, Gomes et al. 2008). These studies find that some rules perform reasonably well (in the sense that households would not be much better off if they adopted a more sophisticated rule), and that rules of thumb for asset allocation tend to be less inefficient than rules of thumb for saving or retirement withdrawal. These results are intriguing because they suggest that there may be a bridge between the simplistic advice offered by personal finance websites and the ‘first-best’ decisions that emerge from studies of optimal consumption and portfolio choice.

Optimal rules of thumb for saving and asset allocation

In my own work (Love 2013), I attempt to extend this bridge by developing a framework for studying ‘optimal rules of thumb’ for saving and asset allocation. The starting point for the project is the recognition that a rule of thumb is just a particular specification of some more general class of functions (e.g. Baumol and Quandt 1964). Instead of determining whether common rules of thumb seem reasonable, I search for the best specification of a rule within a given class – that is, the rule that minimises the welfare losses associated with using that rule instead of one derived from a standard life-cycle model. The framework provides an algorithm for identifying rules of thumb that are as simple as those offered on personal finance websites, but that lead to better outcomes on average.

There are at least two advantages to studying optimal rules of thumb.

  • First, because the rules have been chosen to minimise welfare losses relative to an optimal benchmark, the framework addresses the question of whether any rule of a given type represents a viable alternative to more sophisticated models of decision-making. If an optimal rule of thumb still generates large welfare losses relative to the standard life-cycle model, it makes sense to hunt for a different class of rules or to invest the time, effort, and resources required to understand the more sophisticated problem.
  • Second, the rules of thumb that emerge from the framework turn out to be interesting in their own right. I find, for example, that while typical rules of thumb tend to be relatively inefficient, some simple alternatives perform surprisingly well.

Optimal rule of thumb: An example

As a concrete example of an optimal rule of thumb, consider the case of a portfolio allocation rule that mirrors the structure of the common 100-minus-age rule. This common rule is merely one parameterisation of a rule of thumb of the general form – constant minus slope times age. An optimal rule of thumb for this general form searches for the combination of the constant and the slope such that the rule minimises the welfare inefficiency associated with using an approximate rule rather than the decision rule from the life-cycle model. If younger investors had to choose the best possible version of a linear age-based rule that they would stick with for the rest of their lives, the optimal rule of thumb would have them place 125 – 1.30*age percentage of wealth in stocks. Applying such a rule would generate welfare losses on the order of about 0.5% of annual consumption.

One can do much better, however, by moving to a (piecewise) linear rule based on the share of financial wealth relative to the sum of financial wealth and a simple approximation of the present value of future income. The welfare losses in this case become almost negligible at around 0.04% of annual consumption, or $20 for a household consuming $50,000 a year. The wealth-based rule performs much better than the age-based rule for the simple reason that it tracks the relevant state variable – the exposure of future consumption to fluctuations in financial wealth. The wealth-based rule directly captures the changing importance of financial market risk, while the age-based rule does not.

Optimal rules of thumb for portfolio choice may, therefore, offer reasonable alternatives to the complex decision rules obtained from traditional life-cycle models. When it comes to saving, however, the welfare stakes are higher. I consider two general rules of thumb for saving decisions: one that mirrors the simple advice that people save a set fraction of income (e.g., 10%) during the working years and withdraw a fraction of assets in retirement (e.g., 4%), and another rule based on a simple approximation of total annuitised wealth (composed of both financial and human capital). An optimised version of the first type of rule leads to welfare losses in the range of 3-6% of annual consumption, suggesting that these kinds of rules may not offer reasonable alternatives to more sophisticated advice. The rule based on annuitised wealth, however, is much more successful, with welfare losses in the range of 0.2-2% of annual consumption.

Conclusions

The overall message of this research is that there is a trade-off between the complexity and the efficiency of financial advice, and that there are times when a simple rule can do almost as well as the full-blown solution to a complicated life-cycle model that requires, in the words of Carroll and Allen, a “supercomputer and a doctorate.” The framework in the paper establishes a method for seeing whether a given class of rules of thumb offers a promising alternative to the complicated model, and it identifies some examples of rules that outperform those currently offered on personal finance websites. It can help identify whether ‘good’ rules of thumb are likely to exist, and it can make good rules even better.

References

Allen, T W and C D Carroll (2001), "Individual learning about consumption", Macroeconomic Dynamics 5(2), pp. 255-271.
Baumol, W J and R E Quandt (1964), "Rules of thumb and optimally imperfect decisions”, The American Economic Review 54(2), pp. 23-46.
Cocco, J F, F J Gomes, and P J Maenhout, (2005),"Consumption and portfolio choice over the life cycle", Review of Financial Studies 18(2), pp. 491-533.
Gomes, F J, L J Kotlikoff and L M Viceira, (2008), "Optimal Life-Cycle Investing with Flexible Labor Supply: A Welfare Analysis of Life-Cycle Funds", The American Economic Review 98(2), pp. 297-303.
Love, D A (2013), “Optimal Rules of Thumb for Consumption and Portfolio Choice”, The Economic Journal 123, pp. 932–961.
Lusardi, A and O S Mitchell (2011), “Financial Literacy and Retirement Planning in the US”, Journal of Pension Economics and Finance, October, pp. 509-525.
Winter, J K, K Schlafmann and R Rodepeter (2012), "Rules of Thumb in Life‐cycle Saving Decisions", The Economic Journal 122(560), pp. 479-501.

Topics: Financial markets, International finance
Tags: Financial literacy, optimal personal finance

Associate Professor of Economics, Williams College