#### You've reached the end of your free preview.

Want to read all 7 pages?

**Unformatted text preview: **’—-—_” Example — Credit Wheelﬂwand Tranching
Increase Liquidity - Greenhaum and Thakor (1995:407) Investors cannot distinguish between a good bank (G) and a
bad bank (13) that each hold two loans that are identical.
The banks differ from each other in that although the loans
have the same dollar pay-off in a favourable or
unfavourable state, the probability that bank G’s loans will
have a favourable outcome is higher. Investors believe that
a bank will be either good or bad with equal probability- Bank G wishes to securitise its loans and to signal their quality. This can either i; done:
i) at a cost of 3" o of the value of the loans, or ii) by creating two tranches of bonds, or -
iii) by obtaining a credit enhancement Banks” Loon Portfolios: $250
Loan 1 <::
$125
Book G
$250
Loan 2 <:
$125
$250
Loan 1 <:
$125
Bank B
$250
Loan 2 :<:
$125 Case 1 — No Signalling, Tranching or Enhancement \ W“ A“ EKAQ
‘L k
NP me = 2 x prob Bank G x expect value Bank G loan R» J, 17‘" 9
+ 2 x prob Bank B x expect value Bank B loan 9"“
m 2 x Dix [0.8x$250 + 0.2 x3125] +2xi4x [0.5 x $250+ 0.5x$125]
= $420
However,
NPVBR = $450 Case 2 — Communicating at Cost ’1, G = 2xexpect vahJe BankG loan BK 64's 9’" ,9
= 2x [0.8x $250+ 0.2x$125] «ch The cost of communicating is 8% of value of loan portfolio. That is, 0.08 x $450 = $36. Thus NPVBankG = $450 '— $36 2 $414. L?Qj 3’0“!“ *0 h“? Case 3 ... 2-Tranche Structure plus Signalling 250 250 250 250
+ = +
0 ﬂ. 1- {1'
25 25 50 0
em; [3, chB Class A bond-holders will receive $250, and Class B
bond holders will receive $250 or the residual cashﬂow. Irrespective of whether the class A tranche came from
Bank G or Bank B, bondholders would receive $250
with certainty since the portfolios payoff at least $250 in
any state. Class A bonds are therefore worth:
NPVA=$250. If Bank G does not signal the quality of the Class B“§"““‘E“\“"‘M bonds to the market, the market would therefore value
them at: NPVE = NPVimstm- NPVA = $420 —~ 250 = $1'?'{]l.~>L ”‘3 04"" 1} Class B bonds however are worth $450 — $250 = $200. W8 if
‘4ch class ) This may be signalled to the market at a eost of 8% x $200 = $16. The total market vaiue of Bank G seeuritised in this manner is therefore: NPVBmkG = $250 + $200 - $16 Z$434 —— — Clays“ dogs cgmms Case 4 - Z-Tranche Structure plus Enhancement The credit enhancer will guarantee the credit quality of
Bank G’s Class B bends such that the market will value
them at $250, and charge a fee that will cover its
eXpected casts exactly. Examine cash ﬂows I116
125 335
0.15
25[} 375
are 125 25:] Meg-‘5 Bee‘mpossibltpso + 4mg , _ «- 0.2% o.
i) oth loans Pay $250 with a probability of [1.8 x 0.8 = 0.64 _
ii) One loan pays $250 and the other $125 with a
probability of2 x 0.3 x 0.2 = 0.32 —7 0 8»! o 2 8‘
iii) Both loans pay $125 with a probability of 0.2 x
0.2 = 0.04
In states (ii) and (iii) the enhancer will need to make up
$125 and $250 respectively to the Class B bondholders.
35‘6” C s\f\0 ﬂ‘u‘ 0“ M73) The expected cost 1s therefore: $125 :5: 0.32 + $250 x 0.04 = $50 The value of Bank G secoritised and enhanced in this
manner is therefore: NPVBankG = $250 + $250 - $50 ﬁ$450 ...

View
Full Document

- Spring '17
- class a, Bank B, Bank G