About Westpac
Westpac Banking Corporation—also known simply as Westpac—is a diversified financial services conglomerate based in Sydney, Australia. The product of a merger between the Bank of New South Wales and the Commercial Bank of Australia in 1982, Westpac is considered by many to be Australia’s first and oldest bank. The institution traces its roots all the way back to 1817, when the Bank of New South Wales first established its operations in Sydney.
Westpac’s current name is an amalgamation of “Western” and “Pacific”, a reflection of the company’s ambition to evolve into the pre-eminent bank in the region. In line with this vision, the company has made significant progress in major banking domains over the years. Within the financial sector, Westpac is best known for its efforts in promoting environmental and business sustainability. Over the past two decades, the bank has been recognized no less than 16 times in the annual ranking undertaken by the Dow Jones Sustainability Indices (DJSI) Review.
Across its global franchise, Westpac employs approximately 40,000 professionals that serve 14 million retail and institutional clients. Five main business divisions collectively form the Westpac franchise – Consumer Bank, Business Bank, BT Financial Group, Westpac Institutional Bank, and Westpac New Zealand.
The Consumer Bank division services the bank’s retail clients in Australia, covering the full spectrum of consumer banking products and services. The Business Bank division caters to the unique needs of the small and medium enterprise segment, providing these clients with specialized asset and equipment financing in conjunction with traditional cash management and transaction banking services.
The BT Financial Group is the wealth management arm of the group, catering to high net worth individuals. Westpac Institutional Bank focuses on servicing larger corporates, as well as sovereign and quasi-sovereign entities, offering a range of specialized services including transactional banking, margin lending, and equity and debt capital markets advisory. Westpac New Zealand, the bank’s fifth division, caters to individual and corporate clients based in New Zealand.Using credit default swaps to value Westpac bonds
We present a market-led valuation approach driven by credit default swap pricings, with the aim of selecting the most attractively priced Westpac bonds. Before we can get started, however, we need to make a brief detour into the world of credit default swaps and understand how they work.
A credit default swap or CDS is a derivative (an asset class that includes futures and contracts for difference) that allows the buyer to insure against the risk of default by a particular company. In this case, the company is known as the reference entity.
When a buyer purchases a CDS, he purchases the right to sell the bond at par value should the reference entity default on its bonds. Naturally, this protection comes at a cost, and the buyer of the credit default swap pays a fee (or premium) to the seller.
As long as the buyer owns or maintains a position in the CDS, he makes periodic premium payments to the seller until the end of the contract or until the reference entity defaults on its bonds. No payment is made by the seller unless the reference entity defaults on its obligations.
The pricings of bond and CDS are intrinsically linked. Imagine a situation where an investor holds bonds issued by Company A. Assume also that the investor is able to purchase CDSs on the company. Because the investor is able to eliminate default risk through the purchase of CDS contracts, the bond yields and CDS premiums have to be correlated in a certain manner, otherwise arbitrage opportunities would exist.
To understand the relationship between bond yields and CDS premiums, we need to first understand how a CDS is priced.
An investor who owns a T-year par yield bond issued by the reference entity and a CDS on the same reference entity has effectively eliminated the default risk associated with the bond. If the yield to maturity of the T-year bond is y and the CDS annual premium is s, the approximate net return would be y – s.
In fact, if we assume that there is no counterparty risk between the CDS buyer and seller, the investor effectively finds himself in a position where he earns a risk-free return. For this reason, CDS and bond prices rarely diverge to a great extent.
Based on the above reasoning, the difference between the bond yield and CDS spread (y – s) should be approximately equal to the risk-free rate of return, which is the T-year Treasury yield (we denote this as x). For the purpose of this article, we use US government bonds as our benchmark, however it is worth bearing in mind that there are other government securities that could equally be regarded as being risk-free.
Whilst it may be tempting to come to the conclusion that the CDS premium is simply the difference between the corporate bond yield and T-year Treasury rate, this relationship is only approximate at best. We also need to take into account, inter alia, accrued interest and eventual recovery of assets (assuming the company eventually defaults). In addition, we also need to consider the probability that a default occurs.Valuation of CDS
This section covers the derivation of the fair value premium of a standard vanilla CDS. Readers who do not wish to delve into the derivation of the model may skip this section and continue from The CDS Basis.
We define the following variables:
- T: Term of the credit default swap
- q(t): Risk-neutral default probability at time t (Note: Risk-neutral probabilities are real world probabilities adjusted for risk, they do not usually correspond to the actual default probabilities)
- R: Recovery rate (as a percentage) when a default occurs. If the bond carries a nominal value of $1000 and only $300 is recovered by the investor after a default occurs, the recovery rate is 0.3 or 30%.
- u(t): Present value of payments at the rate of $1 per year between time zero and time t
- e(t): Present value of an accrual payment at time t, where interest accrual only occurs between the last date of coupon payment and t
- v(t): Present value of $1 at time t
- s: CDS premium (per year)
- pi: Risk-neutral probability that the reference entity does not default (or a no credit event) during the life of the swap
- A(t): Accrued interest on the bond as a percent of its face value
The probability that the underlying bond will not experience a default between t=0 and t=T is
A CDS investor (the seller) continues to receive premiums until the underlying bond experiences a default, or until the CDS contract expires at time T. Given that there are two possible scenarios—default or no default—the present value of payments could fall into one of the following categories.
If a default occurs, the present value of CDS premiums is: s . [u(t) + e(t)]
If no default occurs, the present value of CDS premiums is: s . u(T)
The expected present value of the CDS premiums is the sum of the two terms, weighted by their respective probabilities:
The payoff from the CDS is the face value of the bond, less the amount recovered and the accrued interest on the recovered amount:
Consequently, we can write the present value of the expected payoff from the CDS as
The term q(t) appears because we need to take into account the probability of a default occurring.
Putting ourselves in the shoes of the credit default swap buyer, the value of the transaction is the difference between the present value of the expected payoff and the present value of the CDS premiums paid.
The first term is the expected payoff when a default occurs whilst the second and third terms reflect the expected present value of the CDS premium payments.
The fair value CDS premium may be determined by solving for s (the CDS premium payment per year) when the above expression is set to zero i.e. when the expected payoff equals the CDS premiums.
An idealized CDS
Admittedly, the equation is mathematically intractable for most people and is not readily adapted for day-to-day use. We now set out to find a more practical solution.
Consider the situation where an investor purchases both the credit default swap and the underlying bond, with both instruments expiring at t=T. In this idealized situation, we let the payoff when the bond defaults be [1+A*(t)](1-R) , where A*(t) is the accrued interest for the underlying par yield bond and R the recovery rate, in percentage terms.
Let s* = y – x where s* is the difference between the bond yield (y) and the risk-free Treasury rate (x). If the bond default occurs at time t, the CDS buyer has to make an accrual payment for the period between t and t* (the last payment date before time t). Bearing in mind that s* = y - x, the net payoff for the CDS is
Given the relationship of A*(t) = y(t-t*) governing the accrual of interest in the underlying bond, the above equation may be simplified accordingly.
We recall that the investor owns both the underlying bond and the CDS contract. Further to the default event, the bond’s market value is R[1+A*(t)] and the net value of the CDS and bond holdings is [1 +x(t-t*)]. This expression brings to mind the value of a risk-free Treasury bond at time t.
The logical conclusion is that the difference between the bond’s yield to maturity and the risk-free Treasury yield reflects the fair value CDS pricing, but only in the case of an idealized CDS. The CDS payoff of [1+A*(t)](1-R) only occurs in theory. In practice, the actual payoff is more closely represented by the expression 
Therefore, it is possible to derive the following equations:
Where a* is the average value of A* over t=[0,T]
Taking the ratio of s over s*, we obtain the desired result
The fair CDS premium, s, can thus be approximated if the bond’s yield to maturity (y), the Treasury risk-free rate (x), the recovery rate (R) and the bond coupon rate (a) are known. This methodology is known as the Hull-White approximation.
The CDS basis
In practice, relying on the above approximation to generate the fair value CDS premium (or bond price) is tenuous at best. This is because much depends on the assumed recovery ratio. Any such endeavor is necessarily fraught with subjectivity, and by implication, inaccuracy.
As a workaround, bond researchers and traders typically look at the CDS basis, which is the difference between the CDS premium and Z-spread.
The Z-spread is the premium of the underlying bond yield over Treasuries. While this is a gross simplification, further precision is not required for the purpose of this article.
The CDS basis may largely indicate whether a bond is fairly priced relative to its CDS contract. When the bond’s Z-spread is greater than the CDS premium, the CDS basis takes on a negative value, which could indicate that the bond is undervalued relative to the CDS contract.
Conversely, when the CDS premium exceeds the Z-spread by a significant amount, it could be an indication that the bond is overvalued.
Hence, to determine whether a bond is undervalued relative to its credit default swap, it is worthwhile to look for bonds trading at a negative basis. The more negative the basis, the more attractive the bond is relative to its CDS contract.
CDS and bond valuation: a case study on Westpac bonds
Applying the philosophy described in the earlier sections, we list below some attractively priced Westpac bonds (relative to their CDS) that investors may wish to consider.
Table 1: Westpac USD bonds
| Bond | Currency | Yield | CDS Basis (bps) |
|---|---|---|---|
| WSTP 5.005% 31Mar2031 | USD | 3.844% | -28.6 |
| WSTP 5.000% 24Mar2031 | USD | 3.842% | -28.5 |
| WSTP 5.210% 19Apr2031 | USD | 3.842% | -28.4 |
| Source: Bloomberg, iFAST compilations | |||
Table 2: Westpac AUD bonds
| Bond | Currency | Yield | CDS Basis (bps) |
|---|---|---|---|
| WSTP 3.10% 03Jun2021 | AUD | 2.256% | -38.8 |
| WSTP 4.125% 04Jun2026 | AUD | 2.998% | -32.1 |
| WSTP 4.04% 08Aug2033 | AUD | 3.410% | -24.1 |
| Source: Bloomberg, iFAST compilations | |||
References:
- Hull, John and White, Alan (2000), Valuing Credit Default Swaps I: No Counterpart Default Risk, Joseph L. Rotman School of Management, University of Toronto, Canada
- Hofberger, Bastian and Wagner, Niklas (2007), Pricing CDX Credit Default Swaps Using The Hull-White Model
- Wagner, N (2008), Credit Risk – Models, Derivatives and Management, Financial Mathematics Series Vol. 12 Chapman & Hall / CRC, Boca Raton, London, New York
Declaration:
For specific disclosure, at the time of publication of this report, IFPL (via its connected and associated entities) and the analyst who produced this report hold a NIL position in the abovementioned securities.