Swap spreads maturity

Making comparison between bonds could be difficult and several aspects must be considered. One of these is the bond s maturity. For instance, we know that the yield for a bond that matures in 10 years is not the same compared to the one that matures in 30 years. Therefore, it is important to have a reference yield curve and smooth that for comparison purposes. However, there are other features that affect the bond s comparison such as coupon size and structure, liquidity, embedded options and others. These other features increase the curve fitting and the bond s comparison analysis. In this case, the swap curve represents an objective tool to understand the richness and cheapness in bond market. According to O Kane and Sen (2005), the asset-swap spread is calculated as the difference between the bond s value on the par swap curve and the bond s market value, divided by the sensitivity of 1 bp over the par swap. 

For the calculation, we cancel out the principal payments of par at maturity. We assume that cash flows are annual and take place on the same coupon dates. The breakeven asset-swap spread A is calculated by setting the present value of all cash flows equal to 0. From the perspective of the asset swap seller, the present value is ... 

Figure 8.2 shows the Bloomberg YAS page for Tesco bond SVi% 2019, as at October 9, 2014. The bond has a price of 109.345 and yield to maturity of 3.46%. On the date, the yield spread over a government bond benchmark UK 41 % Treasury 2019 is 200 basis points. The G-spread over an interpolated government bond is 181.5 basis points. Conventionally, the difference between these two spreads is narrow. We see also that the asset-swap spread is 173.6 basis points and Z-spread is 166.3 basis points. 

As we have seen, interest rate swaps are valued using no-arbitrage relationships relative to instruments (funding or investment vehicles) that produce the same cash flows under the same circumstances. Earlier we provided two interpretations of a swap (1) a package of futures/forward contracts and (2) a package of cash market instruments. The swap spread is defined as the difference between the swap s fixed rate and the rate on the Euro Benchmark Yield curve whose maturity matches the swap s tenor. 

Exhibit 19.11 presents Bloomberg s World Swap screen which presents swap spreads for various countries around the world for June 27, 2003. In this screen, the tenor of the swaps in this screen is five years as can be seen in the box labeled Maturity in the upper left-hand corner. Among the other choices available, a user can choose to display swap rates rather than spreads. Exhibit 19.12 is a time series plot obtained from Bloomberg for daily values of the 5-year euro swap spread (in basis points) for the period June 27, 2002 to June 27, 2003. 

Naturally, this presupposes the reference rate used for the floating-rate cash flows is EURIBOR. Furthermore, part of swap spread is attributable simply to the fact that EURIBOR for a given maturity is higher than the rate on a comparable maturity benchmark government. 

Put simply, the Z-spread is the basis point spread that would need to be added to the implied spot yield curve such that the discounted cash flows of the bond are equal to its present value (its current market price). Each bond cash flow is discounted by the relevant spot rate for its maturity term. How does this differ from the conventional asset-swap spread Essentially, in its use of zero-coupon rates when assigning a value to a bond. Each cash flow is discounted using its own particular zero-coupon rate. The bond s price at any time can be taken to be the market s value... 

Craisider a hypothetical situation. Assume that an option-free bond paying a semi-annual coupon 5.5% on par value, with a maturity of 5 years and discount rate of 8.04% (EUR 5-year swap rate of 1.04% plus credit spread of 700 basis points). Therefore, the valuation of a conventional bond is performed as follows (Figure 9.4). 

The minimum interest rate that an investor should require is the yield available in the marketplace on a default-free cash flow. For bonds whose cash flows are denominated in euros, yields on European government securities serve as benchmarks for default-free interest rates. In some European countries, the swap curve serves as a benchmark for pricing spread product (e.g., corporate bonds). For now, we can think of the minimum interest rate that investors require as the yield on a comparable maturity benchmark security. 

The terms spread or credit spread refer to the yield differential, usually expressed in basis points, between a corporate bond and an equivalent maturity government security or point on the government curve. It can also be expressed as a spread over the swap curve. In the former case, we refer to the fixed-rate spread. In the latter, we use the term spread over EURIBOR, or over the swap curve. 

In the pre-euro days, traders were usually organized by currency. Now, sector specialization is the rule. For most issues, buy or sell indications are initially indicated on a spread basis. The spread can be either over the swap curve or over a specified government benchmark. A corporate bond issue keeps the same benchmark for its entire life they roll down the curve together. This is in contrast to the United States, where the convention is to quote a corporate bond s spread over the nearest on-the-run (most recently issued) 2-, 5-, 10-, or 30-year maturity Treasury bond. 

The fixed rate is some spread above the benchmark yield curve with the same term to maturity as the swap. In our illustration, suppose that the 10-year benchmark yield is 8.35%. Then the offer price that the dealer would quote to the fixed-rate payer is the 10-year benchmark rate plus 50 basis points versus receiving EURIBOR flat. For the floating-rate payer, the bid price quoted would be EURIBOR flat versus the 10-year benchmark rate plus 40 basis points. The dealer would quote such a swap as 40-50, meaning that the dealer is willing to enter into a swap to receive EURIBOR and pay a fixed rate equal to the 10-year benchmark rate plus 40 basis points and it would be willing to enter into a swap to pay EURIBOR and receive a fixed rate equal to the 10-year benchmark rate plus 50 basis points. 

EXHIBtT 19.11 Swap Rates and Spreads for Various Maturities... 

The credit curves (or default swap curves) reflect the term structure of spreads by maturity (or tenor) in the credit default swap markets. The shape of the credit curves are influenced by the demand and supply for credit protection in the credit default swaps market and reflect the credit quality of the reference entities (both specific and systematic risk). The changing levels of credit curves provide traders and arbitragers with the opportunity to measure relative value and establish credit positions. 

After assessing a bond with the help of credit analysis, the question arises to what extent the market price of this bond corresponds with the investor s judgement. The market price should compensate the investor for all risks connected with holding the bond. This market price (spread) is often referred to as the return differential between the analysed bond and the benchmark. Frequently, government bonds or the swap rate with matching maturities are used as benchmarks. Another standard reference are bonds of other issuers that are active in the same business field. Since one debt instrument is assessed relative to another debt instrument, this analysis is also called relative value analysis, the basic principles of which are described in this section. 

A bank s swap screen on Bloomberg or Reuters might look something like FIGURE 7.3. The first column represents the length of the swap agreement, the next two are its offer and bid quotes for each maturity, and the last is the current bid spread over the government benchmark bond. 

The conventional approach for analyzing an asset swap uses the bonds yield-to-maturity (YTM) in calculating the spread. The assumptions implicit in the YTM calculation (see Chapter 2) make this spread problematic for relative analysis, so market practitioners use what is termed the Z-spread instead. The Z-spread uses the zero-coupon yield curve to calculate spread, so is a more realistic, and effective, spread to use. The zero-coupon curve used in the calculation is derived from the interest-rate swap curve. 

In effect, this is the standard bond price equation with the discount rate adjusted by whatever the Z-spread is it is an iterative calculation. The appropriate maturity swap rate is used, which is the essential... 

We illustrate the Z-spread calculation at FIGURE 19.6. This is done using a hypothetical bond, the XYZ PLC 5 percent of June 2008, a three-year bond at the time of the calculation. Market rates for swaps. Treasury, and CDS are also shown. We require the spread over the swaps curve that equates the present values of the cash flows to the current market price. The cash flows are discounted using the appropriate swap rate for each cash flow maturity. With a bond yield of 5-635 percent, we see that the I-spread is 43-5 basis points, while the Z-spread is 19.4 basis points. In practice, the difference between these two spreads is rarely this large. 

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