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Size matters: capital market size and risk-return profiles

The Arrow-Lind (1970) proposition on risk sharing is the public sector analogy of the well-known proposition of the theory of finance that, as the membership of an insurance syndicate is increased (where each member of the syndicate is risk averse and where his income is uncorrelated with the payoffs of the syndicate) then the syndicate tends to act in a manner that approaches risk neutrality, and that the syndicate acts in a risk neutral manner as the membership tends to infinity. The logic underlying this proposition is relatively easy to grasp. As the population of a syndicate is increased, two opposing effects occur. The first tends to undercut the incentive to take on risks, as the increase in an insurance syndicate’s population dilutes the rewards to each member. The second effect tends to encourage increased risk-taking by the syndicate, as it diminishes the risk faced by each individual and this itself tends to encourage greater risk-taking. Ultimately, as membership rises, the second effect is the stronger because the risk borne by each syndicate member declines at a faster rate than the reduction in each member’s mean income. As a result, larger insurance syndicates are generally able to insure larger corporate risks because the risks faced by individuals within the syndicate are smaller than they are for members of smaller syndicates. This consideration has relevant policy implications: if we think of capital markets as performing a quasi-insurance function for the investors who compose it (by allowing them to share risks), and risk aversion is randomly distributed across the world population, a country with a small (investor) population is predicted to price a given level of risk at a higher level than a country with a large population. As a result, the ‘natural advantage’ of the large country in funding risky ventures originating from a small country makes it inefficient, for the latter, to attempt developing a domestic venture capital market to fund local start-ups, new ventures, and even research and development (R&D). Is this the case? Will Australian, New Zealand, and Canadian inventors always find it cheaper to fund their ideas in England or the United States? This note explores this implication. In so doing, it develops a simple theoretical model capturing the various forces at work. We conclude that large capital markets do not always have a better risk-return profile than small capital markets for a given level of risk, as the marginal return for an additional investment in a risky asset is not constant, as implicitly assumed by finance theory models. The rest of this note is organized as follows: Section 2 briefly reviews the relevant literature prior to developing the theoretical framework to derive testable propositions in Section 3. Section 4 concludes.