When Smaller Menus are Better: Importance of Menu Setter

Choice is central to economics and menus become the natural companion for such research. Menus contain choices and economists are now interested in menu design and available choices. Earlier, it was believed more is better for choices and hence larger the menu better. Now with behavioral economics research we know more choices does not really mean better. There is a diminishing return after a threshold of choices and any more additions leads to lesser utility.

David Goldreich and Hanna Halaburda write this paper showing another aspect. They say what also matters is quality of menu setters. A good menu setter offers lesser choices and a better menu. The paper says:

  • When the cost of increasing the size of a menu is sufficiently small, a low-ability, or less skilled, menu setter will offer more items in the menu than a high-ability menu setter, who will be more discriminate in deciding which menu items to include.
  • Combining the two results leads to a negative relation between menu size and menu quality: Larger menus are worse. This counterintuitive finding follows from the fact that the smaller menu set by the high-ability menu setter is not a subset of the larger menu set by the low-ability menu setter.
  • One must be aware of the role played by menu setters in designing the menu offered to individuals. An unskilled menu setter may offer many choices, but the quality of those choices may be inferior

The authors add theirs is not a behavioral economics explanation but a more rational perspective:

We take a different approach, and show that larger menu may be objectively worse. We recognize that menus are generally pre- selected by menu setters from a larger universe of items, and that these menu setters may differ in their ability to construct menus. Our theoretical results show that when the marginal cost of increasing a menu size is low, menu setters with lower ability offer larger menus than expert menu setters. At the same time, the higher-ability menu setter’s menu is of higher quality in the sense that it offers a larger number of distinct item types. Together, these two results lead to a prediction that smaller menus can be of higher quality than larger menus.

Empirically, we study the relation between the number of investment choices offered by 401(k) plans and the quality of those plans. We measure plan quality by the maximum expected Sharpe ratio achievable given the investment choices in the plan. Excluding the funds with the fewest investment choices, we find a statistically significant negative relation between the number of investment choices and plan quality.

So, the more the number of choices in the 401 k plan the worse are the returns. The returns are measured by Sharpe ratio.

When a company provides a 401(k) plan for its employees, it typically hires an outside firm to design and manage the plan. Each plan is a menu of investment choices for employees’ retirement savings, typically mutual funds or similar investments, as well as a money market fund. Frequently the company’s own stock is one of the possible investments. Each employee allocates his 401(k) money across the various choices in the plan.

We study how the number of fund choices in a plan menu affects the quality of the plan. We define a plan’s quality as the highest expected Sharpe ratio achievable within the plan. The portfolio of investment choices that achieves this maximum expected Sharpe ratio is referred to as the optimal portfolio of the plan. The expected Sharpe ratio of a portfolio is the expected return of the portfolio above the risk-free rate divided by the standard deviation of the portfolio’s returns. Thus, the Sharpe ratio increases in the expected return and decreases in the risk of the portfolio. The idea is that in the absence of any differences in menu setters’ abilities, larger menus are more likely to include high expected return funds and/or provide more scope for diversification of risk.

For instance say a menu has around 4-10 funds the sharpe ratio is 0.305. If it is 11-16 funds the ratio improves to 0.31. However, when the number if funds increased to 17-28 funds, the ratio dips to 0.27.  So offering 11-16 funds in the 401 (k) plan  is optimal.

This has some more interesting applications. Choose a menu which offers lesser choices as there are chances it might be better researched and the quality of menu setter is high:

While the empirical application in our paper addresses only investment portfolios, the central insight that menus are pre-selected by a menu setter is applicable to many scenarios. or example, one ice cream store might offer ten flavors of ice cream, while another store may offer only three  flavors. It should be immediately apparent that the three  flavors are unlikely to be a random subset of the ten flavors, but are chosen with forethought to appeal to as many customers as possible. Following the logic in our theory, if a skilled ice cream purveyor offers the flavors favored by almost all customers, the marginal benefit of adding one more  flavor may be small (and in particular, may be less than the cost of stocking the additional flavor); whereas an unskilled vendor who does not know the preferences of customers may not carry the most desired flavors, and thus may find it profitable at the margin to offer more  flavors. Of course, other forces come into play when evaluating  menus.

Certainly the behavioral effects recently addressed in the literature a ect choices made by agents facing menus of different sizes. Nevertheless, we argue that one must be aware of the role played by menu setters in designing the menu offered to individuals.

Insightful stuff. Discussion of choices and menus is really exciting. Such a different kind of study and research.


One Response to “When Smaller Menus are Better: Importance of Menu Setter”

  1. Sim Con Says:

    Interesting article, but I’d point out that the sortino ratio is argubly a more suitable method of judging mutual fund performance because it only penalizes downward swings in a portfolio’s performance (most investors enjoy upward swings!). Anyway, there’s an excel spreadsheet to calculate the Sharp Ratio at http://optimizeyourportfolio.blogspot.com/2011/05/calculating-sharpe-ratio-with-excel.html

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