Bond Yield Spreads

The binomial model evaluates a bond s return by measuring the extent to which it exceeds those determined by the risk-free short rates in the tree. The spread between these returns is the bond s incremental return at a specified price. Determining the spread involves the following steps  

Price VolatilMy of Bonds with Embedded Options 

As explained in chapter 2, the duration for any bond may be calculated using equation (11.12) (assuming annualized yields). 

= the bond cash flow at time t P = the bonds fair price C = the annual coupon payment rm = the redemption yield n = the number of years to maturity 

To calculate the modified duration of a bond with an embedded option, the bondholder must assume a fixed maturity date based on the bond s current price. When it is unclear what redemption date to use, modified duration may be calculated to both the first call date and the final maturity date. This is an unsatisfactory compromise, however, since neither date, and so neither measure, may be appropriate. The problem is more acute for bonds that are continuously callable or putable from the first call or put date until maturity. 

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Duffee, G.R., 1996a. Treasury Yields and Corporate Bond Yield Spreads An Empirical Analysis. Federal Reserve Board, Washington, DC. 

Duffee, G.R., 1996b. Estimating the Price of Default Risk. Federal Reserve Board, Washington, DC. Duffee, G.R., 1998. The relation between treasury yields and corporate bond yield spreads. J. Financ. 53 (6), 2225-2241. 

This discussion covers the main factors affecting bond returns in the European fixed income market, namely, the random fluctuations of interest rates and bond yield spreads, the risk of an obligor defaulting on its debt, or issuer-specific risk, and currency risk. There are also other, more subtle sources of risk. Some bonds such as mortgage-backed and asset-backed securities are exposed to prepayment risk, but such instruments still represent a small fraction of the total outstanding European debt. Bonds with embedded options are exposed to volatility risk. However, it is not apparent that this risk is significant outside derivatives markets. 

Also the simple difference between the yield of conventional and inflation-linked bonds or yield spread is an indicator for expected inflation. For example, on 18 September 2014 the 10-year UK 0 1/8% inflation-linked 2024 had a money yield of 2.125% and a real yield of -0.410%, assuming an inflation of 2.571%. Differently, the 10-year benchmark, the UK T A% 2023 had a gross... 

Therefore, the yield spread is around 2% reflecting the expected inflation during the life of the bond. A higher inflation expectation will mean a greater spread between inflation-linked and conventional bonds. 

Traditionally, information on inflation expectations has been obtained by survey methods or theoretical methods. These have not proved reliable however, and were followed only because of the absence of an inflation-indexed futures market. Certain methods for assessing market inflation expectations are not analytically valid for example, the suggestion that the spread between short- and long-term bond yields cannot be taken to be a measure of inflation expectation, because there are other factors that drive this yield spread, and not just inflation risk premium. 

Equally, the spread between the very short-term (overnight or 1 week) interest rate and the 2-year bond yield cannot be viewed as purely driven by inflation expectations. Using such approaches to glean information on inflation... 

In a conventional positive yield curve environment, it is common for the 30-year government bond to yield say 10-20 basis points above the tlO-year bond. This might indicate to investors that a 100-year bond should yield approximately 20-25 basis points more than the 30-year bond. Is this accurate As we noted in the previous section, such an assumption would not be theoretically valid. Marshall and Dybvig have shown that such a yield spread would indicate an undervaluation of the very long-dated bond and that should such yields be available an investor, unless he or she has extreme views on future interest rates, should hold the 100-year bond. 

The default spread in relation to the outright government bond yield... 

The general rule of corporate bonds is that they are priced at a spread to the government yield curve. In absolute terms, the yield spread is the difference between the yield to maturity of a corporate bond and the benchmark, generally a yield to maturity of a govermnent bond with the same maturity. Corporate bonds include a yield spread on a risk-free rate in order to compensate two main factors, liquidity premium and credit spread. The yield of a corporate bond can be assumed as the sum of parts of the elements as shown in Figure 8.1, in which the yield spread relative to a default-free bond is given by the sum of default premium (credit spread) and liquidity premium. 

The yield of a benchmark government bond depends on expected inflation rate, currency rate, economic growth, monetary and fiscal policy. Conversely, the spread of a corporate bond is influenced by the credit risk of the issuer, taxation and market liquidity. Moreover, the yield spread depends on other factors such as ... 

There are several ways to measure the yield spread of a corporate bond ... 

G-spread It is the yield spread over the govermnent bond curve. This spread takes into account the credit risk, liquidity risk and other risks that affect corporate bonds ... 

I-spread It is the yield spread of a corporate bmid relative to an interpolated swap rate. According to this approach, the yield of a corporate bond is built in the following way ... 

Z-spread The Z-spread or zero volatility spread calculates the yield spread of a corporate bond by taking a zero-coupon bond curve as benchmark. Conversely to other yield spreads, the Z-spread is constant. In fact, it is found as an iterative procedure, which is the yield spread required to get the equivalence between market price and the present value of all its cash flows. The Z-spread is given by Equation (8.2) ... 

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. 

The price of a corporate bond is a yield spread for conventional bonds or on an OAS basis for callable or other option-embedded bonds. If an OAS calculation is undertaken in a consistent framework, price changes that result in credit events will result in changes in the OAS. Therefore, we can speak in terms of a sensitivity measure for the change in value of a bond or portfolio in terms of changes to a... 

To assess the impact of changing yield spreads therefore, it is necessary to carry out a simulation on the effect of different yield curve assumptions. For instance, we may wish to analyse 1-year holding period returns on a portfolio of investment-grade corporate bonds, under an assumption of widening yield spreads. This might be an analysis of the effect on portfolio returns if the yield spread for triple-B-rated bonds widened by 20 basis points, in conjunction with a varying government bond yield. This requires an assessment of a different number of scenarios, in order to capture this interest-rate uncertainty. 

We have stated that the yield premium required on a corporate bond accounts for the default risk exposure of such a bond. The level of yield spread is determined by the expected default loss of the bond and it is assumed that investors can assess the level of the default risk. This makes it possible to calculate the level of the theoretical default spread. 

For lower- and non-rated bonds, the observed effect is the opposite to that of an investment-grade corporate. Over time the probability of default decreases therefore, the theoretical default spread decreases over time. This means that the spread on a long-dated bond will be lower than that of a short-dated bond because if the issuer has not defaulted on the long-dated bond in the first few years of its existence, it will then be viewed as a lower risk credit, although the investor may well continue to earn the same yield spread. 

The Default Spread in Relation to the Outright Government Bond Yield... 

FIGURE 8.4 Correlation of theoretical yield spread with outright government bond yield, 10-year corporate bonds. 

As shown in previous sections, the credit spread on a corporate bond takes into account its expected default loss. Structural approaches are based on the option pricing theory of Black Scholes and the value of debt depends on the value of the underlying asset. The determination of yield spread is based on the firm value in which the default risk is found as an option to the shareholders. Other models proposed by Black and Cox (1976), Longstaff and Schwartz (1995) and others try to overcome the limitation of the Merton s model, like the default event at maturity only and the inclusion of a default threshold. This class of models is also known as first passage models . 

Like Black and Cox s work, the authors find spreads similar to the market spreads. Moreover, they find a correlation between credit spread and interest rate. In fact, they illustrate that firms with similar default risk can have a different credit spread according to the industry. The evidence is that a different correlation between industry and economic environment affects the yield spread on corporate bonds. Then, the duration of a corporate bond changes following its credit risk. For high-yield bonds, the interest-rate sensitivity increases as the time to maturity decreases. 

The option-adjusted spread (OAS) is the most important measure of risk for bonds with embedded options. It is the average spread required over the yield curve in order to take into account the embedded option element. This is, therefore, the difference between the yield of a bond with embedded option and a government benchmark bond. The spread incorporates the future views of interest rates and it can be determined with an iterative procedure in which the market price obtained by the pricing model is equal to expected cash flow payments (coupons and principal). Also a Monte Carlo simulation may be implemented in order to generate an interest rate path. Note that the option-adjusted spread is influenced by the parameters implemented into the valuation model as the yield curve, but above all by the volatility level assumed. This is referred to volatility dependent. The higher the volatility, the lower the option-adjusted spread for a callable bond and the higher for a putable bond. 

There is no generally accepted definition of bondholder value. It could be set equal to the market value of a company s debt. The market value of outstanding debt could be increased by issuing more bonds. This would adversely affect the market value of existing debt. Alternatively, bondholder value is based on the yield spread to government bonds the wider the spread, the higher the risk associated with the issuer. A spread widening due to the company s activities leads to a reduction of bondholder value. 

A bond s yield is a measure of its potential return. Market participants commonly assess a security s relative value by calculating a yield or some yield spread. There are a number of yield measures that are quoted in the market. These measures are based on certain assumptions necessary to carry out the calculation. However, they also limit effectiveness of a yield measure in gauging relative value. In this section, we will explain the various yield and yield spread measures as well as document their limitations. 

Traditional yield spread analysis for a nongovernment bond involves calculating the difference between the risky bond s yield and the yield on a comparable maturity benchmark government security. As an illustration, let s use a 5.25% coupon BMW Finance bond described in Exhibit 3.10 that matures on 1 September 2006. Bloomberg s Yield Spread Analysis screen is presented in Exhibit 3.14. The yield spreads against various benchmarks appear in a box at the bottom left-hand corner of the screen. Using a settlement date of 9 July 2003, the yield spread is 31 basis points versus the interpolated 3.1-year rate on the Euro Benchmark Curve. This yield spread measure is referred to as the nominal spread. 

We will discuss two approaches for assessing the interest rate risk exposure of a bond or a portfolio. The first approach is the full valuation approach that involves selecting possible interest rate scenarios for how interest rates and yield spreads may change and revaluing the bond position. The second approach entails the computation of measures that approximate how a bond s price or the portfolio s value will change when interest rates change. The most commonly used measures are duration and convexity. We will discuss duration/convexity measures for bonds and bond portfolios. Finally, we discuss measures of yield curve risk. 

That said, there are two reasons why the performance of German swap spreads are related to Euro peripheral spreads. The first one is that, flows apart, the bond-swap spread reflects the yield difference between a government rate and the composition of a string of EURI-BOR rates (i.e., a swap fixed rate). As the average credit quality of the banks in the EURIBOR panel is A-AA, any increase in the investors preference for credit quality will make both swap and peripheral spreads widen versus the core Euro government rate, thus increasing the correlation between both differentials. Yet this increase in the correlation will be mainly due to the outperformance of the benchmark asset... 

Although this strategy creates the potential for an investor to treble his money for a 50 bp drop in bond yields, the investor would lose everything if bond prices stay the same or fall. An alternative strategy is to create a bull call spread by ... 

Swap rates (frequently quoted as government bond yield for a chosen benchmark adjusted for swap spreads)... 

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