What is the optimal design for lottery-linked savings programmes?

Abstract

In this article, we determine the optimal design of lottery-linked savings (LLS) programmes. LLS vehicles, such as lottery bonds, are financial instruments that preserve depositors’ principal but provide randomized variable returns to these depositors through periodic lottery drawings, in lieu of the regular coupon payments traditionally received by bondholders. This type of asset is very popular in Europe. We note that the framing of LLS instruments is linked to their popularity, and we attempt to elucidate that link and thereby determine the optimal structure of payments for LLS programmes. Our goal is to frame LLS programmes in a manner that both maximizes their investors’ satisfaction and preserves their ability to serve as inexpensive sources of capital for their issuers. We demonstrate that the optimal pay-off structure is characterized by a high level of skewness, as investors are willing to accept a decrease in the small and medium prizes of the lottery in exchange for an increase in the grand prize. Thus, to attract a maximum number of depositors, the issuers of LLS programmes should prioritize the jackpot size relative to the other lottery pay-offs and insist on high skewness for the lottery pay-offs relating to the LLS assets.