Treasury bonds

In an unrelated study, Stewart estimated the market risk premium by comparing Standard and Poor s 500 stocks with long-term (20-year) U.S. Treasury bonds from 1925 to 1989 (409). He found that the risk premium was only 5.8 percent over the period. This would imply a risk premium over the Treasury bill rate (adjusted for long-term forecasts) of just 7.0 percent. 

Black, F., Derman, E., Toy, W., 1990. A one-factor model of interest rates and its application to Treasury bond options. Financ. Anal. J. 46, 33-39. 

Where Y is the yield of a corporate bond 1 is the /-spread over the swap S is the swap spread and T is the yield of a treasury bond ... 

As introduced, the reference rate represents the interest rate or index used to obtain the linkage. In the European market, the major parts of floating-rate note issuances are linked to the Euribor and the remaining to the constant maturity swap. In the US and UK markets, they are tied to the Libor and short-term treasury bonds. 

Consider the following example. We assume to have two hypothetical bonds, a treasury bond and a callable bond. Both bonds have the same maturity of 5 years and pay semiannual coupons, respectively, of 2.4% and 5.5%. We perform a valuation in which we assume a credit spread of 300 basis points and an OAS spread of 400 basis points above the yield curve. Table 11.1 illustrates the prices of a treasury bond, conventional bond and callable bond. In particular, considering only the credit spread we find the price of a conventional bond or option-free bond. Its price is 106.81. To pricing a callable bond, we add the OAS spread over the risk-free yield curve. The price of this last bond is 99.02. We can now see that the OAS spread underlines the embedded call option of the callable bond. It is equal to 106.81-99.02, or 7.79. In Section 11.2.3, we will explain the pricing of a callable bond with the OAS methodology adopting a binomial tree. 

TABLE 11.1 OAS analysis for a Treasury Bond, Conventional Bond and Callable Bond... 

Treasury Bond Conventional Bond Callable Bond ... 

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 Bund future was launched on 29 September 1988. With the introduction of the German government bond futures contract LIFFE was now trading bond contracts in the US Treasury bond, the Japanese government bond, the Italian government bond and UK gilts. It was the first financial futures exchange to have achieved this position. The contract specifications on the UK and European bond futures offered at that time appear in Exhibit 16.1. 

Eisher Black, Emmanuel Herman, and William Toy, A One-Eactor Model of Interest Rate and its Application to Treasury Bond Options, Financial Analysts Journal (1990), pp. 33-39. 

An investor follows a strategy that involves going long of a Latin American sovereign bond. The bond is currently yielding 350 bp over the benchmark US Treasury bond. If the sovereign bond falls in price then the investor will purchase it. The investor expects that the target price for the purchase should be when the spread is 400 bp. 

We derive daily zero-coupon yield curves from five countries of the Eurozone (France, Germany, Italy, Spain, and the Netherlands) during the period from 2 January 2001 to 21 August 2002, using zero-coupon rates with 26 different maturities ranging from one month to 30 years. The yield curves are extracted from daily Treasury bond market prices by using a standard cubic B-splines method. Our input baskets are composed of... 

Corporate bonds are less frequently traded than Treasury bonds. Thus stale prices can contribute to the lower volatility of corporates. 

The risk averse investor with an investment horizon of three years (row 3) allocates his capital according to the weights in 8% corporate bonds with AA rating, 15% in A, 70% in BBB, and 8% in Treasury bonds (columns 2 to 5). His optimal term structure consists of 52% bonds with a 1-3Y maturity, 6% with 3-7 year, 5% with a 7-10 year, and 37% with a 10 year+ maturity (row 3, columns 6 to 9). 

Surprisingly, the share of Treasury bonds increases with lower risk aversion (column 5). Conversely, corporates make up a higher portion of the portfolio the greater risk aversion is. This is due to the inferior risk/return characteristics of government bonds relative to corporates (Exhibit 27.1). For a 5-year horizon, for example, the risk averse portfolios consist of 71% BBB corporates, whereas this share declines to 64% for the aggressive investor (rows 6 and 7, column 4). 

For an investment horizon of at least three years it pays on average to include risk in the form of corporates in a bond portfolio the optimized portfolios contained 58% to 79% corporates of the BBB segment. The A category was represented with portions between 0% and 15%, the AA corporates between 0 and 8%. Treasury bonds were weighted between 8% and 35%. 

Bonds. Exchange-traded options on bonds are invariably written on the bonds futures contracts. One of the most popular exchange-traded options contracts, for example, is the Treasury bond option, which is written on the Treasury futures contract and traded on the Chict o Board of Trade Options Exchange. Options written on actual bonds must be traded in the OTC market. 

Their yields are usually higher than those of corporate bonds with the same credit rating. In the mid-1990s, mortgage-backed bonds traded around 100 to 200 basis points above Treasury bonds by comparison, corporates traded at a spread of around 80 to 150 for bonds of similar credit quality. This yield gap stems from the mortgage bonds complexity and the uncertainty of mortgage cash flows. 

The market is large and thus very liquid agency mortgage-backed bonds have the same liquidity as Treasury bonds. 

U.S. Treasury price quotes are in ticks, or thirty-seconds of a price point. A half tick is denoted by a plus sign. On May 10, 1994, the 10.25 percent Treasury bond maturing July 21, 1995, was quoted at 104-28+— in other words, an investor would pay 104.28625 for every 100 in face value. It pays coupons on January 21 and July 21. On May 11, 1994, the settlement date, it will have accrued 109 days of interest, for a total of 10.25 X 109/365 x 0.5, or 1.53048 for every 100 of face value. The dirty price of the bond on this date is thus 104-28+ plus 1.53048, or 106.421105. 

Because of the analysis s assumed restrictions, however, investors applying it must continually adjust their portfolios if they wish to remain immunized. Fabozzi (1996) contains a very accessible discussion of the key issues involved in dynamically managing a portfolio. A number of other considerations also limit the use of duration in portfolio management. For instance, as Blake (1990) 5-8.1 points out, most Treasury bonds have durations of less than twelve years. This makes portfolio immunization difficult when liabilities are very long dated. 

As noted in chapter 2, a Treasury bond can be seen as a bundle of individual zero-coupon securities, each maturing on one of the bond s cash flow payment dates. In this view, the Treasury s price is the sum of the present values of all the constituent zero-coupon bond yields. Assume that the spot rates for the relevant maturities—ri,r2,rg,.rj f—can be observed. If a bond pays a semiannual coupon computed at an annual rate of C from period 1 to period N, its present value can be derived using equation (16.7). 

Burghardt, G. 1994. The Treasury Bond Basis. New York McGraw-Hill. 

Black, E, E. Derman, and W. Toy. 1990. A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options. Einancial Analysts Journal, Spring, 33-39. 

Example A Treasury bond with a face value of 100,000 is issued with a coupon rate of 8.75 percent. Coupon payment dates for this bond are November 15 and May 15. If this bond is purchased on January 5, what is the value of accrued interest ... 

Example An investor settles on an 8 percent Treasury bond on September 17, 1992. This bond pays coupons on November 15 and May 15 and matures on November 15, 1992. The maturity value of this bond is 100,000, the current quoted price is 99,960,48, and the amount of accrued interest is 2,717.39. What is the approximate yield and the true yield on this security ... 

TABLE 12.2 OAS Analysis for Corporate Callable Bond and Treasury Bond... 

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