HBS Case Study
First American Bank: Credit Default Swaps SUNWOO HWANG*
* KDI School of Public Policy and Management, Hoegi-ro 87, Dongdaemun-gu, Seoul, 130-868, Korea.
Introduction
Introduction
Charles Bank International (CBI) Protection Buyer
(A rump sum or) periodic payment
Payment
First American Bank (FAB) Protection Seller
3
The
st 1
Issue
Pricing the CDS spread
The fair value of the CDS spread is the number that sets the initial value of the CDS contract to zero. The 1st Issue Kittal had to determine the semi-annual fee to be charged to CBI for the default swap Solution
- Pricing a CDS
V = (PV Payoff) – s(PV Spread) = where s: spread : present value of a dollar paid at time t : marginal default rate from now to year t : survival probability until the end of year t f: recovery rate (see exhibit 14) r: risk-free interest rate (See Exhibit 8. Treasury STRIP yields)
5
Pricing the CDS spread (cont.)
But, how to compute the marginal probability of d(t)? Apply the Merton model and, in turn, compute the fair value of CDS spread using the marginal probability. In the Black-Scholes model, N(d2) is also the probability of exercising the call, or that the bond will not default. Conversely, 1 – N(d2) = N(-d2) is the risk-neutral probability of default. where
Parameters Computation
* N(.) is the cumulative distribution function for the standard normal distribution
S: Market value of the CEU’s asset = $6.8 + $4.1 = $10.9bn K: Strike price or the face value of the bond = FV(Current market value of the bond) : Time to maturity or duration = 4.2 years : Implied volatility = 49.9%
6
Pricing the CDS spread (cont.)
The fair value of the CDS spread is the number that sets the initial value of the CDS contract to zero. We compute it using the default probability and recovery rate.
Pricing the CDS spread Probability (%) Year t
Default. k(t)
Survival S(t)
Risk-free Int. Rate
Discount Factor P V(t)
Payoff Payments Expected k(t)x(1-f)
PV
Spread payments Expected sxS(t-1)
PV
0.5
0.0514
0.9486
1.47%
0.9927
0.0093
0.0092
0.0093
0.0092
1
0.0488
0.8998
2.14%
0.9788
0.0088
0.0086
0.0088
0.0086
1.5
0.0463
0.8536
2.67%
0.9607
0.0083
0.0080
0.0083
0.0080
2
0.0439
0.8097
3.20%
0.9380
0.0079
0.0074
0.0079
0.0074
Total
0.0332
0.0332
CDS spread = 92.52bp!! 7
The
nd 2
Issue
Solution to the Second Issue
To hedge its risk exposure to the credit event occurrence of CEU, FAB may issue a credit-linked note (CLN), which is structured security that combine a credit derivative with a regular bond. The 2nd Issue Kittal needed to ensure that First American Bank could hedge its end of the default swap by selling off the credit exposure in the form of another default swap or through another means. Solution
Credit Default Swap
Option
+
Regular Bond
Bond
=
Credit-Linked Note
Structured Product
Some of the principal amount are able to be used to cover the loss given default. 9
Accounting interpretation
The note is a liability on the bank’s balance sheet.
B/S (CapEx Unlimited)
B/S (Charles Bank International)
Asset
Liability
Asset
$100m
$100m
$100m
$50m
$50m
$50m
Cash Debit
B/S (First American Bank)
Liability
Asset
Liability
$50m
Credit-Risk Hedged Loan Credit
$50m
Debit
Credit
$50m
10
CLN Structure
CLNs are notes with an embedded short position in a CDS on CEU. In a CLN, the buyer of protection transfers credit risk to an investor via an intermediary bondissuing entity, which can be the buyer itself or a special purpose vehicle (SPV).
First American Bank (FAB)
R1 Contingent Payment
LIBOR + R1+R2 Contingent Payment
$ 50m
LIBOR+R2
$ 50m
Charles Bank International (CBI)
(Top-rated Asset in trust + CRS)
Investor 1 Investor 2
…
R’
SPV
$ 50m
CLN CapEx Unlimited (CEU)
OR
Investor N-1 Investor N
Top-rated Asset
Source: Financial Risk Manager Handbook, Jorion, P., Wiley, 5th edition, 2009.
11
CLN Structure (cont.)
The investor’s initial funds are placed in a top-rated investment that pays LIBOR plus a spread of R2. The FAB or SPV takes a short position in a credit default swap, for an additional annual receipt of R1. The annual payment to the investors is then LIBOR + R1 + R2. First American Bank (FAB)
R1 Contingent Payment
LIBOR + R1+R2 Contingent Payment
$ 50m
LIBOR+R2
$ 50m
Charles Bank International (CBI)
(Top-rated Asset in trust + CRS)
Investor 1 Investor 2
…
R’
SPV
$ 50m
CLN CapEx Unlimited (CEU)
OR
Investor N-1 Investor N
Top-rated Asset
Source: Financial Risk Manager Handbook, Jorion, P., Wiley, 5th edition, 2009.
12
Additional Remarks
Pros and Cons -
Investors receive a high coupon but will lose some of the principal if CEU defaults on its debt. This structure achieves its goal of reducing the bank’s exposure if CEU defaults. In this case, because the note is a liability of the bank, the investor is exposed to a default of either ECU or of the bank FAB. Attractiveness
-
-
Relative to a regular investment in, say, a note issued by the government of the United States, this structure may carry a higher yield if the CDS spread is greater than the bond yield spread. This structure may also be attractive to investors who are precluded from investing directly in derivatives.
13
