Finals Study Flashcards
MM setup returns on trade
R=(S_B+D)/S_A\alpha*x-\alpha(1+r_f)D-\alpha(x-(1+r_f)D)
MM assumptions
no taxes, bankruptcy, t-costs, asymm. info, agency conflict, two period, identical firm
What is ROE for MM
return on unlevered equity + debt / share ratio * risk premium (rho-r_f).
Stiglitz and Miller result
Using account, GE implies that if financing decisions are changed, consumption and prices remain constant. Allows firms to be borrowing and lending at the same rate, no bankruptcy as well.
Implication of Stiglitz and Miller
information asymmetry, commitment, agency has to be the solution for standard preferences
Tradeoff Theory
Debt creates net tax benefit but also default costs.
What is the tax shield benefit (equity, corporate tax, and interest rate tax)
\Delta = (1-(1-t_c)(1-t_e)/(1-t_i))
5 conditions for signaling equilibrium
- IR constraint; 2. IC constraint; 3. PBE RE; 4. Reasonable beliefs OEP; 5. Each type different inference
Ross setup (2 type)
M=(1+r_f)\gamma_0V_0+\gamma_1[v_1-1_{v
Ross 2 type solution
High type issues debt because it’s cheaper. Firm b issues 0 debt, provided cost of default is high enough. Cutoff F^*.
Cont. Type Ross Model Setup
Type determines upper bound on the support of project type.
Cont. Type Ross Model Utility
\gamma_0 a(F)/2+gamma_1(t/2-LF/t) if F
Ross REE definition
a(F(t))=t
Ross REE brute force solution (separating) steps
Steps:
1) Get DE using FOC within default probability region. Use appropriate boundary conditions.
2) Show equilibrium cannot have default for sure. Get corresponding parameters.
3) Never optimal to deviate to debt region (get parameters).
Ross cont. pooling steps
conjecture a debt level (0) and check the IC constraints
Intuitive criterion definition
OTP beliefs are zero for a type that does not benefit from deviation. Benefiting from deviation must be that the types inference is kept constant in the new setting.
What does intuitive criterion rule out?
Pooling disappears. Only the most efficient separating equilibrium remains.
In efficient separating equilibrium, high type deviates epsilon lower and gains from issuing less debt. Since it is still not profitable for the low type to deviate, high type gets inference with probability 1 and remains well off.
What does intuitive criterion rule out?
Pooling disappears. Only the most efficient separating equilibrium remains.
In efficient separating equilibrium, high type deviates epsilon lower and gains from issuing less debt. Since it is still not profitable for the low type to deviate, high type gets inference with probability 1 and remains well off.
It is key that the low type never gains.
Write down the four conditions for Mailath
IC, SIC (equality for IC), SM (U_3/U_2 monotonic in type), IV (outcome when take the choice of the worst type, given everyone knows your outcome, important restriction)
Additional restrictions for Mailath (5)
1) U is twice differentiable, 2) U_2\neq 0; 3) U_13\neq0; 4) worst type full information decision defined; 5) U_33>0.
Mailath Theorem 1 and 2
dt/da = -U_2/U_3 if it exists. t is the menue that maps types to actions.
Doesn’t imply existence.
Mailath: sign of t’?
Same as U_13
Mailath Theorem 3
A menu satisfies SIC iff 1) the menu satisfies the DE (T1 and 2); 2) If U_2>0, then U_3 / U_2 is a strictly increasing function of type for the graph of the menu.
Leland and Pyle Model Purpose
Equity can also be signal for project quality–firms want to own more of their project all else equal.
Leland and Pyle W_0
W_0+D+(1-\alpha)(V(alpha)-D)-K-beta V_m-Y=0
Leland and Pyle W_1
W_1=alpha[\tilde x+mu-(1+r_f)D)+beta\tilde M + (1+r_f)Y
Leland and Pyle Combined BC
W_1 = alpha[\tilde x+m-mu(alpha)+lambda]+beta[\tilde m-(1+r_f)V_m]+(W_0-K)(1+r_f)+mu(alpha)-lambda
LP Util
Mean variance with risk aversion b.
LP Util
Mean variance with risk aversion b.
Myers and Majluf Setting
Ownership dynamics, prioritize old shareholders. Trade off equity dilution against positive NPV projects.
Myers and Majluf utility before and after investment
a+S vs P’/(P’+E)[(E+S)+a+b]
Simpler version of Myers and Majluf (who invests?)
two types, no uncertainty regarding outcome, S=0. Only low type invests (opposite of Leland and Pyle)
What is the price under Myers and Majluf
P=value of firm post investment - I
Pecking Order
Second argument of Myers and Majluf. Funding should be in the order of cash, riskless bonds, risky bonds, then equities.
Markets fear adverse selection.
Miller and Rock Setup
Two periods, x_1=F(I_0)+epsilon_1 and x_2=F(I_1)+epsilon_2 where I_1=x_1-D the dividend.
E[epsilon_2\midepsilon_1]=gamma_1epsilon_1
Util = kV_1(D)+(1-k)(D+1/(1+i)[F(F(I_0)+epsilon_1-D)+gamma\epsilon_1])
where V_1(D)=D+1/(1+i)[F(F(I_0)+\hat epsilon_1(D)-D)+gamma\hat\epsilon_1 (D)]
Miller and Rock Solution
U_13=(1-k)f_12(D,\theta) is the sign where f is the production function.
Jensen and Meckling two conflicts
Managers and shareholders: managers underproduce effort relative to entrepreneur
Debtholders and Equity holders: equity is an option which reduces the value of debt, which is conservative.
Myers Debt Overhang
Excessive debt distorts managers incentives to take on efficient projects, since the returns are only accrued by the shareholders (when amt outstanding is suff. high)
Jensen and Grossman and Hart
Empire building, debt reigns in excessive investment.
Write down Brander and Lewis assumptions (for R)
R_ii<0, R_j<0, R_Z>0, R_ij<0, and R_iz\neq0
Write down Brander and Lewis assumptions (for V)
V_ii<0, V_ij<0, V^i_iiV^j_jj-V^i_ijV^j_ji>0
Townsend, Gale, and Hellwig CSV idea
optimal TT mechanism with commitment which raises funding for a project.
Townsend, Gale, and Hellwig CSV idea
optimal TT mechanism with commitment which raises funding for a project.
sketch the proof for the optimal mech
remember iff, have to prove in both directions.
1) Assume feasibility, then in default region pays constant; in verification, pay less than constant otherwise would be worse off.
2) second and third are sufficient for IC.
Diamond Banking Setup
I=1, risky outcome, E[y]\geq R+K. What is the optimal p(s) and s(y) such that s(y)\leq y
Write down Diamond max problem
max_p,s E[y-s(y)-p(y)]
s(y)\leq y
y\in arg\min(p(x)+s(x))
E[s(y)]\geqR
what are the five observations in Diamond’s banking paper.
1) BE holds tight
2) c(y)=s(y)+p(y) must be weakly decreasing, and there exists a point at which c(y)D and c(y)>D for all y
Why do intermediary costs fall?
Monitoring costs fall when aggregated–likelihood of default lowers so lower cost.
