securitization and asset prices · 2014-09-04 · introduction securitization and financial markets...
TRANSCRIPT
Securitization and Asset Prices
Yunus Aksoy (Birkbeck, London) Henrique S. Basso (Banco de Espana)
IX Annual Seminar on Risk, Financial Stability and Banking
14th August 2014
Introduction
Jan−93 Jan−94 Feb−95 Feb−96 Mar−97 Apr−98 Apr−99 May−00 Jun−01 Jun−02 Jul−03 Aug−04 Aug−05 Sep−06 Oct−07 Oct−08 Nov−09 Dec−100
50
100
150
200
abs mbs all (in billion USD)
Figure: Securitization in the United States
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 2 / 43
Introduction
Jan−93 Jan−94 Feb−95 Feb−96 Mar−97 Apr−98 Apr−99 May−00 Jun−01 Jun−02 Jul−03 Aug−04 Aug−05 Sep−06 Oct−07 Oct−08 Nov−09 Dec−100
1
2
3
4
5
6
7
8
Figure: Ratio of ABS Securitization to Total Market Cap (Wilshire 5000)
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 3 / 43
Introduction
Jan−93 Jan−94 Feb−95 Feb−96 Mar−97 Apr−98 Apr−99 May−00 Jun−01 Jun−02 Jul−03 Aug−04 Aug−05 Sep−06 Oct−07 Oct−08 Nov−09 Dec−100
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Non−financial corporates Household Commercial Banks Shadow Banks and Sec Brokers
Figure: (Growth of Assets in Different Sectors)
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 4 / 43
Introduction
Securitization and Financial Markets
I Securitization volume has increase substantially.
I Increase in securitization and asset holdings of FI seem to correlate.
I These financial institutions hold more diverse portfolio of assets.
I Securitization through FI’s portfolio choice may affect asset classesother than credit.
I Closely related to work by Tobias Adrian and co-authors. By lookingat securitization activity and portfolio choice we attempt to shed lighton the mechanism.
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 5 / 43
Introduction
This paper
I Empirically: Assess the link between the volume of securitization andasset prices (Equity and Bonds)
Question 1 - Does securitization affect risk premia in various assetclasses?
I Theoretically: Look at the importance of financial intermediaries (in abroad sense) portfolio decisions to explain the link betweensecuritization and risk premia. Explore the importance of asymmetricinformation and banks as marginal price setters (see also He andKrishnamurthy (2013), Adrian, Etula, and Muir (2013)).
Question 2 - Can we provide a rationale/mechanism behind thiseffect?
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 6 / 43
Introduction
What We Find
I Empirically: volume of securitization impact risk premia (monthlyfrequency). Increase in securitization (particularly asset backedsecurities) lead to lower term spread, bond and equity premium.
I Theoretically: develop a model of securitization as a source of fundingto finance the bank’s purchase of diversified asset portfolio, providinga rationale for the empirical results. The main driver of the volume ofsecuritization is the degree asymmetric information.
I Mechanism: securitization relaxes cash and risk constraints faced bythe banks allowing expansion of bank’s balance sheet holding equityconstant (leverage).
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 7 / 43
Empirical Analysis
Benchmark Estimation
I Focus on dynamics of asset prices. Use Campbell, Chan, and Viceira(2003) VAR plus measure of securitization volume. The monthlymoving average specification is given by
zt = B(L)ut ,
z′t =[$i ′
t , x′2t
]with $i
t the securitization measure and i = {dabst ,dmbst}
I x2t = [spreadt , rpdt , xbrt , xrt , realr 3mt ].
I Identification - securitization volume is the month in which auction oftranches took place. The volume of asset involved is normally decidedin advanced to ensure ratings is done and SPV is properly set up.Hence, securitization can only respond to asset prices with a lag.
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 8 / 43
Empirical Analysis
Data
I Dealogic: US asset (dabs) and mortgage (dmbs) backed securities (inannualized monthly log differences).
Dealogic Sample
I Equity Premium (xr from Fama-French): excess return on the marketover the risk free rate (3 months T-Bill rate).
I Bond Premium (xbr) over 2,3,4 and 5 years horizons.(based onFama-Bliss Discount Bonds as reported by CRSP)
I Yield spreads (spread): difference between the five year governmentbond rate and 3 months T-Bill in percentages per annum.
I Monthly real price dividend ratio (rpd) that is calculated using thelog difference in real dividends and real stock prices (S&P CompositeStock Price Index)
I Real short term rates (realr 3m): 3 months T-Bill rate and the CPIinflation.
I Sample period: January 1993 - November 2007.
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 9 / 43
Empirical Analysis
Term Spread
2 4 6 8 10−1.5
−1
−0.5
0
0.5
1
1.5x 10
−3 Bond Premium
2 4 6 8 10
−2
−1
0
1
2
x 10−5 Equity Premium
2 4 6 8 10−1.5
−1
−0.5
0
0.5
1
1.5x 10
−4
2 4 6 8 10−1.5
−1
−0.5
0
0.5
1
1.5x 10
−3
2 4 6 8 10
−2
−1
0
1
2
x 10−5
2 4 6 8 10−1.5
−1
−0.5
0
0.5
1
1.5x 10
−4
ABSShock
MBSShock
Figure: Benchmark: ABS and MBS
Extra
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 10 / 43
Empirical Analysis
Introducing ControlsNew vector of variables - z′t =
[$i ′
t , xa2t , xb′2t
]with
xb2t = [spreadt , rpdt , xbrt , xrt , realr 3mt ]
I Market volatility measure (vix): a measure for risk; use the CBOEVolatility Index (S&P 500 market index option prices) as provided byBloomberg.
I Changes in expected Earnings per Share (deps): the twelve monthsforward weighted average expected earnings per share based on S&P500 composite (I/B/E/S).
I Expected Future Economic Conditions (E5Y ): an index that isderived from a five years forward looking question on confidence fromthe Michigan Index of Consumer Expectations
I Credit Spread index (GZ ) - Gilchrist and Zakrajsek (2012): controllingfor the evolution of credit supply/ credit market conditions.
I Conditional Heteroscedastic Discount Factor (CPFactor) (Cochraneand Piazzesi (2005))
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 11 / 43
Empirical Analysis
Figure: Augmented Models - Results
0 2 4 6 8 10 12 14 16 18 20−0.1
−0.05
0
0.05
0.1
Horizon
Per
cent
Term Spread
benchmark vix e5y deps gz cp
0 2 4 6 8 10 12 14 16 18 20−3
−2
−1
0x 10
−3
Horizon
Per
cent
Bond Excess Return
0 2 4 6 8 10 12 14 16 18 20−0.01
−0.005
0
0.005
0.01
Horizon
Per
cent
Equity Excess Return
(a) Impulse Response to Asset-backed Securities
Other
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 12 / 43
Theoretical Framework
Model Overview
We build a partial equilibrium model focusing on two key decisions of abank
1. Securitization decision (design and sale of synthetic securities F ,whose value is a function of basket of credit assets [Yi ]
ni=1) following
DeMarzo and Duffie (1999) closely. Security Design: Risky debt -F ∗(Y ) = min(d ,Y n).
2. Portfolio decision - which assets (credit basket, equity, bonds) to holdand external funding to use.
See Timeline
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 13 / 43
Theoretical Framework
Securitization Volume (Sale) in a nutshell
I Main issue - asymmetric information. Banks know more about [Yi ]ni=1
and thus F than final investor. Yi = Xi + Zi , Xi ∈ [X0,X1] isbank/SPV information, Zi is the remaining risk the bank faces.
I If SPV tries to sell all synthetic assets F created ⇒ investor concludelemons, pay low price
I Thus, if information is good, SPV is not willing to sell everything atsuch low price, hence decide to keep some tranches in balance sheet
I As SPV is willing to hold stuff ⇒ signal to investor that assets aregood, investor bid higher price
I Equilibrium fully revealing ⇒ banks/SPV hold exact amount (1-q)such that investors bid true value of asset based on information.
Detail Securitization
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 14 / 43
Theoretical Framework
Portfolio Decision in a nutshell
I Banks will select a portfolio of assets (Qy ,QB ,QE ,Υ) to maximizeexpected returns (profit) s.t.
I (i) a cash constraintI (ii) a risk constraint (akin to Value-at-risk)
I Variance Covariance matrix given. As the bank increases Qy creditmark-up decreases. As the bank increases QB/ QE price ofbond/equity increases. As the bank increases Υ, cost of fundingincreases.
Detail Portfolio Problem
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 15 / 43
Theoretical Framework
Figure: Model with and without Securitization - Mechanism
Assets0 Assets0Assets0 Υ ΥΥ
Γ0 Γ0Γ0
qFqFCash Assets1
1
(a) Balance Sheet ExpansionPay-off Credit
−Xn
Xn
Y nY nY n
Pay-out Synthetic Sec. (F )
PF
(PF−d)
dd
Combined Portfolio Pay-off
(PF−Xn)
1
(b) Risk Profile
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 16 / 43
Theoretical Framework
Figure: Benchmark Model
0 0.05 0.1 0.15 0.2−0.4
−0.39
−0.38
−0.37
−0.36
−0.35
−0.34
−0.33Bond Premium − %Change
Information Asymmetry0 0.05 0.1 0.15 0.2
−0.36
−0.35
−0.34
−0.33
−0.32
−0.31
−0.3Equity Premium − %Change
Information Asymmetry
Effect of Allowing Banks to Securitize Credit Assets (Model with Sec vs Model No Sec)
0 0.05 0.1 0.15 0.2−0.014
−0.013
−0.012
−0.011
−0.01
−0.009
−0.008Credit Spread − %Change
Information Asymmetry
0 0.05 0.1 0.15 0.20.94
0.95
0.96
0.97
0.98
0.99
1Share of Securitized Asset Sold − q
Information Asymmetry0 0.05 0.1 0.15 0.2
0.36
0.365
0.37
0.375
0.38
0.385
0.39
0.395
0.4Balance Sheet − %Change
Information Asymmetry0 0.05 0.1 0.15 0.2
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45Ratio of Funding Sources to Total BalanceSheet
Information Asymmetry
ϒ − No Sec ϒ − with Sec Vol of Sec
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 17 / 43
Theoretical Framework
Figure: Model with and without Securitization - Mechanism
Assets0 Assets0Assets0 Υ ΥΥ
Γ0 Γ0Γ0
qFqFCash Assets1
1
(a) Balance Sheet ExpansionPay-off Credit
−Xn
Xn
Y nY nY n
Pay-out Synthetic Sec. (F )
PF
(PF−d)
dd
Combined Portfolio Pay-off
(PF−Xn)
1
(b) Risk Profile
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 18 / 43
Theoretical Framework
Figure: Higher Face Value of Synthetic Security
0 0.05 0.1 0.15 0.2−0.55
−0.5
−0.45
−0.4
−0.35
−0.3
−0.25
−0.2
−0.15Bond Premium − %Change
Information Asymmetry0 0.05 0.1 0.15 0.2
−0.65
−0.6
−0.55
−0.5
−0.45
−0.4
−0.35
−0.3
−0.25
−0.2
Equity Premium − %Change
Information Asymmetry
0 0.05 0.1 0.15 0.20.2
0.4
0.6
0.8
1
1.2Balance Sheet − %Change
Information Asymmetry0 0.05 0.1 0.15 0.2
0.4
0.5
0.6
0.7
0.8
0.9
1Share of Securitized Asset Sold − q
Information Asymmetry
Higher Face Value of Synthetic Security (d) Benchmark
Go to Sensitivity Analysis
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 19 / 43
Conclusion
Discussion
I Pooling and tranching of assets held in the balance sheet of financialcompanies not only creates liquidity, alleviating their cash constraint,but also relaxes their risk constraint. That allow banks to expandasset holdings, depressing risk premia.
I As a result, although the payoff outlook of assets has remain thesame, as do their risk profile, the compensation to undertaking risk inthe economy decreases. As Rajan (2005) pointed out risks are stillthere.
I Securitization volumes are related to degree of informationasymmetry. Thus, our results indicate the key variables to understandthe link between financial intermediation and asset prices is thedegree of information asymmetry.
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 20 / 43
Conclusion
Discussion II
I Our results highlight the importance of looking at financialintermediation, as well as final investors, to increase ourunderstanding of the dynamic movements in asset prices. (He andKrishnamurthy (2013) and Adrian, Etula, and Muir (2013) point toimportance of financial institutions).
I In 2005/2006 commentators pointed out the yield curve conundrum.Although short-term rates increased substantially, long-term ratesremained unchanged (fall in term premium). General view - somecombination of diminished macroeconomic and financial marketvolatility.
I Our work provide a different channel. The period of 2003 - 2006 weobserved a sharp and consistent increase in the volume of ABStransacted in the US. That would have allow banks to increase theirasset allocations, leading to a downward pressure on risk premia.
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 21 / 43
Conclusion
Figure: ABS issuance versus Bond Premium
−0.02
−0.01
0
0.01
0.02
0.03Bo
nd P
rem
ium
Jan93 Jan94 Feb95 Feb96 Mar97 Apr98 Apr99 May00 Jun01 Jun02 Jul03 Aug04 Aug05 Sep06 Oct07 Oct08 Nov09 Dec100
20
40
60
80
100
abs
Bond Premium abs (in billion USD)
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 22 / 43
Conclusion
Going Forward
I Looking at retention, price discount and tranching strategies (settingd), can we link these to volume?
I Extend the model to general equilibrium, embedding into DSGE.
I Study information acquisition process to understand better theunderlying mechanism
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 22 / 43
Appendix
Pricing Date Deal Total
Value $ (Face)
Issuer Collateral Type
Maturity Date
Years to Maturity
Tranche Value $ (Face)
Bank Parent Bookrunner Parent
Deal Bank Parent Issue Type Coupon Yield to
Maturity
22-May-90 1,250,000,000
Standard Credit Card Master Trust Series 1990-5
Credit-card receivables 10-Jun-95 5.01389 1,250,000,000
JPMorgan; UBS; Goldman Sachs; Deutsche Bank; BNP Paribas; Nomura; RBS; Daiwa Securities; Credit Suisse; Citi; Bank of America Merrill Lynch Citi
JPMorgan; UBS; Goldman Sachs; Deutsche Bank; BNP Paribas; Nomura; RBS; Daiwa Securities; Credit Suisse; Citi; Bank of America Merrill Lynch Fixed rate 9.375 9.686
22-May-90 155,000,000
Standard Credit Card Master Trust Series 1990-5
Credit-card receivables 10-Jun-95 5.01389 155,000,000 Citi Citi Citi Fixed rate 9.625 10.000
19-Jun-90 1,000,000,000
First Chicago Master Trust II Series 1990 - A
Credit-card receivables 15-Jun-95 4.96389 1,000,000,000
Mizuho; JPMorgan; UBS; Goldman Sachs; Deutsche Bank; Nomura; RBS; SG Corporate & Investment Banking; Credit Suisse; Citi Credit Suisse
Mizuho; JPMorgan; UBS; Goldman Sachs; Deutsche Bank; Nomura; RBS; SG Corporate & Investment Banking; Credit Suisse; Citi Fixed rate 9.25 9.485
20-Jun-90 155,000,000
Standard Credit Card Master Trust 1 Series 1990-6
Credit-card receivables 10-Jul-97 7.03333 155,000,000
Credit Suisse; Citi Credit Suisse
Credit Suisse; Citi Fixed rate 9.625 9.994
20-Jun-90 1,095,000,000
Standard Credit Card Master Trust 1 Series 1990-6
Credit-card receivables 10-Jul-97 7.03333 1,095,000,000
Mizuho; JPMorgan; UBS; Goldman Sachs; BNP Paribas; Nomura; ING; Daiwa Securities; Credit Suisse; Citi; Credit Suisse
Mizuho; JPMorgan; UBS; Goldman Sachs; BNP Paribas; Nomura; ING; Daiwa Securities; Credit Suisse; Citi; Fixed rate 9.375 9.679
(a) Dealogic Sample
Back
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 23 / 43
Appendix
Term Spread
2 4 6 8 10−5
0
5x 10
−3 Bond Premium
2 4 6 8 10−5
0
5x 10
−5 Equity Premium
2 4 6 8 10−5
0
5x 10
−3
2 4 6 8 10−5
0
5x 10
−3
2 4 6 8 10−5
0
5x 10
−5
2 4 6 8 10−5
0
5x 10
−3
2 4 6 8 10−5
0
5x 10
−3
2 4 6 8 10−5
0
5x 10
−5
2 4 6 8 10−5
0
5x 10
−3
ABS Shock
Brokers Shock
Shadow Shock
Figure: Quaterly VAR - ABS vs Asset Growth
Back
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 24 / 43
Appendix
What is left?
I Potential Explanation - Securitization creates a new contingent assethelping economy to get close to completing the market. Thatdecreases the risk premia in the economy. (see for instance Allen andGale (1994))
I Problem: if that were to be the case we should see together with thetrend in securitization, which include different original assets, to beaccompanied by a trend on premia. We do not see that.
I Also Simsek (2013) argues that under belief disagreement, new assetsmight improve insurance but also open opportunities for more risktaking (speculative trading).
I Hence, we try to look at the drivers of securitization and portfoliochoice of financial intermediaries to try and provide a rationale for ourempirical results.
Back
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 25 / 43
Appendix
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
1993
M01
19
93M
06
1993
M11
19
94M
04
1994
M09
19
95M
02
1995
M07
19
95M
12
1996
M05
19
96M
10
1997
M03
19
97M
08
1998
M01
19
98M
06
1998
M11
19
99M
04
1999
M09
20
00M
02
2000
M07
20
00M
12
2001
M05
20
01M
10
2002
M03
20
02M
08
2003
M01
20
03M
06
2003
M11
20
04M
04
2004
M09
20
05M
02
2005
M07
20
05M
12
2006
M05
20
06M
10
2007
M03
20
07M
08
2008
M01
20
08M
06
2008
M11
20
09M
04
2009
M09
20
10M
02
2010
M07
20
10M
12
2011
M05
20
11M
10
2012
M03
20
12M
08
Equity Premium (Fama-French)
Figure: Equity Premium
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 26 / 43
Appendix
Figure: Model Timeline
Bank sets up the SPV
Selects the design of
synthetic security (F )
given preference
for cash δ.
Payoff Information (X)
revealed. Bank selects
assets {[Yi]ni=1, B,E},
funding Υ. Security F
is created at SPV.
Assets are transacted.
SPV sells a fraction q of
synthetic securities, and
transfers cash to Bank.
Assets pay-out
Bank’s retained earnings
and preference for
cash are determined.
1 2 3 4
1
Back
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 27 / 43
Appendix
Theoretical Framework - Key features I
I Payoff of credit asset is given by Yi = Xi + Zi .
I Xi ∈ [X0,X1] is the bank’s private information about credit payoff.Zi = εi + η is the remaining risk the bank faces.
I A fourth asset, denoted F , whose payoff depend on Yi will be createdby the bank (SPV).
I Denote f0 = E [F | X = X0] and f = E [F | X ]
I Information asymmetry: final investor do not know X , but know thatit is ∈ [X0,X1].
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 28 / 43
Appendix
1) Securitization Decision
I We solve it backwards, first looking at the creation of SPV andissuance and then looking at the optimal design of F .
a) Issuance and marketing of synthetic securities F
b) Optimal Design of F
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 29 / 43
Appendix
a) Issuance Decision I
I Main issue - asymmetric information. Banks know more than finalinvestor.
I If bank tries to sell all assets created ⇒ investor conclude lemons, paylow price
I Thus, if information is good, bank is not willing to sell everything atsuch low price, hence decide to keep some F in balance sheet.
I As bank is willing to hold stuff ⇒ signal to investor that assets aregood, investor bid higher price
I Equilibrium fully revealing ⇒ banks hold exact amount such thatinvestors bid true value of asset based on information.
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 30 / 43
Appendix
1) a) Issuance Decision II
I Thus, the equilibrium in the market of F is essentially the result of asignalling game between the issuer and buyer of the security. Thegame ensures that true value of the security is revealed to buyers,based on the share of F held by the bank (SPV).
I The unique separating equilibrium is
q = (f /f0)−1/(1−δ) and PF = f0(q)δ−1 = f (1)
I The ratio f0/f implicitly determines the information advantage of thebank on the valuation of security f . Greater is this advantage, lowerq, the proportion of F sold to final investors.
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 31 / 43
Appendix
1) b) Optimal Design of F
DeMarzo and Duffie (1999) and DeMarzo (2005) show that optimalmonotone security design is a standard debt contract, thusF ∗(Y ) = min(d ,Y n) for a constant d .
I Assume that the bank/SPV would like to maximize the volume ofsecuritized assets (cash preference)
I but in order to close the informational gap in a fully revealingequilibrium, it is forced to retain some synthetic assets in the portfoliowhen the signal is good (higher information asymmetry).
I Thus, it is optimal for the SPV to select a security that is as payoffinsensitive as possible for the range of signals where asymmetry is atits highest, thus making the retention a more powerful signal.
I Standard debt has this property since f does not change significantlyas X increases in the range X > d .
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 32 / 43
Appendix
Figure: Choice of d (Synthetic Security Payoff for the Final Investor and Optimald)
X0
X0 X1X1 dd
Y nY n
d−PF (d)d−PF (d)
−PF (d)
AB
Pay-off of Synthetic Security Pay-off of Synthetic Security
−PF (d)
1
Back
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 33 / 43
Appendix
2) Portfolio Decision I
I Banks select the portfolio composition (Qy ,QB ,QE ,Υ) to maximizethe expected profits E [ΠB | X nΓ0]
ΠB |X n = Qy (Y n−E [Y n|X n])+µ(X n,Qy )Qy
+QB(VB−PB)+QE (VE−PE )−qQy (F−PF )−RF Υ (2)
I subject to a cash constraint
QyE [Y n | X n] + QBPB + QEPE 6 Γ0 + qQyPF + Υ (3)
I and a risk constraintσΠB 6 χΓ0. (4)
I due to the diversification of idiosyncratic risks (εi ), the only source ofrisk of the basket of credit comes from the aggregate uncertainty (η).
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 34 / 43
Appendix
2) Portfolio Decision II
Market Structure
I The cost of bank borrowing is given by RF = R + κ(Υ/Γ0).
I Bank mark-up on loans µ(X n,Qy ) = µ+ µ1(X n − X0)/X0 − µ2Qy .
I Price of Equity and Bonds
PB = αB + βBQB (5)
PE = αE + βEQE . (6)
I The standard deviation of the portfolio returns is given by
σΠB |X n =
(Q2
yσ2+Q2
Bσ2B+Q2
Eσ2E+2QyQBσyB+2QyQEσyE+
2QBQEσEB−2qQ2yσFY−2qQyQBσFB−2qQyQEσFE+q2Q2
yσ2F
)1/2
.
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 35 / 43
Appendix
Parametrization
Table: Parameter Values - Benchmark Model
Return Variance Bank$E 0.03+1/0.95 σY 0.1 δ 0.983$B 1/0.95 σB 0.02 Γ0 5αB $B - 0.02 σE 0.06 χ 0.07αE $B +0.01 ρEY -0.49βB
1Γ0
0.025 ρEB -0.57
βE1
Γ00.025 ρBY -0.4
R 0.01κ 1
Γ00.05 Information
µ1 0.01 X0 1.02µ2
1Γ0
0.005 m 0.2
µ 0.04 X1 X0 + m
Back
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 36 / 43
Appendix
Sensitivity Analysis
Changing key parameter values used in the benchmark model.
I increase the standard deviation of all assets (σ, σB , σE ).
I decrease the price sensitivity of bank demand for credit, bonds, equityand bank borrowing, altering respectively (µ2, βB , βE and κ)
I alter the correlation structure of asset payoffs
1. reverse the sign of all correlation, so assets are all positively correlated,2. reverse only the credit and equity correlation, leaving government
bonds to be negatively correlated to equity and credit.
I decrease the risk aversion of banks (higher χ).
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 37 / 43
Appendix
Figure: High Variance of Assets
0 0.05 0.1 0.15 0.2−0.4
−0.38
−0.36
−0.34
−0.32
−0.3
−0.28Bond Premium − %Change
Information Asymmetry0 0.05 0.1 0.15 0.2
−0.36
−0.34
−0.32
−0.3
−0.28
−0.26
−0.24
−0.22Equity Premium − %Change
Information Asymmetry
0 0.05 0.1 0.15 0.20.26
0.28
0.3
0.32
0.34
0.36
0.38
0.4Balance Sheet − %Change
Information Asymmetry0 0.05 0.1 0.15 0.2
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1Share of Securitized Asset Sold − q
Information Asymmetry
High Variance of Assets Benchmark
BackAksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 38 / 43
Appendix
Figure: Low Price Sensitivity of Demand
0 0.05 0.1 0.15 0.2−0.4
−0.38
−0.36
−0.34
−0.32
−0.3
−0.28
−0.26
−0.24Bond Premium − %Change
Information Asymmetry0 0.05 0.1 0.15 0.2
−0.36
−0.34
−0.32
−0.3
−0.28
−0.26
−0.24
−0.22
−0.2Equity Premium − %Change
Information Asymmetry
0 0.05 0.1 0.15 0.20.33
0.34
0.35
0.36
0.37
0.38
0.39
0.4Balance Sheet − %Change
Information Asymmetry0 0.05 0.1 0.15 0.2
0.94
0.95
0.96
0.97
0.98
0.99
1Share of Securitized Asset Sold − q
Information Asymmetry
Asset Prices less Sensitive to Bank Demand Benchmark
Back
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 39 / 43
Appendix
Figure: Correlation Structure
0 0.05 0.1 0.15 0.2−0.8
−0.7
−0.6
−0.5
−0.4
−0.3Bond Premium − %Change
0 0.05 0.1 0.15 0.2−0.4
−0.35
−0.3
−0.25
−0.2
−0.15
−0.1
−0.05Equity Premium − %Change
0 0.05 0.1 0.15 0.20.3
0.32
0.34
0.36
0.38
0.4
0.42
0.44Balance Sheet − %Change
Information Asymmetry
Reverse Sign of All Correlations Benchmark Reverse the Sign of Credit−Equity Correlations
0 0.05 0.1 0.15 0.20.94
0.95
0.96
0.97
0.98
0.99
1Share of Securitized Asset Sold − q
Information Asymmetry
BackAksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 40 / 43
Appendix
Figure: Lower Bank Risk Aversion
0 0.05 0.1 0.15 0.2−0.42
−0.4
−0.38
−0.36
−0.34
−0.32Bond Premium − %Change
Information Asymmetry0 0.05 0.1 0.15 0.2
−0.42
−0.4
−0.38
−0.36
−0.34
−0.32
−0.3Equity Premium − %Change
Information Asymmetry
0 0.05 0.1 0.15 0.20.36
0.38
0.4
0.42
0.44
0.46Balance Sheet − %Change
Information Asymmetry0 0.05 0.1 0.15 0.2
0.94
0.95
0.96
0.97
0.98
0.99
1Share of Securitized Asset Sold − q
Information Asymmetry
Laxer Bank Risk Constraint Benchmark
Back
Aksoy and Basso (IX Annual Seminar on Risk, Financial Stability and Banking) 14th August 2014 41 / 43
Appendix
References I
Adrian, T., E. Etula, and T. Muir (2013): “FinancialIntermediaries and the Cross-Section of Stock Returns,” Journal ofFinance, forthcoming.
Allen, F., and D. Gale (1994): Financial Innovation and RiskSharing. MIT Press, Cambridge, MA.
Campbell, J. Y., Y. L. Chan, and L. M. Viceira (2003): “Amultivariate model of strategic asset allocation,” Journal of FinancialEconomics, 67(1), 41–80.
Cochrane, J. H., and M. Piazzesi (2005): “Bond Risk Premia,”American Economic Review, 95(1), 138–160.
DeMarzo, P., and D. Duffie (1999): “A Liquidity-Based Model ofSecurity Design,” Econometrica, 67(1), 65–100.
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Appendix
References II
DeMarzo, P. M. (2005): “The Pooling and Tranching of Securities: AModel of Informed Intermediation,” Review of Financial Studies, 18(1),1–35.
Gilchrist, S., and E. Zakrajsek (2012): “Credit Spreads andBusiness Cycle Fluctuations,” American Economic Review, 102(4),1692–1720.
He, Z., and A. Krishnamurthy (2013): “Intermediary Asset Pricing,”American Economic Review, 103(2), 732–70.
Rajan, R. G. (2005): “Has financial development made the worldriskier?,” Proceedings, (Aug), 313–369.
Simsek, A. (2013): “Speculation and Risk Sharing with New FinancialAssets,” The Quarterly Journal of Economics, 128(3), 1365–1396.
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