Kyoto University,
Graduate School of Economics
Research Project Center Discussion Paper Series

A Model for Bank’s Optimal Asset Securitization Program

Masahiko Egami and Kaoru Hosono

Discussion Paper No. E-10-003

Research Project Center
Graduate School of Economics
Kyoto University
Yoshida-Hommachi, Sakyo-ku
Kyoto City, 606-8501, Japan

June 2010

A Model for Bank’s Optimal Asset Securitization Program I
Masahiko Egamia , Kaoru Hosonob
a Graduate School of Economics, Kyoto University, Yoshida-honmachi, Kyoto, 606-8501, Japanb Faculty of Economics, Gakushuin University, Mejiro, Tokyo, 171-8588, Japan

Abstract
We propose a framework to examine banks’ asset securitization program. It provides a comprehensive view that explains various separate findings and claims in the literature. We derive
optimal timing and quantity of banks’ asset securitization by explicitly incorporating stochastic asset returns and leverage constraints. We also quantify how much additional value can becreated by asset securitization program, which gives some insights into why banks securitize assets. We further conduct some comparative analysis by varying the asset quality and economic
environment, obtaining results that can account for the actual securitization trends including the
bubble and crisis periods. Our empirical analysis using a Japanese data set also provide evidencesthat are consistent with our theoretical implications.
Key words: Asset securitization program, Leverage, Impulse control, Bubble and crisis
JEL Classification: D81, G21, G32.

1. Introduction
Why do banks securitize assets? The literature points out various incentives of asset securitization. First, securitization reduces banks’ assets and thus leverage, contributing to the risk
management in light of the value-at-risk (VaR). Under capital regulations, securitization also
reduces the risk asset (i.e., loans) and thus the level of regulatory capital required (regulatory
arbitrage documented by Brunnermeier [5], among others). Second, securitization contributes
to banks’ profits through low funding costs or greater availability of funds as compared to traditional corporate finance (Shin [25]). Given the opaqueness and riskiness of bank assets, a bankfaces severe asymmetric information problems in corporate finance. In contrast, securitized assets are more transparent and less prone to asymmetric information (James [12]; Flannery [8]).
Risk allocation between banks and investors are also more flexible in securitization than in corporate finance (Greenbaum and Thakor [9]; Boot and Thakor [3]; Riddiough [23]). In addition,
securitization permits banks to specialize in originating loans and to free from funding and warehousing them. If banks have a comparative advantage in the former rather than the latter, whichis plausible under capital requirements and reserve requirements, securitization enhances banks’I This research is in part supported by Grant-in-Aid for Scientific Research (B) No. 22330098, Japan Society for the
Promotion of Science. It is also conducted as a part of the GEM Research Project at Gakushuin University.
1 M. Egami also acknowledges the support by Grant-in-Aid for Scientific Research (C) No. 20530340, Japan Society
for the Promotion of Science.

Preprint submitted to Elsevier

April 21, 2010

profits (Pavel and Phillis [20]; Pennacchi [21]; Flannery [7]; Jaffee and Rosen [11]; Passmore[18]; Twinn [27]).
Though the various effects of securitization on leverage and profits have been discussed separately in the literature, they are not mutually exclusive or incompatible with one another. In
fact, if the marginal return to asset is decreasing due to higher informational or regulatory costs
associated with higher leverage, then controlling of asset size and leverage through securitization
may contribute to raise profits and reduce volatility. Of course, securitization involves some sales
costs and securitized products may sell at discounted prices. Taking all these factors into consideration, we formulate securitization in a unified way as a bank’s value-maximizing behavior
to control their asset size (or leverage). As a solution of stochastic optimization problem, we
can derive when and to what extent banks securitize assets. In formulating a bank’s optimization
problem, we impose the constraints on the asset size (or leverage) both at its maximum (leverage
constraints or capital regulations) and its minimum (solvency constraints). We will also quantify
how much additional value can be created by asset securitization program. This analysis gives
some insights into why banks securitize assets. We further conduct some comparative analysis
by varying the asset quality and economic environment.
Our theoretical analysis yields some interesting and realistic results. First, securitization ismore beneficial when banks’ asset quality is deteriorating because in this situation, banks takeadvantage of the existing good asset by repeatedly making asset securitization of small size.
In the real world, investors may regard the high frequency and low volume of securitization as
the deterioration of asset quality of the originating banks. Second, when the asset quality isabnormally improving (in the bubble economy), banks have an incentive to hold the asset byincreasing the leverage. This result is consistent with the U.S. banks’behavior just before thesub-prime mortgage loan debacle in 2007 (Adrian and Shin [1]). Third, when the asset quality
is deteriorating and the sales value of securitized product is severely discounted (in the financial
crisis), banks wait for the asset to grow for a long time until they securitize assets. The delay insecuritization in this case leads to a large sales volume when it is made. This result is consistent
with the fire-sales of securitized products observed in the recent financial turmoil (Brunnermeier[5]).
We also provide some empirical evidences consistent with our theoretical analysis. Using
the data set of securitized products originated by Japanese banks, we find that low capital ratios(or high leverage) tend to increase securitization, suggesting that banks actively control theirleverage through securitization. Second, the issuance of securitized products results in lower
abnormal stock returns. Securitization seems to serve as a bad signal concerning the originatingbanks’ asset quality.
The remaining part of this article is structured as follows: In Section 2, we introduce thedynamic model of bank’s securitization problem in the form of stochastic impulse control. In
Section 3, we solve and implement the model. We compare four cases that depend on the bank’s
asset quality and underling economic climate, providing numerical examples. In Sections 4 and
5, we discuss the Japanese banks’ securitization programs as our empirical evidence.
2. The Model
Let (Ω, F, (Ft )t≥0 , P) be a complete probability space with a standard Brownian motion
W = {Wt ; t ≥ 0}. We model the market value of the normalized total asset value process X by2

a geometric Brownian motion:(2.1)

dXt = µXt dt + σXt dWt

and

X0 = x,where µ and σ are positive constants. We normalized the bank’s total asset value by the bookvalue of its equity. The bank invests their own and borrowed capital in various assets whose
profitability is summarized by a function f : R+ 7→ R. Let us assume that f (x), representing the
profit of the bank at (normalized) asset level x, is an increasing concave function. The bank canearn positive profits (at least for a sufficiently small asset size) either due to the restrictions onentry into the banking industry (i.e. the franchise value stressed by Hellmann et al. [10], among
others) or its advantage in processing the customers’ private information (information monopoly
advocated by Sharpe [24] and Rajan [22]. The bank has an incentive to increase the leverage andinvests in risky assets. However, investment opportunities are finite and the bank chooses appropriate transactions by evaluating their risk-return profile of available opportunities. It should bepointed out that the bank has to also take its asset-diversification requirements into account. For
example, even if there still remains a substantial number of opportunities of attractive risk-return
profile in one industry segment, the bank shall cap them at certain level. Therefore, as the bankstarts depleting attractive transactions, the profitability flattens out (i.e., f ′′ (x) < 0) for some xlarge enough.
The increased leverage leads to further fluctuations of the market value of the assets. For
example, a negative µ and/or high volatility σ shall imply that the overall asset quality has deteriorated and shall be penalized by possible bankruptcy/insolvency threat. We define the insolvency
time byτ := inf{t ≥ 0 : Xt ≤ x}
as the first time the bank’s normalized total asset value hits level x, a certain number exogenously
provided. Note that any level x in (0, 1) represents balance sheet’s (cash flow) insolvency.
On the other hand, the bank needs to consider some regulatory issues. For example, thebank has to maintain a certain level of its own capital measured by the ratio of the total asset toshareholders’ equity. We call this ratio “capital ratio” hereafter. In our notation, the bank cannot
increase the asset X beyond that level. To incorporate this issue, we postulate that the bank has
to reduce its total asset size as soon as it reaches that level, say x̄. Of course, the compliance tothe regulation can be accommodated by issuing more capital. But to focus on short run analysis,
we keep the level of the bank’s own capital constant. It should also be pointed out that theshareholders’ equity in the regulatory requirements is usually referred to the book value, a factthat justifies our formulation here. Moreover, the bank may have a formula that transforms thebook value of its equity to the market value, provided that the bank knows the market value ofthe total asset2 .
To maintain sufficient equity in its book, the bank from time to time sells its assets in themarket to reduce the total asset size and hence its volatility. In this way, the bank can secure theprofit by the sale of the assets and reformulate its marketing plan for making a room to invest in
2 This transformation is in fact the other way round. The observable is the market value of the equity, not the market
value of the asset. The option-theoretic view of equity as in Black-Scholes and Merton allows one to estimate the value ofthe unobservable asset value. For example, Moody’s KMV commercializes a model (based on this approach) to estimate
the probability of default on the firm’s debt obligations.

3

”better” transactions. The timing and size (measured by the normalized asset size) of asset sales,
to be controlled by the bank, are denoted by a double sequence:ν := (T1 , T2 , ....; ξ1 , ξ2 , ....)
where 0 ≤ T1 < T2 < .... are an increasing sequence of Ft -stopping times and ξ1 , ξ2 ... are
FTi -measurable random variables representing the amount of the securitization exercised at thecorresponding intervention times Ti . In other words, ξi = XTi − − XTi > 0 represents theamount of the asset reduction at time Ti . If a strategy ν satisfies the above specification, it iscalled admissible. We call V the set of all admissible strategies. Namely, for a strategy to be
in V, it has to satisfy (1) ξi = XTi − − XTi > 0 for each i and (2) the controller (bank) must
maintain X on or below the level x̄ for all t ∈ [0, τ ).
The costs involved in this control consist of proportional (to the size of the asset sales) and
fixed-amount portions. The latter deals with administrative work including negotiations with theunderwriters. It follows that when the bank sells its assets at the level of x to y, then the total
cash flow is λ(x − y) − K where (1 − λ) measures the securitization’s proportional cost andK ∈ R+ is the fixed cost incurred at the time of sales. The bank’s objective is to maximize thediscounted expected profit
[∫
]
τ
∑
(2.2)
v(x) := sup Ex
e−αs f (Xs )ds +e−αTi (λ(XTi − − XTi ) − K)
ν∈V

0

Ti <τ

by finding an optimal strategy ν ∗ among all the admissible strategies in V such that v(x) =∗J ν (x) where the performance measure J ν (·) is
[∫
]
τ
∑
ν
x
−αs
−αTi
J (x) = Eef (Xs )ds +e(λ(XTi − − XTi ) − K)
0

Ti <τ

for each ν ∈ V.
In the short run analysis where the bank’s own capital is held constant, we focus on the following
two cases:
Case 1 Positive drift and medium-to-low volatility: In this case, the bank has sound investment
assets. It then uses asset sales mainly to keep the capital ratio within a comfortable range.
Case 2 Negative drift and high volatility: This reflects deteriorating overall asset quality. Given
the constant equity level, the bank needs to improve its capital ratio by cashing out its
future income stream (i.e., selling assets). Then p(x, y) := λ(x − y) − K represents thenet cash flow from the asset sale. That improves the value J ν (·) and, accordingly, helps
to improve the capital ratio in the next period. Simultaneously, however, this transaction
brings the asset size closer to level x in the current period.
Note that in either case, cash flows from the sale, i.e., p(·, ·) is not reflected in the computation of
the bank’s capital ratio in this period. In the next period, however, this amount shall be added tothe bank’s capital and the initial capital ratio X0 = x shall be renewed. In a sense, this time-lagof practical accounting matter is automatically incorporated in our model.

43. Model implementation: Theoretical results
To solve (2.2), we shall specify the form of profit function as(3.1)

f (x) := c · xγ ,0 < γ < 1, a ∈ R+ , c ∈ R+

and compute(3.2)

g(x) := E

x

[∫ ∞

−αt

e

]
f (Xt )dt =

0

c
xγ
α−m

with m := (µ − 21 σ 2 )γ + 12 σ 2 γ 2 . Then, by the method to solve stochastic impulse control
problems of linear diffusions (see for example a standard textbook by Øksendal and Sulem [16]),
we can find the solution{v0 (x) := βψ(x) + δφ(x) + g(x), x ≤ x < b(3.3)
v(x) =
λ(x − a) − K + v0 (a),b ≤ x,
where
ψ(x) := xp1

and

φ(x) := x−p2

with p1 > 1 and −p2 < 0 being the two roots of 12 σ 2 p(p − 1) + pµ − α = 0. Hence the strategy
is to make asset sales at time
τb := inf{t ≥ 0 : Xt ≥ b}in the amount of Xτb − a.
It is useful to identify the value of the securitization program itself. The latter can be obtained
as the difference of the two value functions v(x) and
[∫ τ
]
x
−αs
(3.4)
v̂(x) := Eef (Xs )ds .
0

because this v̂ function gives us the value of the bank’s operation without any securitization
program. In this sense, the quantity (v − v̂)/v̂ indicates the relative improvement of the value inthe presence of securitization program. By using the standard computation, we obtainv̂(x) = g(x) − Ex [e−ατ g(Xτ )] = g(x) − g(x)

φ(x)
.
φ(x)

Case 1 vs Case 2: First we consider Case 1 (normal asset quality). Figure 1-(a) illustrates
a numerical example with c = 1 and γ = 0.25 for the profit function (3.1), µ = 0.05 andσ = 0.25 for the diffusion (2.1) and x = 1, λ = 0.95, K = 0.5 and α = 0.25 for the objectivefunction (2.2). For given a, we can compute the optimal threshold value b = b(a) and thecoefficient β = β(a) as functions of a. Figure 2-(a) presents that for each a we can computethe value of β(a), which is maximized at a = 2.55. Let us say this point a∗ . The values for(3.3) that correspond to this a∗ are the solution as long as b∗ < x̄ is satisfied. In our example,
the solution set is (a∗ , b∗ , β, δ) = (2.55, 6.26, 0.0158, −4.125). Namely, the asset sales is ofsize b∗ − a∗ = 3.71. Figure 1-(a) shows the value function v(x) (above) and the value without
any securitization v̂(x) (below). Observe that the vertical distance between the two curves is the
5

vHxL

vHxL
10

5
8
4
6

3

4

2

2

1
x
2

4

6

x

8

1

2

(a)

3

4

5

6

(b)

Figure 1: A numerical example of the asset sales problem: The first part of the value function v (corresponding to no-action region) is plotted in solid red and the second part (corresponding to intervention
region) in solid black. (a) normal asset quality and (b) deteriorating asset quality.

bHaL

ΒHaL
0.015846.30

0.01582
6.29

0.015800.01578

6.28
0.015760.01574

6.27

0.01572
a
a
2.5

2.6

2.7

2.5

2.6

2.7

2.8

2.8

(b)

(a)

Figure 2: The optimal post-securitization point a. (a) For various values of a, β(a)’s are computed andthe maximum value of β ∗ is attained by a∗ . (b) At the same a∗ , the value of b(a) is minimized.

6absolute improvement of the value in the presence of the program. Note the steep decent of thevalue function in the neighborhood of x. If the regulatory level x̄ is, say 12.5 that translates into
the bank’s own capital divided by its asset size being 8%, we have b < x̄ in this example.
Now, we consider Case 2 (i.e., deteriorating asset quality). We change our parameters toc = 0.5, µ = −0.05, σ = 0.35, while the others remain the same. See Figure 1-(b) for thechange of the shape of v(x). The solution is now (a∗ , b∗ , β, δ) = (1.88, 4.65, 0.0090, −1.834).
The size of asset sales is 2.77. The size is smaller despite the same variable (1 − λ) and fixed
cost K of securitization. That is, the bank needs to make asset sales more frequently by paying
a large fixed cost. This inefficiency affects also the value function v(x) which is much smaller
than the one in Case 1.
Then we take a look at the relative improvement of the value created by the securitization
efforts v−v̂v̂ . See Figure 3. It is interesting to observe that the greater improvement is attained inCase 2. In this situation, the bank may collect the value (within its asset portfolio) as quickly as
it can by repeatedly making asset sales of small size. Recall that the sale is made almost at par
λ = 0.95. Hence the bank in Case 2 that faces deteriorating asset quality takes advantage of theexisting good asset.
Program Value

0.8

0.6

0.4

0.2

x
2

4

6

8

Figure 3: The relative improvement of the value: In the relative sense, the value is enhanced in Case 2

more than in Case 1. The two lines plot (v − v̂)/v̂ for Case 1 (below) and Case 2 (above).

However, we also have to consider the danger involved. By moving the asset level to the left
via securitization, the bank brings itself closer to the insolvency level x. Especially in Case 2
with the negative drift and large volatility, the situation is more serious. We quantify this issue.
At the post-securitization point XTi = a∗ for all i ∈ N, the probability that the total asset hits x
before the next securitization time T(i+1)− can be computed as follows:
q := PXTi (τ < T(i+1)− ) = Pa (τx < τb ) =S(b) − S(a)S(b) − S(x)where S : (0, ∞) 7→ R+ is the scale function of the diffusion. See Borodin and Salminen [4]. In
the case of geometric Brownian motion, it is{ −2κ− x2κ , κ ̸= 0,
S(x) =ln x,
κ = 0,
with κ = µ/σ 2 − 1/2. Using this, we compute, for this numerical example, that q = 0.356
and q = 0.860 in Case 1 and 2, respectively. The value maximizing criterion (2.2) leads to a7

Table 1: Parameters and Results of the Four Casescµσ
λ(a∗ , b∗ )b∗ − a∗q
T (a∗ )

Case 1
Normal
1
0.05
0.25
0.95
(2.55, 6.26)
3.71
0.356
13.06

Case 1′
Bubble
1
0.15
0.25
0.95
(2.78, 10.93)
8.15
0.020
11.12

Case 2
Deteriorating
0.5
-0.05
0.35
0.95
(1.88, 4.65)
2.77
0.860
6.47

Case 2′
Crisis
0.5
-0.05
0.35
0.5
(2.70, 7.57)
4.83
0.868
6.62

much higher ruin probability in Case 2. It is because the bank (shareholder) attempts to cash
out the possibly high quality asset as early as possible at the expense of the increased chance ofinsolvency.
In relation to this, we compute the expected duration until the state process hits x or b∗ ,whichever first, from the post-securitization point a∗ . For any x ∈ [x, b∗ ], we have
{
}
∫ ∗
∫
b

T (x) := Ex [τ ∧τb∗ ] = 2 u(x)x[S(b) − S(ξ)]m(dξ) + (1 − u(x))x[S(ξ) − S(x)]m(dξ)
xwhere u(x) = [S(x) − S(x)]/[S(b∗ ) − S(x)] and m(dx) = σ12 x2κ−1 dx, the speed density. For
the given example, it is computed T (a∗ ) = 13.06, and 6.47 in Case 1 and Case 2, respectively.
In Case 2, the duration is much smaller, indicating more frequent asset sales. If this happens in
the economy in which all banks have access to securitization technology, the high frequency andlow volume may be regarded as the deterioration of the asset quality of the bank.
Comparative Statics 1–Bubble Economy: We perform some comparative statics. First, wechanged the parameter of µ in Case 1 from 0.05 to 0.15. Call it Case 1′ (bubble economy). In
this case, the solution set becomes (a∗ , b∗ , β, δ) = (2.78, 10.93, 0.150, −4.729). Now the sizeof asset sales is b∗ − a∗ = 8.15, which is much greater than in the original Case 1. While
the value of a∗ has not changed, that of b∗ becomes very large. Since the increased drift has
made it easier to reach a higher asset value, the bank can wait longer for realizing a larger profit
λ(b∗ − a∗ ) and, at the same time, enjoying a larger running profit f . Hence when the economy isdoing well, the bank has an incentive to hold the asset by increasing the leverage. This result is
consistent with the pro-cyclical leverage observed for U.S. financial intermediations. Adrian andShin [1] found that U.S. investment banks accelerated the growth of leverage when the value of
assets were growing rapidly. This situation, however, could lead to a large loss in case the bubble
in the economy bursts abruptly. In this sense, the regulatory level x̄ should be appropriately
determined. Due to the existence of x̄, the bank cannot accumulate the asset base so much. We
computed how the expected duration until the next securitization (or the ruin) would change forthe bubble economy case. We obtain T (a∗ ) = 11.12 which is shorter than 13.06 of the original
Case 1. The increased drift has made the b value significantly higher (from 6.26 to 13.06) but
still it takes less time until the next securitization.
8

Another interesting phenomenon is that the relative improvement curves (v − v̂)/v̂ of Case 1
and Case 1′ intersect. See Figure 4-(a). For small values of x, Case 1′ has greater improvements
than Case 1. This relationship is reversed for larger values of x. This is mainly due to the highlevel of b∗ in Case 1′ . At this level of initial value of x in the neighborhood of 10, in Case 1, it
is within the intervention region where the optimal strategy is to make asset sales immediately.
Hence the value increases rapidly there (because there is no need to wait) and so the relative
improvement of Case 1 grows rapidly. Note that for smaller values of x in which both cases arein their respective no-action region, the improvement of Case 1′ is greater.
Program Value

Program Value

0.7
0.8

0.6
0.5

0.6

0.4
0.4

0.3
0.2

0.2
0.1
x
2

4

6

(a)

8

10

12

x
2

4

6

8

(b)

Figure 4: Comparative Statics of the relative improvement caused by the securitization program: (a)Comparison between Case 1 (usual quality) and Case 1′ (bubble economy). The relative improvement curveof Case 1 starts below and intersects the other curve (for Case 1′ ) from below. (b) Comparison between
Case 2 (deteriorating asset quality) and Case 2′ (bank run). The relative improvement curve of Case 2′ islocated below that of Case 2.

Comparative Statics 2–Financial Crisis: We reduce the value of λ in Case 2 from 0.95 to
0.5. Call it Case 2′ (financial crisis). In Case 2, the bank’s asset quality is deteriorating reflected by the negative drift µ = −0.05 and the large volatility σ = 0.35 while the existing
asset base is still sound reflected by λ = 0.95. However, in Case 2′ , the market has doubts
about the quality of assets for sale. Outside investors may worry that banks are selling risky or
low-quality assets (”lemons”) and may demand a significant discount (λ = 0.5) at sales (e.g.,
Brunnermeier [5]). Unexpected price shocks may also lead to high asset volatility and to a highmargin or haircut (Brunnermeier and Pedersen [6]). The solution set is now (a∗ , b∗ , β, δ) =(2.70, 7.57, 0.0016, −1.826). Recall that in Case 2 we have (a∗ , b∗ ) = (1.88, 4.65). The valueof b∗ has increased because the reduced profit level λ = 0.5 discourages the bank from making
asset sales in a timely manner. Since the fixed cost has not changed, the bank has an incentive to
reduce the number of transactions. Consequently, the delay in securitization in this case leads toa larger sales volume when it is made. But this could however cause a further price deteriorationin the market as we witnessed in the recent financial crisis (”fire-sale externality” described by
Shleifer and Vishny [26], Brunnermeier [5], and Adrian and Shin [1]). Note that the value of a∗is also higher. It is related to the ruin probability q. In the original Case 2, it was 0.860. It is
computed now to be q = 0.868, no material change. The value of a∗ is arranged to be higher
for the ruin probability remaining the same. For the computation of the expected duration, we
find that T (a∗ ) = 6.62 up from 6.47 in the original Case 2. Since the drift parameter has not9changed, it is presumably explained by the increased distance from a∗ both to x and to b∗ In
the financial crisis case, it is 1.70 and 4.87, while it was 0.88 and 2.77 in the original. It highly
contrasts with the change from Case 1 to Case 1′ where the expected duration gets shorter. Hencein the financial crisis scenario, the reduced profit level deters bank’s securitization initiatives.
As for the relative improvement of the value, the declined λ (from 0.95 to 0.5) affects thevalue of securitization program in Case 2′ . See Figure 4-(b). The improvement is much smaller
as compared to Case 2.
Remark 3.1. When the solution to (2.2) is not feasible, that is, b has a value greater than x̄, we
see that no points of a satisfy x̄ = b(a) because b(a) : R+ 7→ R+ takes its minimum at a∗ (Figure
2-(b)). Hence we do not know a solution when the constraint is binding. To our knowledge, thisis an open mathematical problem. Note that when the fixed cost is zero (K = 0), it is known
that the solution is given by b∗ = x̄ and at this time we have also a∗ = b∗ . See Paulsen [19].
4. Empirical Analysis: Motives for Securitization
We conduct some empirical analysis on the motives and consequences of securitization bybanks. In this section, we investigate the motives of securitization focusing on whether banks
actively control their leverage through securitization.
4.1. Data
Our sample consists of securitized products issued by Japanese banks. Japan has a welldeveloped market of securitized products, though its size is still smaller than the U.S market.
In addition, Japanese banks do not suffer such a serious moral hazard problem associated withsecuritization as we have observed for U.S. banks. These features are well suited to test ourtheoretical analysis. For the data source of securitization, we use “Survey of the Securitization Market” published by Japan Securities Dealers Association, which gathers information on
the securities backed by Japanese domestic assets from April 1, 2004 and publishes the Survey
monthly. Our sample period covers from April 2004 to December 2007. Note that the Japanese
economy was recovering during our sample period from the preceding decade-long stagnation.
(The average growth rate of real GDP is 2.3% during 2004-2007, higher than that of the preceding decade, 1.0%). The banking sector as a whole was also recovering from the non-performing
loan problems, though still some banks were suffering from them. We limit our sample securitization products to those whose originators are Japanese banks. Counting multiple products
issued by the same originator on the dame date as unity, we identified 101 securitized products
originated by Japanese banks. Table 2 summarizes descriptive sample statistics. The medianamount of the securities is 51.8 billion yen (about 563 million dollars). Banks issued securities
constantly without a significant cyclical movement during the sample period. As for the assetsbacking the securities, housing loans occupy about 70 percent of total securities, followed by corporate loans and mortgage loans. The median interval between the issuance dates is 80.5 days,
so that a bank typically originates securities four or five times per year. To investigate the motives and consequences of issuing asset backed securities, we matched the security data with thefinancial statement of the originating bank. The source of financial statement is Nikkei NEEDS
Database, which covered through fiscal year 2005. We could identify 64 securitized products forwhich the originating bank’s financial statement was available. The median amount of securities
is approximately equivalent to 0.4 percent of the bank’s regulatory assets or 0.5 percent of its
total loans outstanding.
104.2. Results
As a (inverse) measure of leverage, we use the regulatory capital ratio in terms of the Baselcapital standards (Basel I).We calculate a counterfactual regulatory capital ratio that a bank would
show if it were not allowed to originate asset backed securities. Figure 5 depicts the counterfactual and actual regulatory risk-based capital ratios for two major Japanese banks. The counterfactual one is the capital ratio attained by the bank if it had not securitized assets. The figures arelinearly interpolated between the ends of fiscal years because the data is available only annually.
Figure 5 illustrates the role of securitization in maintaining the regulatory capital ratio. To investigate the relationship between the amounts of securities issued and bank capital, we estimate thefollowing equation:(4.1)

Securitiesi,t = β0 + β1 CapRatioi,t−1 + β1 log(Asseti,t−1 ) + εi,twhere Securitiesi,t denotes the amount of securities issued by bank i in fiscal year t. CapRatioi,t−1
and log(Asseti,t−1 ) denote the regulatory capital ratio and the logarithm of total assets of bank i
in fiscal year t − 1, respectively. If a less capitalized bank is more likely to issue a larger amountof securities, the coefficient on CapRatioi,t−1 is negative. Note that log(Asseti,t−1 ) is included
to allow for a fixed cost of issuing securities.
Table 3 presents the estimation results. The coefficient on CapRatioi,t−1 is negative and significant, suggesting that banks actively control leverage through securitization. That is, a poorlycapitalized bank tends to issue more securities. This finding is consistent with evidence from
U.K. (Pais [17]). The coefficient on log(Asseti,t−1 ) is also negative and significant, suggestingthat a smaller bank tends to concentrate securities issuance to save a fixed cost.
5. Empirical Analysis: Stock Market Reactions to Securitization
5.1. Methodology
We study the reaction of investors to the securitization of loans applyin the event study
methodology to the securitization data desribed in the preceding section. The theoretical analysis above suggests that the stock market response to securitization depends on the economic
environment. Suppose that the economy is normal but some banks may have a very good investment opportunities. Then, frequent and large-scaled securitization may serve as a good signal as
the comparison between the normal case (Case 1) and the bubble case (Case 1′ ) suggests. On
the other hand, if investors may worry about the possibility of a deteriorating asset quality atsome banks, frequent and small-sized securitization may serve as a bad signal as the comparison
between the normal case (Case 1) and the deteriorating asset case (Case 2) suggests. Existing
evidence is mixed. Lockwood et al. [14] use the U.S. data set and find negative reactions tobanks’ asset securitization. On the other hand, Martinez-Solano et al. [15] use a Spanish data set
and find positive stock market reactions to banks’ securitization.
In order to use the event-study method, we need to estimate the expected returns from holding
the stocks of banks if the securitization event did not occur, which are then used as the benchmark
for computing the abnormal returns. The following equation is estimated over a period whichruns between 40 days prior to the event up to 11 days prior to the event.
(5.1)

Rit = αi + βi Rmt + εit ,11

i = 1 · · · N,

it−1
where Pit
where Rmt is the returns on the market index in period t. We define Rit = PitP−P
it−1
is the stock price of bank i. Then daily abnormal returns (AR) during the event window, i.e. theperiod from 2 days prior to the event to 2 days after the event, can be computed as(5.2)

ARit = Rit − α̂i − β̂i Rmt .

Then we can aggregate across securities to obtain average abnormal return (AAR). The sample
aggregated abnormal returns is defined as
1 ∑ARit .
N i=1
N

(5.3)

AARt =

The associated average Cumulative Abnormal Returns (CAR) over the period (T1 , T2 ) is
(5.4)

CAR(T1 , T2 ) =T2∑AARt ,

t=T1

where generally (T1 , T2 ) ∈ event window. We set (T1 , T2 )=event window.
5.2. Data
We identify the event day as the day when the terms and conditions of the securities are
determined, which is earlier than the day when securities are actually issued. The market returnis the rate of changes in TOPIX. The data source of banks’ stock prices and TOPIX is Nikkei
Financial Quest. The number of events is 193.
5.3. Results
Table 4 shows that CAR is negative and significant. The securitization significantly lowers
CAR by 0.4 percent. Greenbaum and Thakor [9] points out that banks may securitize highquality assets and retain poor quality assets because banks can transfer their liabilities to deposit
insurance. Ambrose et al. [2] posits that banks retain riskier loans due to regulatory capital
incentives (capital arbitrage) or concerns for reputation. Our theoretical analysis comparing thenormal and deteriorating asset quality cases suggests that frequent asset securitization serves as asignal that banks’ investment opportunities are deteriorating and lowers the bank’s market value.
Negative responses to the announcement of securitization are consistent with those hypotheses.
6. Extension and Concluding Remark
We formulate banks’ asset securitization as their value-maximizing behavior to control theirasset size (or leverage). As a solution of stochastic optimization problem, we can derive when
and to what extent banks securitize assets. Our theoretical analysis yields some interesting results
including the high leverage during the boom (or bubble) period and the infrequent but largescaled securtization during the financial crisis period. Empirical evidences from a Japanese data
set are consistent with our theoretical analysis.
While our formulation of securitization is rather comprehensive as compared to previous literature, we could still take into consideration the feedback effects of securitization on banks’
asset quality. For example, the originate-to-distribute business model may result in banks’ loose
12screening of loan applicants and deteriorate loan quality (Keys et al. [13]). Banks may also
distinguish assets between those securitized and those held by themselves (Ambrose et al. [2]).
Take an example of the normal situation (Case 1). If the bank has access to the securitization
market and, by knowing that fact, it may have an incentive to initiate loans which are not necessarily satisfy the bank’s risk-return qualification. Suppose that µ = 0.05 and σ = 0.25 in ourCase 1 meets the lending criteria and that the bank starts lending money to assets with inferior
quality, µ = 0.05 and σ = 0.30, with a view to selling those assets. In this case, however, outside
investors may anticipate the low quality of the securitized asset and consequently the bank may
have to sell these assets at discount (say, λ = 0.8). See Figure 6. The upper and lower curves are
mere reproductions of Figure 1-(a). The curve in the middle (dotted line) is the value function
with inferior risk-return profile (µ = 0.05 and σ = 0.30). If the initial asset level is large enough,the value function has a higher value than v̂(x), the lower curve. Recall that this function v̂(x)corresponds to, when the initial asset level is x, the profit level if there is no asset securitization
done (with µ = 0.05 and σ = 0.25). This picture tells us that there exists an incentive that thebank may have when they have machinery to sell their asset.
vHxL
10

8

6

4

2

x
2

4

6

8

Figure 6: The moral hazard phenomenon quantified: The upper curve is the value function associatedwith Case 1 with µ = 0.05 and σ = 0.25. The lower curve is the value with no asset securitization with thesame risk-return profile. The middle (dotted line) is the value function associated with inferior asset quality
with µ = 0.05 and σ = 0.30 and with access to the asset sales market at some discount λ = 0.8. Note thatin the latter case, (a∗ , b∗ ) = (3.13, 8.20).

References[1] T. Adrian and H.S. Shin. Liquidity and leverage. Journal of Financial Intermediation, Forthcoming, 2010.
[2] B. W. Ambrose, M. Lacour-Little, and A. B. Sanders. Does regulatory capital arbitrage, reputation or asymmetric
information drive securitization. Journal of Financial Services Research, 28(1/2/3):113–133, 2005.
[3] A. W. A. Boot and A. V. Thakor. Security design. Journal of Finance, 48(4):1349–1378, 1993.
[4] A. N. Borodin and P. Salminen. Handbook of Brownian Motion - Facts and Formulae, Second Edition. Birkhäuser,
Basel, Boston, Berlin, 2002.
[5] M. K. Brunnermeier. Deciphering the liquidity and the credit crunch 2007-2008. Journal of Economic Perspectives,23(1):77–100, 2009.
[6] M. K. Brunnermeier and L. H. Pedersen. Market liquidity and funding liquidity. Review of Financial Studies,22(6):2201–2238, 2009.
[7] M. J. Flannery. Capital regulations and insured banks’ choice of individual loan default risk. Journal of Monetary
Economics, 24(2):232–258, 1989.
[8] M. J. Flannery. Debt maturity and the deadweight cost of leverage: Optimal financing banking firms. American
Economic Review, 84(1):320–331, 1994.

13

[9] S. I. Greenbaum and A. V. Thankor. Bank funding modes: Securitization versus deposits. Journal of Banking and
Finance, 11(3):379–401, 1987.
[10] T. F. Hellman, K. C. Murdock, and J. E. Stiglitz. Liberaliztion, moral hazard in banking, and prudential regulation:
Are capital requirements enough? American Economic Review, 90(1):147–165, 2000.
[11] D. M. Jaffee and K. T. Rosen. Mortgage securitization trends. Journal of Housing Research, 1(1):117–137, 1990.
[12] C. James. The use of loan sales and standby letters of credit by commercial banks. Journal of Monetary Economics,
22(3):395–422, 1988.
[13] B. J. Keys, T. Mukherjee, A. Seru, and V. Vig. Financial regulation and securitization: Evidence from subprimeloans. Journal of Monetary Economics, 56:700–720, 2009.
[14] L. J. Lockwood, R. C. Rutherford, and M. J. Herrera. Wealth effects of asset securitization. Journal of Banking
and Finance, 20:151–164, 1996.
[15] P. Martinez-Solano, J. Yague, and F. Lopez-Martinez. Asset securitization: Evidence on value of banking institutions. European Journal of Finance, 15:119–136, 2009.
[16] B. Øksendal and A. Sulem. Applied Stochastic Control of Jump Diffusions. Springer, New York, 2005.
[17] A. Pais. Why do depositors institutions use securitization? Journal of Banking Regulation, 10(3):202–214, 2009.
[18] W. Passmore. Can retail depositories fund mortgages profitably? Journal of Housing Research, 3(2):305–340,
1992.
[19] J. Paulsen. Optimal dividend payouts for diffusions with solvency constraints. Finance and Stochastics, 7:457–473,
2003.
[20] C. Pavel and D. Phillis. Why commercial banks sell loans: An empirical analysis. Federal Reserve Bank of Chicago
Economic Perspectives, 11(4), 1988.
[21] G. G. Pennacchi. Loan sales and the cost of bank capital. Journal of Finance, 43(2):375–396, 1988.
[22] R. G. Rajan. Insiders and outsiders: The choice between informed and arm’s length debt. Journal of Finance,
47(4):1367–1400, 1988.
[23] T. J. Riddiough. Optimal design and governance of asset-backed securities. Journal of Financial Intermediation,
6(2):121–152, 1997.
[24] S. Sharpe. Asymmetric information, bank lending and implicit contracts: A stylized model of customer relationships. Journal of Finance, 45:1069–1087, 1990.
[25] H. S. Shin. Reflections on northern rock: The bank run that heralded the global financial crisis. Journal of Economic
Perspectives, 23(1):101–119, 2009.
[26] A. Shleifer and R. W. Vishny. Liquidation values and debt capacity: A market equilibrium approach. Journal of
Finance, 47(4):1343–1366, 1992.
[27] C. I. Twinn. Asset-backed securitization in UK. Bank of England Quarterly Bulletin, May:134–143, 1994.

14

Table 2. Descriptive Statistics of Securitized Products Issued by Japanese Banks.
A. Amounts by year
Fiscal Year

No. of Products Median
Average
2004
23
351
619.1
2005
29
580
686.2
2006
31
652
909.9
2007
18
455
595.6
Total
101
518
723.4
Notes: 1. Fiscaly Year begins from April 1 to March 31 next year.
2. The sample period of FY 2007 ends on December 31, 2007.
B. Amounts by asset type
Asset TypeNo. of Products Median
Average
Housing loan
69
739
903.5
Corporate loan
9
116
257.5
Mortgage loan
6
322
402.2
Others
17
200
352.5
Total
101
518
723.4

Std. Dev.
683.6
515.8
823.6
577.1
673.8

(100 million yen)
Min
Max
13
2942
85
2005
116
3087
18
2343
13
3087

Std. Dev.
712.9
252.0
298.0
413.8
673.8

(100 million yen)
Min
Max
18
3087
50
750
84.7
870
12.81
1797
13
3087

C. Other Statistics
Statistics
Amounts / Regulatory Capital
Amounts/ Total loans
Intervals (days)

Std. Dev.
0.02149
0.017464187

Min0.00004
0.000031

No. of Products Median
64 0.00407
64 0.00535
84
80.5

Average
0.01203
0.01177572

Max
0.111800.08847
38469

Table 3. Motives for Securitization

Dependent variable=Securitized amounts / Loan
Equity/Asset-0.083 **(0.037)Log(Asset)-0.008 **(0.001)
Constant
0.155 **
(0.017)
No. of Obs.
64
Adj. R2
0.5282** denotes significant at the 5 percent level.
Numbers in the parentheses are standard errors

Table 4. Cumulative Abnormal Returns (CAR) to the Announcement of Securitization

RobustCAR
Std. Err.
-0.0041 0.0022

t
-1.87

P>t
0.063

15

Figure 5. Risk-based capital ratios with and without securitization for major banks

Mizuho Bank, FY 2004
10.25

Risk‐Based Capital Ratio

10.2
10.15
10.1
10.05
Without Securitization(Hypothetical)

10With Securitization (Actual)
9.95
9.9
2004.03.31

2004.06.29

2004.12.17

2004.12.22

2005.03.31

Year/Month/Date

Mitsubushi-Tokyo Bank, FY 2004
12.22

Risk‐Based Capital Ratio

12.2
12.18
12.16
12.14
Without Securitization(Hypothetical)

12.12

With Securitization (Actual)
12.1
2004.03.31

2004.07.30

2005.02.07

Year/Month/Day

16

2005.03.31