Manipulation in Financial Markets and the Implications for Debt Financing

Transcription

1 Manipuation in Financia Markets and the Impications for Debt Financing Leonid Spesivtsev This paper studies the situation when the firm is in financia distress and faces bankruptcy or debt restructuring. The creditors can earn about the prospects of the firm from the stock price, which creates the possibiity of price manipuations by the traders. We investigate the feedback effects from the financia markets and stock price manipuations, and their effect on restructuring and on the debt contract. We show that even though the manipuation equiibrium is ess efficient for the creditors and for the firm than the case when the creditors are perfecty informed about the firm fundamentas, under a certain set of parameters the manipuation equiibrium is sti desirabe when the creditors are uninformed about the fundamentas. We aso consider possibe impications for the poicymakers. The mode Let us first describe the agents in the mode. We consider a pubicy traded firm run by a manager. The firm faces an investment opportunity that requires an initia investment and yieds an uncertain payoff. We assume that the firm needs to raise the funds for the project and focus our attention on the debt contract. The payoffs generated by the project depend on the state of nature. There is a specuator in the mode who can become informed about the state of the word with some probabiity and can make money by trading on that information. The mode has five time periods indexed by t = 0,, 2, 3, 4, 5. In period t = 0 the firm faces an investment opportunity that requires an initia investment of I and yieds and uncertain payoff π {π, π h }, with π < π h in t =. The payoff depends on the state of the word ω {ω b, ω g }, where ω b represents the bad state that happens with probabiity Pr (ω b and ω g represents the good state that happens with probabiity Pr (ω b = Pr (ω g. It is important to note that each reaization of π can happen in each state of the word so that the payoff does not revea the state. In particuar, this means that the ow payoff π does not necessariy indicate the ow state, ω b, as it can happen in ω g as we. We think of this as of a situation when the underying fundamentas are good, but the firm is unucky and faces temporary difficuties. The probabiities of the payoffs in different states are given by conditiona probabiities Pr (π ω. We

2 assume that the firm has no funds and negotiates the debt contract specifying a payment D due in t = 4 with the creditors. Because there is competition among the capita providers, the creditors need to at east break even. In period t = the payoff π {π, π h } is reaized and pubicy announced. The specuator observes the reaization of payoff π and aso, with probabiity α receives a perfecty informative signa s {s b, s g } about the state ω. With probabiity α the specuator remains uninformed about ω an in this case we write s =. We ca the specuator who received s = s g positivey informed, the specuator who received s = s b negativey informed and the specuator with s = uninformed. We introduce the trading in the subsequent periods as in Godstein and Guembe (2008. There are two trading dates, t = 2 and t = 3, and the specuator decides to trade in the financia market based on his signa s. In each trading date the specuator submits a trading order to the market maker. We refer to the trading date t = 2 as to the first round of trading and to the date t = 3 as to the second round of trading. For this reason and to make the connection to Godstein and Guembe (2008 more cear, we denote the specuator s orders to the market maker by u and u 2, where u i {, 0, }. There is aso a noise trader who submits the orders n, n 2 {, 0, } to market maker. The noise trader serves the purpose of disguising the specuator s trades. We assume that the noise trader s orders are seriay uncorreated and take each vaue with equa probabiity. Foowing Godstein and Guembe (2008 and Kye (985, the price is set in each round of trade by the market maker who observes the tota order fow Q i = u i + n i { 2,, 0,, 2} but not the individua components. The market maker sets the price to be equa to the expected asset vaue given the pubicy avaiabe information and the order fow history. In particuar, the first-round price is set according to p = E [V π, Q ] and the second-round price is set according to p 2 = E [V π, Q, Q 2 ], where the cacuation of V wi be described ater. In period t = 4 the firm repays the creditors. If the firm is unabe to pay the fu amount, it can renegotiate (restructure the debt with the creditors who can take an action a {a s, a c }, where a s represents stop and a c represents continue. We assume that the manager is perfecty aware of the state of the firm ω, but due to an agency probem never wants to iquidate the firm. If the creditors decide to terminate the project when the firm is unabe to repay the debt (π = π they iquidate the firm and obtain π. Aternativey, they can forego the iquidation payoff of π and et the firm to continue the project to period t = 5 when the second round of payoffs is reaized, π 2 {π 2, π h 2 } and the firm is iquidated. Assuming Nash bargaining, the second-period profits π 2 wi be spit between the creditors and the firm equay. We assume that the payoff is π 2 in ω b and π h 2 in ω g, and that 2 π 2 < π < 2 πh 2, ( which means that the creditors ose money from continuation when the state is bad, but benefit from the high continuation payoff when the state is good. 2

3 Note that when there is renegotiation in period, the creditors can earn about the prospects of the firm from the stock prices. This creates incentive for the specuators to manipuate the price. For simpicity we assume that if the firm is abe to repay the creditors in t = (π = π h, it retains the remaining profits. There are severa reasons for this. First, the computations become more compicated if we incude the remaining profits in the stock price. Second, the assumption that the firms pays out a of the profits and sti operates in t = 5 is inconsistent with the assumption that the creditors need to forego π to keep the firm operationa in t = 5. Finay, we want to expore the effect of manipuation on the creditors continuation decision which is aready captured by considering π 2. Creditors payoffs are not affected by the way the remaining first-round payoffs π h are distributed after the creditors aready got their payments (though indirecty this coud potentiay affect their strategy because it affects specuators payoffs and incentives. This means that the vaue of the firm to the stockhoders is V = π 2, if the firm is abe to repay the creditors in t = 4, it is V = 0 if π = π and the creditors iquidate the firm in t = 4, and V = 2 π 2 if π = π and the creditors decide to continue. Two comments are in order. First, we want to highight the differences in the setup from the Godstein and Guembe (2008. In their mode, the vaue of the firm was the same for the investment decision makers (the manager and for the stockhoders, whie in our mode it is different in the case of iquidation, so we have to anayze the payoffs to creditors and stockhoders differenty. Another difference is that in Godstein and Guembe (2008 the ow reaization of the NPV is negative, whie in our mode the stockhoders aways receive the nonnegative amount and this affects the equiibrium proofs. We aso generaize the setup in the sense that we aow the probabiities of good and bad states other than /2. Finay, in Godstein and Guembe (2008 the specuators may know the state of the word (the fundamentas that determine firm s profits, but the manager is unaware of the state and infers it from the stock prices. In our mode the manager knows the state, but there is an agency probem that prevents creditors from trusting the manager and this creates an incentive for them to earn from the stock price. Another comment concerns the trading setup. We can think of a mode where trading happens before π is announced (or without observing the reaization of π, or even a mode where the debt contract is designed after observing the prices. Whie these modes coud be interesting, the computations turn out to be significanty more compicated, and we want to get intuition from the simpest mode to be abe to extend it to more compicated modes in the future work. The mode where the prices aready incorporate π is simper in the sense that the creditors do not have to combine the information from the prices with the information contained in π (which is what greaty compicates the cacuations. The Perfect Bayesian Nash equiibrium in our mode consists of: ( a trading strategy by the specuator {u (π, s and u 2 (π, s, Q, u } that maximizes 3

4 his payoffs given his information and the other agents strategies; (2 a continuation strategy by the creditors that maximizes the expected payoff given their information and other payers strategies; (3 a price setting strategy {p (π, Q, p 2 (p (π, Q, Q 2 } by the market maker that aows him to break even in expectation given his information and other payers strategies; (4 the agents use Bayes rues to update their beiefs from the observed orders; (5 a agents have rationa expectations. We start with two simpe benchmark cases, the case when no renegotiation is aowed and the case when the creditors do not earn from the stock prices. 2 A mode with no continuation In a situation when the firm has to repay the creditors at time t = 4 ony, the is no renegotiation, the creditors do not need to earn from the stock price and therefore the specuators have no incentives for manipuating the stock prices. The optima debt contract is simpy determined by the condition that the creditors break even in expectation, which is I = E [min{ π, D NC }] = π Pr ( π = π + DNC Pr ( π = π h. This gives us D NC = I π Pr ( π Pr ( π h. (2 3 A mode with uninformed creditors and no feedback Let us consider the mode where renegotiation is aowed in t = 4 but the creditors do not earn from the price and make a continuation decision based on π ony. We assume that 2 π 2 < π E [ π2 2 π ]. (3 The first part of this inequaity means that termination is optima in the bad state of the word. The second part of the inequaity means that conditiona on profits π ony, it is optima to continue the project. Using the fact that the outcome π 2 is uniquey determined by the state of nature, we can rewrite the atter condition as π πh 2 2 Pr ( ω g π π Pr ( ω b π. We see that this condition is satisfied when continuation is attractive (π2 h is high, termination is ineffective (π is ow, and ow profits are not a strong 4

5 signa of the bad state (Pr ( ω b π is ow. For simpicity we sometimes denote Pr ( ω b π = pb, Pr ( ω g π = pg. Assumptions ( and (3 impy π πh 2 2, (4 which means that π h 2 is sufficienty attractive for continuation, given that under Nash bargaining the surpus wi be spit equay between the creditors and the firm. Assuming that the creditors aways continue the project, the expected exante payoff to the creditors in π = π is F UC = 2 π 2Pr ( ω b π + 2 πh 2 Pr ( ω g π. Taking this into account, the creditors choose debt payment D N π h that satisfies I = D UC Pr ( π h + FUC Pr ( π, i.e. the promised payment in the no-feedback mode is given by D UC = I F NIPr ( π Pr ( π h (5 Observe that because of the assumption (3, the expected payoff to the creditors from continuation in π = π is greater than what they get from termination ( 2 πh 2 > π, and thus it foows from (2 and (5 that D UC is ower than D NC. This means that there are firms that are unabe to raise the required funds uness the future profits are taken in account. 4 A mode with informed creditors Let us again consider the mode where renegotiation is aowed in period 4, but the creditors do not earn from the price in making the continuation decision. We assume that the creditors earn the true state after π is reaized and thus the prices do not contain any usefu information. If the ow payoff, π = π, is reaized, the creditors receive π if ω = ω b and 2 πh 2 if ω = ω g. This gives the expected ex-ante payoff in π = π of F IC = πpr ( ω b π + 2 πh 2 Pr ( ω g π. Taking this into account, the creditors choose debt payment D N π h that satisfies I = D IC Pr ( π h + FIC Pr ( π, 5

6 i.e. the promised payment in the no-feedback mode is given by D IC = I F ICPr ( π Pr ( π h (6 Observe that because the payoff to the creditors from continuation in the good state is greater than what they get from termination ( 2 πh 2 > π, the exante payoff to the creditors in π = π, is higher than what they get in the mode with no continuation, F IC > π, and is aso higher than in the mode with the uninformed creditors. It foows from (2, (5 and (6 that D IC < D UR < D NC. We can imagine the situation when the firm can not raise the funds for the project in the no-continuation mode, i.e. when there exists no D NC soving (2 and satisfying D NR π h. This is the case when I > π Pr ( π = π + π h Pr ( π = π h, i.e. when the required investment is high reative to the expected profits. In the mode with renegotiations this constraint can be reaxed if the expected future profits in π = π are sufficienty high to satisfy (5 or (6. This means that financiay constrained (π h is ow or Pr ( π h is ow or temporariy distressed firms (π = π that are actuay in the good state (ω = ω g and expect high future profits can benefit from renegotiation, especiay when the creditors are informed. 5 Manipuation equiibrium in a mode with feedback In this section we consider the situation when the creditors earn from the price when making the continuation decision and examine the manipuation equiibrium as described in Godstein and Guembe (2008. We want to study the effect that manipuation has on debt financing. We assume π > αpr ( ω b π π 2 + ( α π 2 2 αpr ( ω b π, (7 + ( α which impies that the creditors stop the project after the orders that coud be generated by both negativey informed and uninformed specuators. Note that since when the creditors decide to continue in π = π, they forego π. If we define the net payoffs as the payoffs in excess of π, U + = πh 2 2 π, U = π 2 2 π, Ū = Pr ( ω g π U + + Pr ( ω b π U, then (7 is equivaent to αpr ( ω b π U + ( αū < 0, which is anaogous to assumption (4 in Godstein and Guembe (2008. We focus our attention on the manipuation equiibrium that we characterize beow. 6

7 5. Characterization of manipuation equiibrium Since the prices ony matter when π = π, for simpicity we can focus on trading in π = π ony and drop the symbo π from the strategies. The trading strategy of the specuator is given by u (s = s g = {, prob µ u (s {s b, } = 0, prob µ {, if Q {0, } u 2 (s = s g, Q, u = =, 0,, if Q = 2 {, if Q = 0 u 2 (s = s b, Q, u = =, 0,, if Q {, 2} {, if Q {0, } u 2 (s = s b, Q, u = 0 =, 0,, if Q = {, if Q = 0 u 2 (s =, Q, u = =, 0,, if Q {, 2}, if Q = u 2 (s =, Q, u = 0 = 0, if Q = 0,, 0,, if Q = The creditors strategy is a = a s if the trading outcome coud have been generated by either negativey informed specuator or uninformed specuator (and not the positivey informed specuator, i.e when Q { 2, }, or Q = 0, Q 2 =, or Q =, Q 2 { 2, }, or Q = 0, Q 2 = 2. The creditors continue the project in a other nodes. The existence of the manipuation equiibrium is estabished by the foowing proposition, anaogous to Proposition 2 in Godstein Guembe: Proposition. In the mode with feedback, if ( and (3 hod and α is sufficienty arge, there exists an equiibrium in which the uninformed specuator se with stricty positive probabiity µ in the first round of trading, where 0 < µ < 2 Pr ( ω g π α 3 2 Pr ( ω g π. α Proof. We show that no payers have profitabe deviations from the equiibrium strategies. Creditors strategy Given the equiibrium specuators strategy, we want to check the optimaity of creditors continuation strategy. The creditors continue the project after observing the ow payoff π L if and ony if they expect to get in period 5 more than they can get from iquidation in period 4, [ ] π π2 > E 2 π, Q, Q 2. 7

8 This condition can be rewritten as 2π < π h 2 Pr ( ω g π, Q, Q 2 + π 2 Pr ( ω b π, Q, Q 2. (8 We verify this condition for each pair of (Q, Q 2. When Q { 2, }, or Q = 0, Q 2 =, or Q =, Q 2 { 2, }, the conditiona probabiity of {ω = ω g } is given by Pr ( ω g π, ( αpr ( ω g π Q, Q 2 = ( αpr ( (. ω g π + Pr ωb π and thus the creditors optimaity condition (8 can be written as 2π ( αpr ( ω g π π h 2 + Pr ( ω b π π 2 ( αpr ( ( ω g π + Pr ωb π. This condition is vioated by assumption (7, and therefore termination is optima. For Q = 0, Q 2 = 2 we have Pr ( ω g π, ( αpr ( ω g π Q, Q 2 = ( αpr ( ( ω g π (, + Pr ωb π + α µ µ which is stricty beow the probabiity from the previous case. This impies that the right-hand side of the optimaity condition (8 is ower than in the previous case, which, in turn, is beow 2π. Therefore, the optimaity condition (8 is satisfied and termination is optima. For Q = Q 2 = 0 we have Pr ( ω g π, Q, Q 2 = Pr ( ωg π, i.e. stock prices are uninformative. The optimaity condition is satisfied by assumption (3. When Q = 0, Q 2 =, the probabiity Pr ( ω g π, (α + ( αµ Pr ( ω g π Q, Q 2 = (α + ( αµ Pr ( ( ω g π + ( αµpr ωb π is arger than in the case of Q = Q 2 = 0. This means that the righthand side of the optimaity condition (8 is higher than in the case of Q = Q 2 = 0, which is above 2π. For Q =, Q 2 = 0 we have Pr ( ω g π, (α + ( αµ Pr ( ω g π Q, Q 2 = (α + ( αµ Pr ( (, ω g π + µpr ωb π which again is arger than in the case of Q = Q 2 = 0. When Q = 2, or Q =, Q 2 {, 2}, or Q = 0, Q 2 = 2, we have Pr ( ω g π, Q, Q 2 =, i.e. we know that the state is ωg with certainty. Creditors optimaity condition (8 becomes 2π π h 2, which is satisfied by (4. 8

9 Market prices Given the specuators and creditors strategies, we cacuate the price using the no-arbitrage market maker s condition. In order to make the connection to Godstein and Guembe (2008 more cear, we denote the vaue for the equityhoders in the states ω g and ω b by V + πh 2 2, V π 2 2, and we aso denote the expected vaue conditiona on π by [ ] π V E 2 π = V + Pr ( ω g π + V Pr ( ω b π. Using Bayesian updating, we cacuate the t = 3 (second-round trading prices and obtain p 2 (Q, Q 2 = 0, for Q { 2, }, or Q {0, }, Q 2 { 2, }, p 2 (Q, Q 2 = V +, for Q = 2, or Q =, Q 2 {, 2}, or Q = 0, Q 2 = 2, p 2 (0, 0 = V, p 2 (0, = Pr ( ω g π αv + + ( αµ V Pr ( ω g π, α + ( αµ p 2 (, 0 = Pr ( ω g π αv + + ( αµ V + Pr ( ω b π αµv α ( Pr ( ( ω g π + µpr ωb π. + ( αµ Cacuating the expected t = 3 prices, we arrive at t = 2 (first-round trading prices, p (2 = V +, p ( = 3 p 2(, Pr ( ω g π αv + 3 α ( Pr ( ( ω g π + Pr ωb π, µ + ( αµ p (0 = 3 V + [ ( αpr ωg π ] + ( αµ p2 (0, Pr ( ω g π αv +, p ( = 0, p ( 2 = 0. We can see that these expressions are generaizations of the prices in Godstein and Guembe (2008 when the probabiities of states are not necessariy equa to /2. Trading strategies in t = 3 The proof that the trading strategies in t = 3 are optima at each possibe node on the equiibrium path is a generaization of part B of the proof or Proposition 2 in Godstein and Guembe (2008 to aow the state probabiities different from /2. The structure of the proof is unchanged and the generaization is straightforward. We can note that in the case of uninformed specuator who does not 9

10 trade in t = 2 and when Q =, the condition that specuator prefers to se is equivaent to p 2 (, 0 > V. This inequaity can be written as µ < Pr ( ( ω g π V + V Pr ( ( ω b π V =, V i.e. the condition is satisfied when µ <. Trading strategies in t = 2 This part of the proof foows the structure of part B of the proof of Proposition 2 in Godstein and Guembe (2008. As in their proof, both uninformed and negativey informed specuator wi se in t = 2 when p (0 > 3 p 2(, 0, not trade in t = 2 when p (0 < 3 p 2(, 0, and mix between the two when p (0 = 3 p 2(, 0. We can show that p (0 is increasing in µ and p 2 (, 0 is decreasing in µ. We can make the foowing two observations. First, when µ = 2 Pr(ω g πα, p 3 2 Pr(ω g π (0 > α 3 p 2(, 0. To derive this, we can write and thus p (0 3 p 2(, 0 = 3 = 3 p (0 = ( ( V + ( αµ V + 2αPr ωg π 3 V + p 2 (, 0 = V + 2αPr ( ω b π ( Pr ωg π ( V + V, ( ( ( αµ V + 2αPr ωg π ( ( Pr ωb π V + + 2αPr ( ω b π ( Pr ωg π V ( ( ( αµ V + 2αPr ωg π V 0 Second, when µ = 0, p (0 3 p 2(, 0 if and ony if V + ( 2 Pr ( ω g π α V. This means that we get the foowing characterization of equiibrium. When V + ( 2 Pr ( ω g π α V, then µ = 0, and when V + ( 2 Pr ( ω g π α > V then 0 < µ < 2 Pr(ωg π α and µ is uniquey determined by p 3 2 Pr(ω g π (0 = α 3 p 2(, 0. The equiibrium profits are as in Godstein and( Guembe (2008: the equiibrium profits for the uninformed specuator are 3 p (0 V ( 3, the equiibrium profits for the negativey informed specuator are 3 p (0 + V V, and for the positivey informed are V + 3 p ( 3 p (0 9 p 2(0, 9 p 2(, 0 V 9. These profits are stricty positive because π2 < π2 h and Pr ( ω g π (0,. We now show that deviations from the t = 2 trading strategies generate stricty smaer profits. Suppose the uninformed specuator buys in t = 2. If Q = 2, then specua- 0

11 tor s profit is 2V V, if he buys again in t = 3, V + + V, if he does not trade in t = 3, 0, if he ses in t = 4. We see that these profits are either stricty negative or 0. If Q specuator s profit is =, then p ( 2 3 V + 3 p 2(, V, if he buys again in t = 3, (9 p ( V, if he does not trade in t = 3, (0 p ( + 3 p 2(, 0, if he ses in t = 3. ( We can see that ( is negative. To prove that (0 is negative, we can show that it is equivaent to Using assumption ( αµ V 3p g αv + p b αµv + 2p g α V + 2p b αµ V < 0. Pr ( ω g π αv + > Pr ( ω b π αv + ( α V, we can rewrite the eft-hand side of the inequaity as [ pb αv + ( α V ] µ p b αµv 3p g αv + p b αµv + 2p g α V + 2p b αµ V < p g αµv + 3p g αv + 2p b αµv + 2p g α V + 2p b αµ V < 2p g αv + 2p b αµv + 2p g α V + 2p b αµ V = 2α ( µp b ( V V p g ( V + V, which is negative because µ < p g(v + V p b( V =. To prove that (9 is negative, we V can show that this is equivaent to 3p g αv + p b αµv p b αµv + ( αµv + +3p g α V +3p b αµ V +2( αµ V < 0. The eft-hand side of the inequaity can be rewritten as 3α ( ( µp b V V ( p g V + V + 2p b αµv p b αµv + ( αµv + + 2( αµ V < 2p b αµv p b αµv + ( αµv + + 2( αµ V < 2p b αµv p b αµv + + ( αµ V = [ p b αv + ( α V ] µ + p b αµv p b αµv + < p g αµv + + p b αµv p b αµv + = αµ ( p g V + + p b V p b V +,

12 which is negative if V < p b V +. If Q = 0, then specuator s profit is p (0 3 V + 3 p 2(0, V, if he buys again in t = 3, (2 p ( V, if he does not trade in t = 3, (3 p (0 + 3 V, if he ses in t = 3. (4 We can see that (4 is negative. The condition that (3 is negative can be written as 2Pr ( ω g π αv + + ( αµ V > V. We can see that this inequaity is vioated when α is sma, and thus we need a restriction on α. Aso observe that the inequaity can be rewritten as Pr ( ω g π αv + + ( αµ V > Pr ( ω b π αv + ( α V. Note that in Godstein and Guembe (2008 the right-hand side is negative by assumption (4 and thus this inequaity is satisfied. In our mode the right-hand side is positive, but this does not contradict Godstein and Guembe (2008. This is because (4 is used to make sure that the manager (in our mode this roe is payed by the creditors does not invest when he observes the signa that can be attributed to both negativey informed and uninformed specuators, and in our mode a version of (4 sti hods for the creditors. We can make sure that (3 hods by assuming the foowing version of (4 for the specuator: Pr ( ω g π αv + > Pr ( ω b π αv + ( α V. To show that (2 is negative, we can show that it is equivaent to aµ 2 +bµ+c < 0, where a = ( α 2 V < 0, b = ( α ( V + 3 V + p g α V + 2p g αv +, c = 2p g α ( V + ( + p g α 2 V, where c is negative if V + ( + p g α > 2 V. This condition is equivaent to α > where the right-hand side is beow when V + > 2V. We can see that 2 V V + p gv + the sign of (2 on µ [0, 3 is determined by the sign of c when α is sufficienty arge. Therefore, (2 is negative for sufficienty arge α. By considering different cases for the vaue of Q and for the specuator s behavior in t = 3, it can be shown that the profits of the negativey informed specuator who buys in t = 2 do not exceed the profits of the uninformed specuator buys in t = 2. The computations for case when positivey informed specuator does not trade in t = 3 aso foows the proof in Godstein and Guembe. One difference 2

13 is in the proof of equation (23 in Godstein and Guembe (2008, 9 V + 3 p ( 2 3 p (0 9 p 2(0, 9 p 2(, V > 0. This inequaity is equivaent to aµ 3 + bµ 2 + cµ 3 + d > 0, where a = 2(α 2 (( α + p b α V ( b = (α (α V V + 5αp b V + 4αpg V 4α 2 p g V + 4α 2 p g V 5αp b V αp b V + 3αp g V + + 4α 2 p b p g V + + 2α 2 p b p g V c = αp g (7(α V + + V + 4αp b V + 2αpg V 8α 2 p g V + 2α 2 p g V 9αp b V 0αp b V + 3αp g V + + 4α 2 p b p g V + d = 2α 2 p 2 ( g 3V V + 2p g αv +. We can see that d is positive under the assumption 2 V < (3 2p g αv +. This can aso be shown if we assume V + > 2 V, which is equivaent to V + (p b p g > 2p b V, i.e. we must have p b > p g and V + sufficienty high. When α is sufficienty high, the sign of the eft-hand side is determined by the signs of c and d. As α approaches, c converges to c = 2p b p g ( V 5V V + 2p g V + We can see that c is positive because 5V + > V + 2 V + 2p g V +. From the proof we can see that by seing in the first round of trading, the uninformed specuator decreases the expected firm vaue. The foowing proposition estabishes the fact that even though manipuation reduces the expected vaue that the creditors can get when they earn from prices, manipuation equiibrium is sti better than aways terminating the project in t = 4. Proposition 2. For α sufficienty arge, the creditors have higher expected payoff in π in the manipuation equiibrium than in both the no-continuation mode and the mode with uninformed creditors. Therefore, there exist firms that are unabe to raise the required funds in the form of debt in the no-continuation and no-information modes, and benefit from earning from the price even when manipuation is expected. Proof. Let us first cacuate the expected vaue the creditors get after observing π = π. 3

14 Expected vaue for creditors In order to cacuate the expected payoff to the creditors given π, we can combine the outcomes (Q, Q 2 into 5 groups. When Q { 2, }, or Q = 0, Q 2 =, or Q =, Q 2 { 2, }, or Q = 0, Q 2 = 2, the creditors terminate the project and receive π. The tota probabiity of ending up in these nodes is ( α ( µ p g + ( µ + 9 αµ p b. When Q = Q 2 = 0, the project is continued and the expected payoff is 2 E [ π ] 2 π = 2 π 2p b + 2 πh 2 p g. The probabiity of reaching Q = Q 2 = 0 is 9. When Q = 0, Q 2 =, the project is continued and the expected payoff is π2 h (α + ( αµ p g + π2( αµp b 2 (α + ( αµ p g + ( αµp b The probabiity of reaching Q = 0, Q 2 = is p g ( 9 ( αµ + 9 α + p b ( 9 ( αµ. When Q =, Q 2 = 0, the project is continued and the expected payoff is π2 h (α + ( αµ p g + π2µp b. 2 (α + ( αµ p g + µp b The probabiity of reaching Q =, Q 2 = 0 is p g ( 9 ( αµ + 9 α + p b 9 µ. When Q = 2, or Q =, Q 2 {, 2}, or Q = 0, Q 2 = 2, the creditors continue the project and obtain the certain payoff of 2 πh 2. These nodes are reached with the tota probabiity of 2 3 p gα. To sum up, the creditors receive ( 8 π, with probabiity( α µ 2 π 2, with probabiity ( ( αµ + ( + αp g + 9 ( αµ + αp g 2 πh 2, with probabiity ( α + ( αµ + ( + αp g + 9 ( αµ + αp g ( 8 p g µ + 9 αµ p b µ ( + αp g + αµp b p b µ + α( µp g α + ( αµ ( + αp g + αµp b + 6α p g µ + α( µp g 4

15 Using the above derivations, we can see that the probabiity of receiving 2 πh 2 conditiona on π is greater than 9 (3 + α(2p g + µp b + 6 p g, which is greater than p g when α is sufficienty arge. Aso, π is greater than π 2. Therefore, the expected payoff in the manipuation equiibrium is greater than 2 π 2p b + 2 πh 2 p g. 6 Impications It is cear that the manipuation equiibrium is stricty inferior to the situation when the creditors are perfecty informed, and to the no-manipuation feedback equiibrium. Therefore, confirming the intuition from Godstein and Guembe (2008, we concude that the creditors and the firms woud be better off from imposing restrictions on the short saes. Another possibe way to improve the manipuation equiibrium is to introduce additiona signas about the firm fundamentas to the creditors. It is easy to think of the mode when the creditors observe an additiona signa about ω that is independent from π or prices. It is cear that observing such signa woud improve the outcome. 5