TELEVISIÓN Y EDUCACIÓN.

I consider the case of unobservable monitoring effort now. bi is private infor- mation to the bank. Because investors cannot directly observe how well the underlying pool of loans has been monitored, they try to infer bi from the observables αi, Ii, Ri. Investors rationally assume that bank i chooses the monitoring intensity as to maximize its own profit given the securitization contract proposed to investors B(π) = min{π, Ri}. Bankers in the economy

are aware of it and take it into account. The maximization problem is: max ai,bi,αi,Ii,Ri,PiαiIi Z L 0 πdH(π|ai, Y) + (1−αi)Ii Z L Ri (πs−R)dH(πs|bi, Y) (2.14) −f(Ii−Pi)−c(aiαiIi+bi(1−αi)Ii) s.t. P ≤ (1−αi)Ii ρ [ Z Ri 0 πsdH(πs|bi, Y) + Z L Ri RidH(πs|bi, Y)] (2.15) b∈arg max bi equation 2.14 (2.16)

The bank maximizes its expected profit subject to two constraints: the participation constraint for investors equation 2.15 and an incentive con- straint 2.16. The incentive constraint captures that, as it chooses αi, Ii, and

Ri, the bank also bears in mind how this affects investors’ beliefs for bi and ultimately their willingness to pay for asset-backed securities. Using the First Order Approach, see Holmstr¨om (1979), the incentive constraint can be simplified to:

Z L

Ri

(πs−Ri)dHb(πs|bi, Y)−c= 0 (2.17)

Equation 2.17 defines the intensity of monitoringbi, to which the bank can credibly commit. It depends solely on the retained stake in the securitized assets - measured by Ri: bi =b∗i(Ri).23 The bigger the stake, the better the bank will monitor securitized loans and the higher is investors’ anticipation of bi.24

Again the participation constraint will always hold with equality at the optimum, so we can substitute for Pi in the objective function and set up the Lagrangian function. The detailed derivation of the optimally conditions 2.18, 2.19, 2.20, 2.21, and 2.22 is shown in Appendix A.

23_{Solely in the sense thatR}

i is the only variable the bank directly influences.

24_{Note that in this set-up the lower R is, the higher is the stake retained by the bank.} By implicitly differentiating equation 2.17 one can show that decreasing Ri leads to a higherbi.

Z L 0 πdHai(π|ai, Y) =c (2.18) bi =b∗i(Ri) such that Z L Ri (πs−Ri)dHbi(πs|bi, Y)−c= 0 (2.19) Z L 0 πdH(π|ai, Y)−cai = Z L 0 πsdH(πs|bi, Y)−cbi+[ f0(Ii−Pi) ρ −1] Piρ (1−αi)Ii (2.20) Z L 0 πdH(π|ai, Y)−cai =f0(Ii−Pi) (2.21) (1−αi)Ii( f0(Ii−Pi) ρ −1) Z L Ri dH(πs|bi, Y) +f0(Ii−Pi) ∂Pi ∂bi ∂b∗_i(Ri) ∂Ri = 0 (2.22)

Proposition 1 Loans held on the balance sheet of the originating bank are

monitored at a higher intensity than securitized loans: ai > bi, see Innes

(1990), Proposition 1. The marginal on-balance-sheet funding costs exceed the off-balance-sheet funding costs: f0(Ii − Pi) > ρ. The proofs follow in

Appendix A.

The optimality condition for the monitoring intensity of retained loans, equation 2.18, not surprisingly, is the same as in the first best case. Since for on-balance-sheet loans the originating bank bears all the risk and costs and gets all the returns from prudent monitoring, nothing changes. Though, this does not necessarily imply that same level of ai is set at the optimum. The marginal expected per-unit return of monitoring in general may depend on the aggregate lendingYi. To keep the line of argument as simple as possible, I impose the admittedly restrictive assumption that ∂

2_E(π|e

i, Y)

∂ei∂Y

= 0. Securitized loans are monitored at a lower intensity than retained loans, see Proposition 1. Since banks bear all the cost of monitoring but only part

of the downside risks of securitized loans, their monitoring incentives are damaged.

Equation 2.20 determines how many of the originated loans are held until maturity - αi. Holding more loans, instead of securitizing them, has three effects on profits. First, it increases the expected pay-off from the bank’s retained loan portfolio. Second, because less loans are securitized, the ex- pected pay-off from the retained stake in them decreases and the income from issuance of asset-backed securities drops. Third, as the on-balance- sheet funding costs f0(Ii −Pi) are higher than ρ, the overall funding costs rise. At the optimum, the marginal income from holding one more unit of loans on the balance sheet (the left hand side) exactly equals the sum of the foregone marginal benefits: income from retained interest and issuance activity (first two terms on the right hand side), and a possible reduction of funding costs (the third term).

The optimal amount of lending Ii is such that the marginal costs are off-set by the marginal gross income net of induced monitoring, see equation 2.21.25

The last optimality condition, stated in equation 2.22, concerns the size of the retained stake Ri. Retaining a smaller stake26 has two effects. First, incentives for proper monitoring are spoiled, so the intensity of monitoring decreases. This lowers the investors’ willingness to pay for asset-backed se- curities and thus the issuance income of the bank and the expected pay-off from the retained stake. Cost reduction through securitization becomes less effective. This effect is captured by the second term on the left hand side and has a negative sign. Second, holding bi fixed, a higher R implies issuance of asset-backed securities with a higher par value.27 This leads to a higher issuance income. This is reflected in the positive first term on the left hand side. Increasing R leads to a higher par value of the senior tranche of asset- backed securities. These, though, are of lower quality. R is optimally chosen

25_{The equation sets marginal cost equal to marginal gross income on retained loans,} this also holds securitized loans, as at the optimum marginal gross income from both type of lending is equal.

26_{Which corresponds to a higherR} i. 27_{Or a larger senior tranche.}

such that the two effects offset.28

I apply the symmetry argument again. All banks in the economy make the same choices. Thus loans originated by different banks are monitored with the same intensity, banks originate the same amount and securitize the same fraction, retaining first loss pieces of the same size. Let aSB denote the optimal intensity of monitoring for retained loans,bSB- the one for securitized loans,ISB_{be the amount of originated loans and (1−α}SB_{) be optimal fraction} of assets securitized in case effort is not observable by outsiders. The total lending in the economy is YSB _=nISB_{. In equilibrium Y}SB _{adjusts so that} given its level no bank has an incentive to further increase or reduce its loan supply. This is the case if equation 2.23 is fulfilled:

Z L 0 πdH(π|aSB, YSB)−caSB =f0(Y SB n −P), (2.23) where P = (1−α)Y SB ρn [ Z L R πsdH(πs|bSB, YSB) + Z L R RdH(πs|bSB, YSB)]

If Y < YSB _{banks originate additional loans, since the marginal gross}

income minus of monitoring costs exceed the marginal costs of funding. Y

increases and drives the marginal gross income down, and the funding and monitoring costs up until condition 2.23 is fulfilled.