Where do securities come from We view it as natural to trade common stocks WHY? Coase s policemen Pricing Assumptions on market trading? Predictions? Partial Equilibrium or GE economies (risk spanning)
What if your actions affect the Pricing Kernel Allen and Gale (1989) Markets are clearly incomplete But, is there anything systematic that can be determined about the SPAN? 2 Dates, S finite states occur with probability π s No private information, one consumption good, producers and consumers Producers have production plans which specify output y j (s) in state s. At most 2 claims, limited liability. Max market value of claims - cost Consumers have an endowment MAY NOT SHORT SELL Walrasian equilibrium
Tricky Suppose that a firm changed its plan. The endowment in a state changes The MU changes Are firms price takers or should they take prices into account? In this paper, assume firms value securities at the current MU What is a state?
Results Every equilibrium is constrained efficient. Strongly relies on the assumption that firms value securities that have not been issued. Hart (1979) and Hart (1980) find inefficiency Debt and Equity are not necessarily optimal
Duffie and DeMarzo A based model of security design Issuer values cash today (high discount rate) but if he retains a fraction, he leads buyers to believe that the value of the cash flows are high. Optimally trades off the lemons, problem against disutility for holding asset. Riskless debt is insensitive to private information. Predictions on what the issuer RETAINS (not on the actual securities) Issuer retains the most junior tranche.
Issuer owns future CF X All agents are RN Issuer discounts CF at δ (0, 1) Contractible signals s 1,... s m F = φ(s) payoff q is the amount retained, in which case P f (q) is the price of F.
Timing Security design chosen Information revealed to the issuer Security is sold (issuer retains q) Payoffs
Given the design, the issuers problem is to max q q[p F (q) δf] Here, f is the realization of F. At this stage, the issuer is like a monopolist. Construct a signalling equilibrium in which downward sloping demand.
Ex ante security design Consider adding a random variable state by state Does it increase the ex ante payoff? Adding risk free cash flows always increases the payoff of course. No adverse selection premium Market and issuer value the cash flows differently. Adding risky cash flows also increases the payoff if the risk cash flows are not to informationally sensitive.
Main idea: A bit more Concrete Gorton and Pennacchi (1990, 1993). Uninformed investors demand liquid assets, i.e., with a low sensitivity to information. Banks create such securities by offering deposit contracts as riskless claims on the risky assets of the bank. This also leads to a rationale for deposit insurance and government bonds.
Model At t = 0: A mass 1 of investors. Buy one asset at price P 0. At t = 1: Some investors might have to trade (exogenously). They might face better informed traders. At t = 2: The asset generates X {0, X H }. with Pr [ X = X H ] θ.
Trading at t = 1 One speculator: Can learn X by paying a cost k > 0. Submits demand for the asset d S. Noise (or ) traders: Submit an exogenous demand for the asset d L { d, +d}. With Pr [d L = +d] = 1/2. Market maker: Observes the pair {d S, d L } but not the order s origin. Sets the asset price: P 1 = E [X {d S, d L }].
Speculator s trades If she is uninformed, d S = 0 (say small trading cost). If she observes X = X H, d S = +d. If she observes X = 0, d S = d. Price P 1 Proba 1 2, d L = +d Proba 1 2, d L = d Proba θ X = X H d S = +d {+d, +d} P 1 = X H { d, +d} P 1 = E [X] = θx H Proba (1 θ) X = 0 d S = d { d, +d} P 1 = E [X] = θx H { d, d} P 1 = 0
Speculator s trading profit if informed π = d E [ P 1 E [X] ] = d 1 2 0 + 1 2 [ θ(x H θx H ) + (1 θ)(θx H 0) ] = d θ(1 θ)x H. π increases with the variance of asset s value θ(1 θ)x H, π increases in the variance of noise trading d. The noise traders lose π since the Market Maker breaks even. At t = 1, the speculator acquires information iff π k. At t = 0, the investors pay: P 0 = E [X] π.
Punchline Claims with no informational sensitivity are strictly preferred. Prepare a pass through and sell claims that always pay off X l. Gorton and Pennacchi (1993) the bank issues a safe, hence information insensitive, claim on the project.
Bundling Consider N assets with i.i.d. cashflows X i, i = 1,..., N. An intermediary: Bundles the N assets. Allows trading in the bundle only. A mass N of investors: At t = 0, pay P 0 for the bundle. At t = 1, demand d { d, +d} for the bundle. The Speculator acquires N pieces of information iff: However, 1 N π d E 1 N d E 1 N 1 N π k. N i=1 N i=1 X i E X i E [X] N X i i=1 For N large enough, no information acquisition. Investors pay: P 0 = E [X]. 0 as N + by LLN.
Costly State Verification Townsend (1979), Gale and Hellwig (1985). Different informational structure - the issuer is uninformed Incentives to repay are provided by (costly) intervention by investors and the threat thereof (cheap). Under certain assumptions, debt minimizes the expected cost.
Model Cash flows X [0, + ) with known density h(x). The entrepreneur observes X. The investor can verify X at a cost k.
The Problem Absent verification, the entrepreneur can always report X = 0. One possible arrangement is to always verify. Assume (for simplicity) that this is viable: + 0 X h(x)dx > I + k. BUT, the entrepreneur pays the verification cost and will thus minimize the expected verification cost while investors break even.
General Mechanisms Following the realization of X observed by the entrepreneur: The entrepreneur sends a message m M. The investor verifies with probability B(m) [0, 1]. If he does not verify, the entrepreneur repays R(m). If he verifies, the entrepreneur repays R(m, X). The mechanism specifies M, B(m), R(m) and R(m, X) for all m M and X [0, + ).
Revelation Principle:.Any mechanism s outcome can be obtained in a truthful direct mechanism, i.e., such that: The entrepreneur s message is a cash flow, i.e. M = [0, + ). The entrepreneur chooses to report the true cash flow, m(x) = X. So... To find the best feasible achievable outcome, we can restrict to truthful direct mechanisms. The Revelation Principle does not mean that the optimal mechanism is direct and truthful.
Just to convince you Consider a mechanism M = (M, B, R) For all X, the entrepreneur chooses to report some m (X) maximizing his payoff. M is equivalent to M = (M, B, R ) with: M = [0, + ) B ( ˆX ) = B ( m ( ˆX )) R ( ˆX ) = R ( m ( ˆX )) R ( ˆX, X ) = R ( m ( ˆX ), X ) M is a direct truthful mechanism. Intuition: The mechanism incorporates the entrepreneur s computations The entrepreneur would not lie to himself
Back to the Problem Assumption: Focus on deterministic mechanisms, i.e., ˆX, B( ˆX) {0, 1}. The entrepreneur s problem is + 0 + + 0 B(X) (R(X, X) k) h(x)dx (1 B(X)) R(X) h(x)dx I (IC1)B(X) = 1, B( ˆX) = 0 R(X, X) R( ˆX) (IC2)B(X) = 0, B( ˆX) = 0 R(X) R( ˆX (IC3)B(X) = 1, B( ˆX) = 1 R(X, X) R( ˆX, X) (IC4)B(X) = 0, B( ˆX) = 1 R(X) R( ˆX, X) (LL1)B(X) = 1 R(X, X) X (LL2)B(X) = 0 R(X) X
Proposition: Unique solution is a standard debt contract, i.e. K s.t. - for all X < K, B (X) = 1 and R (X, X) = X. - for all X K, B (X) = 0 and R (X) = K.
Step 1. Define R (M) inf {R(X) B(X) = 0}. (IC2) can be rewritten as B(X) = 0 R(X) = R. (IC1) can be rewritten as B(X) = 1 R(X, X) R. Intuition: Why pay more than R? Step 2. The best debt contract is such that (IR) is binding. If (IR) is slack, reduce the face value, and thus the verification probability, while still satisfying (IR). Denote K the best debt contract s face value. Step 3. Any admissible mechanism M is weakly dominated by the debt contract with face value R (M) because verification is less likely and/or some repayments are strictly greater. This also implies that (IR) is slack. Hence, R (M) K. Conclusion: The best debt contract is the optimal mechanism.
A variation Diamond (1984) is similar to CSV except that: The cost is incurred by the entrepreneur. The investors can choose the size of the cost ex post. The investors cannot verify X. Debt is optimal, with cost set equal to the shortfall K X.
Auditing cost. Bankruptcy cost. Interpretation of verification costs. Value loss due to seizure of collatera For the model to be interesting, k has to be large enough. Direct bankruptcy costs or auditing costs are probably not first order. Do investors value collateral much less than borrowers? Maybe. But the investor can sell it to higher-value user which limits the discrepancy. Still, potential users may also be financially constrained, especially if in same industry (Shleifer and Vishny 1992).
Revelation Principle And other Issues are Optimality does not require a truthful direct mechanism. Many contracts are just as optimal as the standard debt contract, i.e. induce the same repayment schedule. Risk-aversion A risk-averse entrepreneur prefers low repayments when income is low. The optimal mechanism provides some insurance: for X > X 0, B(X) = 0 and R(X) = K for X < X 0, B(X) = 1 and R(X, X) < X This is not a standard debt contract (Townsend 1979) Random verification With random verification, standard debt is no longer optimal (see Mookherjee and Png 1989). Interpretation? Maybe, random auditing. But random bankruptcy is more of a stretch.
Renegotiation Once the report is made, incurring k is only wasteful. Thus, both parties could economize on verification costs. Optimal contract is not robust to renegotiation (Gale and Hellwig 1989) Note: The possibility of renegotiation is always weakly harmful when parties can sign complete contracts. Why not incorporate into the initial contract. Dynamics CSV is technically difficult to extend to multiple periods (Gale and Hellwig 1989, Chang 1990, Webb 1992). Can verification occur without affecting the firm s operations? This looks like auditing rather than bankruptcy.
Main idea: THE PECKING ORDER THEORY Myers and Majluf (1984), Myers (1984). Good firms prefer to issue securities whose value is least information sensitive because they are least underpriced. Under certain conditions, securities can be ranked in terms of their information sensitivity. Under certain conditions, the ranking is: Internal funds. Risk-free debt. Risky debt. Hybrid securities (convertible debt). Equity.
Model 2 dates, an entrepreneur needs I > 0 to invest and only has W < I. Cash flows at time t = 1 are X {X l, X h } X L > 0 so that we can talk about different securities. Pr(X = X H ) = θ {θ H, θ l } Prior ν V (θ) = X l + θ x I The bad type project is valuable, i.e., V (θ B ) > 0. Pooling equilibrium with both types investing. Focus on How to sell a cashflow?
DEBT AS THE LEAST INFORMATION-SENSITIVE CLAIM Case 1: X L > I. The entrepreneur can raise I with risk-free debt: R H = R L = K with X L K I. Equilibrium: Good type issues a claim with R H R L. Bad type issues a claim with R H R L. Both types sell fairly priced claims. With more types, all types issue risk-free debt (except maybe the extreme types). Intuition: The value of risk-free debt is insensitive to hidden information. Avoids the costs of asymmetric information.
Case 2: X L < I. The project cannot be financed with risk-free debt. Equilibrium? The good type invests: At worst, he sells the whole firm and is mistaken for a bad type. He gets: V (θ B ) > 0. The bad type invests (same reason). No separating equilibrium: Bad types refraining from mimicking means that they would sell claims at a discount, i.e., R L + θ G R R L + θ B R or R 0. But this would violate the investors participation constraint as: R L + θ G R R L X L < I.
Pooling equilibrium In a pooling equilibrium, the good types expected payoff is V (θ G ) + ( R L + ˆθ }{{} R ) }{{} ( R L + θ G R ) }{{} This can be rewritten as V (θ G ) }{{} ( θ G ˆθ ) R } {{ }
The good type s best pooling PBE is given by: min R s.t. R L + ˆθ R I R L X L R L + R X L + X The claim is given by (F) and (LL1): (F) Feasibility (LL1) Limited Liability (LL2) R L = X L and R H = R L + R = X L + I XL, ˆθ This looks like a debt contract with face value K = R H : R L = min { X L ; K } = X L and R H = min{x H ; K} = K.
ASSETS IN PLACE AND PROJECT FUNDING Consider a firm with: Financial slack W. Assets in place generate X {X L, X H } with θ {θ B, θ G }. New investment opportunity: Invest I to increase θ to θ + N θ (with θ G + N θ < 1). Positive value: N θ X I > 0. Note: As before, the new project s income cannot be contracted upon separately from that of the assets in place. Case 1: X L > I W. We have already analyzed this case. Firms use internal funds and/or risk-free debt.
Case 2: X L < I W. The project cannot be financed with risk-free claims In equilibrium: Bad firms invest. If good firms invest, bad ones mimic them. Equilibrium? Assume for now that the good type invests. In the best pooling PBE (of this modified game), the good type incurs a discount and thus raises as little as needed, I W, in debt with face value: R H = X L + I W XL. ˆθ + N θ For the new project to be worthwhile under pooling, its value has to exceed the discount: This can be rewritten as: Hence: V ( θ G ˆθ ) (R H R L ). N θ X I ( θ G ˆθ ) I W X L. ˆθ + N θ
Pooling (both types invest) is possible only if the inequality is satisfied. Otherwise, only equilibrium is separating (only bad firms invest).
Comments Good firms are less likely to invest, i.e., the inequality is less likely to be satisfied when: More funds need to be raised, i.e. when I, W or X L. Intuition: The firm would need to issue claims against a larger fraction (of the risky part) of the returns generated by assets in place. Greater overall discount. Good firms suffer from a greater information asymmetry, i.e. when ν, θ G or θ B. Intuition: This increases the discount that the good firm would have to incur. Greater overall discount. The new opportunity is less valuable, i.e., N θ. Intuition: The value is not worth the discount. The firm cannot issue debt (for exogenous reasons). Suboptimal contract. Greater overall discount.
Note: Robustness of the proposed order? Risk-free debt is without problem. The theory works best for large firms with high credit ratings. The rest depends on the type of information asymmetry. For instance, if information is about risk, equity may be less information-sensitive than debt. Equity? Can we base a theory of capital structure on a model that predicts that equity will never be issued? Modified version could include costs of financial distress.