Benchmark yield

The duration shows the bond s price sensitivity to its yield to maturity. The change in bond s price is plotted in a curve in which the duration represents the slope of the tangent at any point of the curve. Conversely, the effective duration, or also known as curve duration, shows the price sensitivity to the change of the benchmark yield curve or market yield curve. This duration is more suitable than Macaulay or modified duration for bonds with embedded options because the latter ones have not a well-defined yield to maturity. The effective duration is given by (11.1) ... 

Change the benchmark yield curve with a downward parallel shift ... 

For instance, consider a hypothetical case in which a callable bond has a price equal to 103.78. Suppose that the benchmark yield curve changes by 1 basis point. For a downward parallel shift, the price obtained is 103.83, while for an upward shift the price is 103.73. Therefore, applying Formula (11.1) the bond s effective duration is around 4.93. 

The additional compensation or spread over the benchmark yield that investors will require reflects the additional risks the investor faces by acquiring a security that is not issued by a sovereign government. These yields spreads (discussed later in the chapter) will depend not only on the risks an individual issue is exposed to but also on the level of benchmark yields, the market s risk aversion, the business cycle, and so on. 

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. 

Given the swap rate, the swap spread can be determined. For example, since this is a 3-year swap, the convention is to use the 3-year rate on the euro benchmark yield curve. If the yield on that issue is 4.5875%, the swap spread is 40 basis points (4.9875% - 4.5875%). 

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. 

Estimation of the historical volatility by considering the components historic volatility of the reference asset yield, historic volatility of the benchmark yield, correlation of the returns between the reference asset yield and the benchmark yield. 

Changes in benchmark yields for different terms are highly correlated regardless of the market, which constitutes a strong incentive to step away from a key rate model in which the factors are rate changes at the term structure vertices. The principal component analysis consists in extracting a set of linear combinations of key rate changes that capture... 

Maturities are 1 to 6 months, 9 months, 1 to 12, and 15, 18, 20, 22, 25, 27, and 30 years. For more details, see Lionel Martellini, Phillippe Priaulet, and Stephane Pri-aulet, The Euro Benchmark Yield Curve Principal Component Analysis of Yield Curve Dynamics, in Frank J. Fabozzi (ed.), Professional Perspectives on Fixed Income Portfolio Management Volume 4 (Hoboken, NJ John Wiley Sons, Inc., 2003). 

Historically, comparing the yield of the interesting bond with the benchmark yield may be a first step in relative value analysis. This allows one to examine the implications of events in the past on the spread of the bond. Exhibit 29.3 depicts the yield spread of Swissair and the matching Bund (German government bond) in the period from May 1999 to November 2001. 

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. 

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. 

---