BUS326Lecture7example - Example Credit Wheelwand Tranching Increase Liquidity Greenhaum and Thakor(1995:407 Investors cannot distinguish between a good

BUS326Lecture7example - Example Credit Wheelwand Tranching...

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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 ...
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