Financial stock market abstract graph.

Can members with heterogeneous preferences achieve their first-best within a group?

23 August 2022

The article at a glance

by Dr Shiqi Chen, Research Associate, Cambridge Centre for Finance and Cambridge Endowment for Research in Finance One standard assumption of the …

by Dr Shiqi Chen, Research Associate, Cambridge Centre for Finance and Cambridge Endowment for Research in Finance

One standard assumption of the existing corporate finance literature is firms’ policies are set to maximise total shareholders’ value, irrespective of individual stockholders’ personal preferences. Shareholders who disagree with the firm’s policies can sell off their holdings and invest in alternative investment opportunities. However, this assumption is only valid for public traded firms with well-diversified investors, which is not the norm when we look at the existing business entities in the economy. Indeed, many business entities are not traded on the public market and are governed by a small group of investors with heterogenous preferences, beliefs, investment horizons etc. For example, many small family firms are often owned and run by a few family members whose preferences are different, and whose livelihoods are tied to the firm’s income. Another example is mutual fund management teams, which consist of several managers with different preferences, career stages, risk tolerance etc. These differences are reflected in their choices of assets and therefore determine their compensation. Similarly, VC syndicates often involve partners with different investment preferences and horizons. Under such circumstances, what entities involving heterogeneous stockholders should maximise in the absence of a stock price is less clear. Even in public firms, as long as there are restrictions on the trading of managers’ holdings, this question, to some extent, still applies. Chava and Purnanandam (2010) show that CEOs’ risk preferences affect leverage and cash-holding policies, while CFOs’ risk preferences are relatively more important in explaining debt maturity structure and accrual decisions. They conclude that “closer attention should be paid to the risk preferences and attitudes of managers to better understand the corporate financial decision making”.

Shiqi Chen.
Dr Shiqi Chen

Heterogeneous preferences mean that group members have their own preferred investment, financing and payout policies. Hence, one might jump to a conclusion that heterogeneous stockholders inevitably have to settle for a second-best compromise. The paper by Chen and Lambrecht (2022) shows that it is indeed possible for all members to achieve their first-best life-time utility even without trading. The first-best outcome can be achieved by adopting financial policies that maximise the weighted average of investors’ life-time utility. The utility weights are fixed at the startup of the firm and pinned down uniquely by the individuals’ participation constraints, which are characterised by their outside investment options. These utility weights play an important role in determining how the group synergies are shared.

More specifically, the paper shows that the firm allows members to achieve their first-best life-time utility by issuing financial claims that are tailor-made to individual members’ risk preferences and adopting investment and financing policies that adjust dynamically in response to economic shocks. The least risk averse investor receives an equity claim while all other more risk averse investors receive claims that resemble preferred equities with different seniority and payout yields. This implies that an investor’s payout and claim value depend not only on her own preference but also on her co-investors’ preferences. When collaborating with less risk averse co-investors, more risk averse investors prefer contracts that are less performance-sensitive, which could protect them from the downside at the expense of upside benefits. Such findings provide a rationale for the combination of equity and preferred equities within a firm that is widely observed in practice. Furthermore, these findings also generate new empirical hypotheses regarding the relative compensation within small business entities, which are currently underexplored.

The paper further shows that the firm’s investment and leverage are pro-cyclical. This is because the optimal investment and financing decisions are not merely a weighted average of the individual optimal policies. But more importantly, the weights are time-varying, with more weight shifting toward the less (more) risk averse investors in good (bad) times. Consequently, the group’s risky investment and net debt ratio rise when the firm is doing well and drop when the firm is in trouble. The model, therefore, predicts that startups are often initially all-equity financed, holding a negative net debt position. As its net worth grows, a line of credit is gradually introduced, and a positive net debt position is observed. Such intertemporal variation originates from the misalignment of risk preferences among group members. The dynamic rebalancing financial policies reconcile the heterogeneity in risk preferences and allow members to share risk efficiently thereby achieving their first-best life-time utility.

In the model, each investor has her own outside investment opportunity, and the lead investor (‘entrepreneur’) has an investment opportunity with the highest Sharpe ratio. Therefore, synergies can be generated by pooling all members’ capital into the lead investor’s ‘superior’ project. The paper focuses on the case where capital is supplied competitively such that all synergies accrue to the lead investor, leaving all co-investors indifferent between joining the group or investing in her outside project as a sole proprietorship. In other words, the co-investors receive utility weights such that their participation constraints are binding, while the lead investor receives a weight that makes her strictly better off. The paper shows the utility weights are non-linear and increasing in capital contribution. Moreover, each co-investor’s weight becomes zero in the absence of capital contribution, whereas the lead investor’s weight remains strictly positive even when she contributes zero dollars to the joint pocket. Indeed, the lead investor’s net worth stake in the firm is larger than the monetary capital she contributes, which reflects the synergies she brings into the group with her human capital.  In contrast, the co-investors’ stakes are smaller than the capital they contribute. The wedge reflects the ‘fee’ the co-investors need to pay to access better investment opportunities. The model can also accommodate more general sharing rules that allow co-investors to share part of the synergy.

The paper shows that even though the group’s policies are very different from individual optimal policies, members of the group can still achieve their first-best life-time utility in the absence of trading. The mechanism that allows a group with heterogenous risk preferences to achieve the first-best outcome contains a capital structure consisting of safe debt, equity, and preferred equity, as well as pro-cyclical investment and financing strategies.


Chava, S. and Purnanandam, A. (2010) “CEOs versus CFOs: incentives and corporate policies.” Journal of Financial Economics, 97(2): 263-278

Chen, S, and Lambrecht, B. (2021) “Optimal financial policies for a group.”, SSRN.