Government yield curve

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. 

As we have seen, duration is a measure of the change in a bond s value when interest rates change. The interest rate that is assumed to shift is the government rate which serves as the benchmark interest rate. However, for nongovernment instruments, the yield is equal to the government yield plus a spread to the government yield curve. This is why nongovernment... 

As it is used as a predictive indicator, the spot yield curve needs to be fitted as accurately as possible. This is an area that has been extensively researched (see McCulloch, 1975 Deacon and Derry, 1994 Schaefer, 1981 Waggoner, 1997 Nelson and Siegel, 1987 Svensson, 1994, 1995 inter alia). Invariably researchers use the government debt market as the basis for modelling the term structure. This is because the government market is the most liquid debt market... 

We can compare fitted yield curves to an actual spot rate curve wherever there is an active government (risk-free) zero-couprai market in operation. In the United Kingdom, a zero-couprai bmid market was introduced in December... 

For the purposes of conducting monetary policy and for central government requirements, little use is made of the short end of the yield curve. This is for two reasons one is that monetary and government policy is primarily concerned with medium-term views, for which a short-term curve has no practical input, the second is that there is often a shortage of data that can be used to fit the short-term curve accurately. In the same way that the long-term term stmcture... 

FIGURE 5.7 Fitting short-term yield curves using government repo rates. (Reproduced with permission from the Bank of England Quarterly Bulletin, November 1999.)... 

A common observation in government bond markets is that the longest dated bond trades expensive to the yield curve. It also exhibits other singular features that have been the subject of research, for example, by Pboa (1998), wbicb we review in this chapter. The main feature of long-bond yields is that they reflect a convexity effect. Analysts have attempted to explain the craivexity effects of long-bond yields in a number of ways. These are discussed first. We then consider the volatility and convexity bias that is observed in long-bond yields. 

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. 

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. 

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. 

It is possible to infer market expectations about the level of real interest rates going forward by observing yields in government index-linked bonds, which trade in a number of countries including the US and UK. The market s view on the future level of interest rates may also be inferred from the shape and level of the current yield curve. Again from chapter 6, we saw that the slope of the yield curve also has an information content. There is more than one way to interpret any given slope however, and this debate is still open. 

In an arbitrage-free model, the initial term structure described by spot rates today is an input to the model. In fact such models could be described not as models per se, but essentially a description of an arbitrary process that governs changes in the yield curve, and projects a forward curve that results from the mean and volatility of the current short-term rate. An equilibrium term structure model is rather more a true model of the term structure process in an equilibrium model the current term structure is an output from the model. An equilibrium model employs a statistical approach, assuming that market prices are observed with some statistical error, so that the term structure must be estimated, rather than taken as given. 

In the illustration in Exhibit 4.5, it is assumed that both the 2-year and 30-year yields change by the same number of basis points. The full valuation approach can also handle scenarios where the yield curve does not change in a parallel fashion. Exhibit 4.6 illustrates this for our portfolio that includes the 2-year and the 30-year Italian government securities. The scenario analyzed is for a change in the yield curve s slope combined with changes in the level of yields. In the illustration in Exhibit 4.6, the following yield changes are assumed for the 2-year and the 30-year yields ... 

As we discussed above, one draw is the scope to outperform. With yields among government markets all tightly compressed, the only way to add alpha (fund manager-generated outperformance versus a benchmark) in the government sector is via a yield curve or duration call. 

So the prime obstacle to the development of a Euro-zone real yield curve was gone. And, as we have said, Greece has now joined the sector and other governments are understood to be considering entry, potentially adding points to the real yield curve and investor choice. 

So, we have argued, the economics of supply and demand make the risk premium a slippery concept. Bond mathematics now makes matters worse. This new aspect centres on the issue of convexity. We know that a forward curve of implied future short-term nominal rates can be derived from the nominal government bond curve. In principle, a forward curve of implied future short-term real rates can be similarly derived from the inflation-linked bond real yield curve. These two curves, taken together, should imply a future path of inflation, if we can set aside the risk premium for the moment. Unfortunately, that is not the case. 

A variation on these futures contracts based on German Government paper is offered by Euronext Paris—MATIF. Both the Euro Notional Future, which covers the 8.5-10.5 year section of the yield curve and the 30-year E-Bond Future which covers the 25-35 year segment, allow delivery of either French or German Government bonds into the contract on settlement. 

Swap spreads are quoted off specific government benchmarks. When a benchmark issue is replaced, it can have a technical effect on swap spreads. Swap spreads can either narrow or widen, depending on the new benchmark issue used and the shape of the yield curve. The change is only technical, however, and absolute swap rate levels remain unchanged. 

In this example, the bank is quoting an offer rate of 5-25 percent, which is what the fixed-rate payer will pay, and a bid rate of 5-19 percent, which is what the floating-rate payer will receive. The bid-offer spread is therefore 6 basis points. The fixed rate is always set at a spread over the government bond yield curve and is often quoted that way. Say the 5-year Treasury is trading at a yield of 4.88 percent. The 5-year swap bid and offer rates in the example are 31 basis points and 37 basis points, respectively, above this yield, and the bank s swap trader could quote the swap rates as a swap spread 37-31. This means that the bank would be willing to enter into a swap in which it paid 31 basis points above the benchmark yield and received LIBOR or one in which it received 37 basis points above the yield curve and paid LIBOR. 

Another indicator of credit risk is the credit risk premium the spread between the yields on corporate bonds and those of government bonds in the same currency. This spread is the compensation required by investors for holding bonds that are not default-free. The size of the credit premium changes with the market s perception of the financial health of individual companies and sectors and of the economy in general. The variability of the premium is illustrated in FIGURES 10.2 and 10.3 on the following page, which show the spreads between the U.S.-dollar-swap and Treasury yield curves in, respectively, February 2001 and February 2004. 

IDNs can be structured to enable investors to take positions on the yields in different currencies at the same maturity. A note s coupon, for example, could be determined by the difference between the 10-year government benchmark yields in two specified countries. The notes can also be linked to spreads between yields at different maturities in the same currency. This would be a straight yield-curve, or relative-value, trade in a domestic or foreign currency. 

The OAS-derived yield spread is based on the present values of expected cash flows discounted using government bond—derived forward rates. The spread berween the cash flow yield and the government bond yield is based on yields to maturity. The OAS spread is added to the entire yield curve, whereas a yield spread is over a single point on the government bond yield curve. For these reasons, the two spreads are not strictly comparable. 

In contrast to the situation in most strip markets. Treasury strips with very short maturities do not trade expensive relative to the curve. When the yield curve is positive, short strips are often in demand because they enable investors to match liabilities without reinvestment risk and at a higher yield than they could get on coupon bonds of the same maturity. The Treasury strip yield curve, on the other hand, has been inverted from before there was a market. In other government strip markets, such as Frances, however, short maturities of up to three years are often well bid. 

This section discusses the factors that must be assessed in analyzing the relative values of government bonds. Since these securities involve no credit risk (unless they are emerging-market debt), credit spreads are not among the considerations. The zero-coupon yield curve provides the framework for all the analyses explored. 

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