Title: INFORMATIONAL ASYMMETRIES, FINANCIAL STRUCTURE, AND FINANCIAL INTERMEDIATION
Abstract: Numerous markets are characterized by informational differences between buyers and sellers. In financial markets, informational asymmetries are particularly pronounced. Borrowers typically know their collateral, industriousness, and moral rectitude better than do lenders; entrepreneurs possess “inside” information about their own projects for which they seek financing. Lenders would benefit from knowing the true characteristics of borrowers. But moral hazard hampers the direct transfer of information between market participants. Borrowers cannot be expected to be entirely straightforward about their characteristics, nor entrepreneurs about their projects, since there may be substantial rewards for exaggerating positive qualities. And verification of true characteristics by outside parties may be costly or impossible. Without information transfer, markets may perform poorly. Consider the financing of projects whose quality is highly variable. While entrepreneurs know the quality of their own projects, lenders cannot distinguish among them. Market value, therefore, must reflect average project quality. If the market were to place an average value greater than average cost on projects, the potential supply of low quality projects may be very large, since entrepreneurs could foist these upon an uninformed market (retaining little or no equity) and make a sure profit. But this argues that the average quality is likely to be low, with the consequence that even projects which are known (by the entrepreneur) to merit financing cannot be undertaken because of the high cost of capital resulting from low average project quality. Thus, where substantial information asymmetries exist and where the supply of poor projects is large relative to the supply of good projects, venture capital markets may fail to exist. For projects of good quality to be financed, information transfer must occur. We have argued that moral hazard prevents direct information transfer. Nonetheless, information on project quality may be transferred if the actions of entrepreneurs (“which speak louder than words”) can be observed. One such action, observable because of disclosure rules, is the willingness of the person(s) with inside information to invest in the project or firm. This willingness to invest may serve as a signal to the lending market of the true quality of the project; lenders will place a value on the project that reflects the information transferred by the signal. As shown by the seminal work of Akerlof [1970] and Spence [1973], and by the subsequent contributions of Rothschild and Stiglitz [1975] and Riley [1975], [1976], equilibrium in markets with asymmetric information and signalling may have quite different properties from equilibrium either with no information transfer, or with direct and costless information transfer. Signalling equilibria may not exist, may not be sustainable, and may not be economically efficient. In subsequent sections, we develop a simple model of capital structure and financial equilibrium in which entrepreneurs seek financing of projects whose true qualities are known only to them. We show that the entrepreneur's willingness to invest in his own project can serve as a signal of project quality. The resulting equilibrium differs importantly from models which ignore informational asymmetries. The value of the firm increases with the share of the firm held by the entrepreneur. In contrast with Modigliani and Miller [1958], the financial structure of the firm typically will be related to project or firm value even when there are no taxes.1 And firms with riskier returns will have lower debt levels even when there are no bankruptcy costs. Signaling incurs welfare costs by inducing entrepreneurs to take larger equity positions in their own firms than they would if information could be directly transferred; we show, however, that the set of investment projects which are undertaken will coincide with the set which would be undertaken if direct information transfer were possible. Finally, we suggest that financial intermediation, which is difficult to explain in traditional models of financial equilibrium, can be viewed as a natural response to asymmetric information. Consider an investment project which involves a capital outlay K and a future return μ + x ˜ , where µ is the expected end-of-period value of the project and x ˜ is a random variable with zero mean and variance σ 2 . We shall consider an entrepreneur who wants to undertake this investment project and plans to hold a fraction α of the firm's equity, raising the remainder of the equity from other lenders. Throughout our analysis, the firm and the entrepreneur (on personal account) are both assumed to be able to issue debt at the riskless rate.2 The entrepreneur has information that leads him to assign a specific value to µ, but he has no credible way to convey this information directly to other potential shareholders, who have a subjective probability distribution for µ. However, other potential shareholders will respond to a signal by the entrepreneur regarding his evaluation of µ if they know that it is in the self-interest of the entrepreneur to send true signals. The signal which we shall examine is α, the fraction of the equity in the project which is retained by the entrepreneur. This will be taken by other lenders as a (noiseless) signal of the true µ. That is, the market perceives µ to be a function of α. We shall assume that μ(α) is a differentiable function.4 In addition to the possibility of investing in his own project, the entrepreneur can invest in the market portfolio. Define We shall make the “perfect competition” assumption that the project is small relative to the market as a whole; the entrepreneur perceives his decisions with respect to the project to have a negligible effect on the returns and value of his share of the market portfolio. We are not interested in arbitrary functions μ(α); rather, we shall restrict our attention to schedules which have an equilibrium property. More precisely, we define an Condition (5) is a natural notion of equilibrium given competitive capital markets. If the imputed μ(α) were greater than the actual μ of an entrepreneur retaining α, outside investors would on average receive less than the return required for the project's risk, and equity financing would not continue on such terms. If, on the other hand, μ(α) consistently underestimated the entrepreneur's true μ, given α, excess returns would exist for outside investors. Competitive forces would eliminate these excess returns. Thus, for levels of μ for which entrepreneurs undertake their projects, (5) must hold in equilibrium.7 We shall not address the difficult problem of whether an equilibrium schedule μ(α) exists.8 Rather, we shall presume that at least one equilibrium schedule exists, and examine its properties. In the subsequent section, we consider an example in which we can actually compute an equilibrium valuation schedule. Equation (7) can now be used to solve for β as a function of α and μ Substituting this relationship for β into (8) yields a differential equation relating μ and α. Any equilibrium schedule must satisfy this differential equation over the relevant domain. The necessary conditions (8) and (9) will be used to examine properties of equilibrium valuation schedules. But first, we need a definition: An individual's demand for an asset is said to be normal if, in a portfolio choice situation without signaling, the individual will always demand a larger amount of that asset when its price falls. Theorem I.The equilibrium valuation function μ(α) is strictly increasing with α over the relevant domain, if and only if the entrepreneur's demand for equity in his project is normal. Proof 1.See Appendix. I provides a fairly strong characterization of equilibrium schedules: under normal conditions they are monotonically increasing with the fraction of ownership α retained by the entrepreneur. The market reads higher entrepreneurial ownership as a signal of a more favorable project. And the entrepreneur is motivated to choose a higher fraction of ownership in more favorable projects, given the equilibrium valuation function. Theorem II.In equilibrium with signaling by a, entrepreneurs with normal demands will make larger investments in their own projects than would be the case if they could costlessly communicate their true mean. Proof 2.See Appendix. II can be viewed as a welfare result: the “cost” of signaling the true μ to the market through α is the welfare loss resulting from investment in one's own project beyond that which would be optimal if the true μ could be communicated costlessly. Of course, less costly communication may not be possible. And, as argued in the introduction, equilibrium with no communication could result in no projects being undertaken. To examine further aspects of equilibrium valuation schedules and their implications for financial structure, we turn our attention to a specific example. Entrepreneur's expected utility can be expressed in the form The risk adjustment coefficient can be expressed as λ = λ ∗ Cov ( x ˜ , M ˜ ) , where Note that Z will always be nonnegative, and can be interpreted as the specific risk of the project. If the project is independent of the market returns, Cov ( x ˜ , M ˜ ) = 0 and Z is simply the variance of x ˜ . If the market and project returns are perfectly correlated, Z = 0 . In most cases, of course, Z will lie between these extremes. Equilibrium signaling schedules Figure 1 shows some examples of valuation functions satisfying the equilibrium form (15). We will now show that further equilibrium arguments can be used to reduce this family of curves to a single schedule which will be viable in the market. Thus, at α = 0 , schedules such as JJ′ have the property that entrepreneurs with true μ < μ J ( 0 ) could undertake the project, retain zero equity, and be better off than they would if they abandoned the project. Lenders offering the schedule JJ′ would lose money on projects in which the entrepreneur held zero equity. And indeed, even if lenders attach a minimum permissible α > 0 to the schedule JJ′, there will always be some “freeloaders” at α whose μ's are less than those expected by the market. Schedules such as JJ′ therefore will not satisfy the equilibrium condition (5) at their left endpoint. If the schedule KK′ is offered, the same freeloading problem as above may arise at α = 0 , (Since α = 0 implies V K ( 0 ) = K , entrepreneurs with μ < μ K ( 0 ) are indifferent between undertaking (holding zero equity) or not undertaking their projects.) But for α > 0 , no freeloading will take place, since even the smallest amount of required equity holding would reduce potential freeloaders to a level of utility less than that which would result if they did not undertake the project. Now consider schedules below and to the right of KK′, such as LL′. (These schedules do not reach α = 0 because the relevant domain does not include α's associated with levels of μ less than μ*.) Such schedules would indeed satisfy the equilibrium requirement (5). But they will not be competitive with schedule KK′, in the sense that, if KK′ were offered by some lenders when others were offering LL′, all entrepreneurs would do business with lenders offering schedule KK′. This is because the entrepreneur will have a higher level of expected utility along KK′, since the required α to signal any given level of μ is less with KK′ than with LL′. The cost of signaling is less along KK′ than along any other schedule which satisfies the equilibrium requirement everywhere.11 An immediate implication of (17) is Proposition I.A project will be undertaken if, and only if, its true market value, given μ, exceed its cost.12 This result implies that information transfer through signaling possesses a key efficiency property: the set of projects which are undertaken will coincide with that set which would be undertaken if information could be communicated costlessly.13 We now consider the effects of parametric changes on the signaling equilibrium. Proposition II.An increase either in the specific risk Z of the project or in the risk aversion b of the entrepreneur will reduce the entrepreneur's equilibrium equity position α*(μ), for any value of μ at which the project is undertaken. Proof 3.For any fixed value of μ, we have from the equilibrium requirement μ ( α ) = μ A more fundamental question concerns entrepreneurial welfare: does the expected utility “cost” of signaling vary with Z? We can show Proposition III.An increase in specific risk Z results in greater expected utility for the entrepreneur, for any level μ at which the project is undertaken. Proof 4.Tedious calculations show that Thus projects which are “more distinct” (higher specific risk) from the market are relatively easier to signal, in the sense that they result in lower signaling costs in equilibrium. We have shown that in equilibrium the entrepreneur's equity position α in his project is related to the value of his project. We now address the relationship between the value of the project (or firm) V and the financing decision D. In a world of symmetric information, the Modigliani-Miller theorem suggests that there will be no systematic relationship between the financing decision and the value of the firm. In a world with asymmetric information, we show that this will not always be the case. But our results must be interpreted with considerable caution. For the subsequent discussion, we consider the example introduced in the previous section, with the additional assumption that the project's returns are independent of the market returns. This implies cov ( x ˜ , M ˜ ) = 0 , which in turn can be shown to imply that β is independent of α. Thus we can talk of Z as the variance of the project's returns, and can treat β V M as a constant with respect to the choice α. We shall make the assumption that (as both debt and lending are at the riskless rate) the entrepreneur will not simultaneously borrow and lend: borrowing will be done through the firm, and lending will be done privately. Institutional arrangements and (even small) transactions costs can be invoked to support the realism of this argument. Proposition IV.For any level of μ, greater project variance σ X 2 implies lower optimal debt. Proof 5.Differentiating (19) with respect to Z ( = σ X 2 ) , keeping μ constant, yields By our previous analysis, ∂ D / ∂ α > 0 ; by II, d α / d Z < 0 . Since [ log ( 1 − α ) + α ] < 0 for all α > 0 , it follows that d D / d Z < 0 . IV shows that, independent of possible bankruptcy costs, firms with riskier returns will have lower optimal debt levels.15 Consider now the relationship between value V and debt D of seemingly similar projects. By “seemingly similar,” we mean that observers without inside information on μ view the projects as identical. Since both V and D are positive functions of α, and therefore of μ, a regression of value on debt would show a positive relationship. Does this invalidate the Modigliani-Miller theorem that value is independent of capital structure? Not really. In the MM world with symmetric information, a change in D will not change the project's perceived returns, and financial structure will be irrelevant. In a world with asymmetric information in which α can be observed, a change in D with α constant will not change perceived returns, and financial structure will also be irrelevant. But we have argued that observed D, given small transactions costs, will be related to α. And a change in α does give rise to a change in perceived returns and therefore in market value. Thus there is a statistical but not a causal relation between V and D of seemingly similar firms. If transactions costs were sufficiently high, or institutions such that borrowing through the firm entirely precluded lending privately, then D itself could serve as a signal of μ and therefore of firm value, since a choice of D would (through the budget constraint) determine a unique choice of αD as well as α would then be a function of μ and could serve as a signal. But when transactions costs are minimal, D cannot serve as a signal, since entrepreneurs with any μ would be willing to incur small transactions costs to have (say) high D's in order to receive a high project value, while at the same time choosing Y so that α remained at a level appropriate to their true μ. Thus D could not serve as a signal with equilibrium properties. Traditional models of financial markets have difficulty explaining the existence of financial intermediaries, firms which hold one class of securities and sell securities of other types. If transactions costs are not present, ultimate lenders might just as well purchase the primary securities directly and avoid the costs which intermediation must involve. Transactions costs could explain intermediation, but their magnitude does not in many cases appear sufficient to be the sole cause. We suggest that informational asymmetries may be a primary reason that intermediaries exist. For certain classes of asset—typically, those related to individuals, such as mortgages or insurance—information which is not publicly available can be obtained with an expenditure of resources.16 This information can benefit potential lenders; if there are some economies of scale, one might expect organizations to exist which gather and sell information about particular classes of assets. Two problems, however, hamper firms which might try to sell information directly to investors. The first is the appropriability of returns by the firm—the well known “public good” aspect of information. Purchasers of information may be able to share or resell their information to others, without diminishing its usefulness to themselves.17 The firm may be able to appropriate only a fraction of what buyers in totality would be willing to pay. The second problem in selling information is related to the credibility of that information. It may be difficult or impossible for potential users to distinguish good information from bad. If so, the price of information will reflect its average quality. And this can lead to market failure, if entry is easy for firms offering poor quality information. Firms which expend considerable resources to collect good information will lose money because they will receive a value reflecting the low average quality. When they leave the market, the average quality will further fall, and equilibrium will be consistent only with poor quality information, much as Akerlof's market for used cars will result in only “lemons” for sale. Both these problems in capturing a return to information can be overcome if the firm gathering the information becomes an intermediary, buying and holding assets on the basis of its specialized information. The problem of appropriability will be solved because the firm's information is embodied in a private good, the returns from its portfolio. While information alone can be resold without diminishing its returns to the reseller, claims to the intermediary's assets cannot be. Thus, a return to the firm's information gathering can be captured through the increased value (over cost) of its portfolio.18 Of course, a return to information can be gathered only if the buyers of the intermediary's claims believe that the intermediary uses good information. Without some signal of quality, the average return may be low. But, just as in previous sections, this problem can be overcome through signaling. The organizers' willingness to invest in their firm's equity serves as a signal of the quality of the firm's information and the assets selected on the basis of this information. We previously have shown that the financial structure of the firm—the types and amounts of securities it issues—will be related to the owner's equity share. If, as seems often the case, most intermediaries’ assets have low specific risk, IV implies the high degrees of leverage (through debt or deposits) which characterize most intermediaries. It is of interest to note that, once an organization or group of organizations becomes more capable than other lenders of sorting a class of risks, there is a natural tendency for such assets to be sorted—even when the information costs of doing the sorting may be relatively high. Sellers of risks with favorable characteristics wish to be identified, and would deal with an informationally-efficient intermediary rather than with an uninformed set of lenders offering the value of the average risk. With the best risks “peeled off,” the average risk will be less valuable, inducing owners of the next best risks to deal with the intermediary. The end of this chain of logic is that sellers of all types of risks will sell to the intermediary, except perhaps the group at the bottom of the barrel. An open question is whether, in equilibrium, an optimal amount of sorting occurs. R > 0 is required for a regular local maximum of expected utility. For a set of measure zero in which the second-order condition vanished (but higher-order conditions were satisfied), we would have μ α = 0 . k = 0 . In this case, the resulting solution to (A.8), α(0), is the optimal holding of the project by the entrepreneur if he could communicate μ costlessly to the public. k = − [ ( 1 − α ∗ ) μ a ∗ ] E [ U ′ ( W 1 ∗ ) ] where α ∗ = α ∗ ( μ ) , the optimal holding of the project when the market perceives μ through the equilibrium schedule μ(α), and E U ′ ( W 1 ∗ ) is expected utility when α = α ∗ , β = β ∗ . The solution α(k) is simply α*, since (A.8) in this case coincides with the conditions (6) and (7) when (5) holds. We finally observe that, in going from costless communication of μ to signaling, the relevant first-order conditions go from k = 0 to k = − ( 1 − α ∗ ) μ α ∗ E [ U ′ ( W 1 ∗ ) ] < 0 , by I. Since d α / d k < 0 , α will be larger with signalling.