A REAL CORPORATE BOND
Let's assume that your career in fixed-income markets is moving along splendidly and now you plan to buy your loved one an investment-grade corporate bond for Valentine's Day. Figure 3.5 shows the Bloomberg Yield and Spread Analysis page for the 8 3/8% IBM bond that matures on November 1, 2019. Its flat price is 132.209 (percent of par value) for settlement on February 14, 2014. Look first at the Invoice section on the lower right side of the page. The total purchase price is shown for $1,000,000 in par value (also called the face amount – you can scale that down to a lower amount to fit your budget). The flat (or clean) price, here called the principal, is $1,322,090.00. The accrued interest is $23,961.81, calculated as:
The day-count convention is 30/360, giving 103 days between the last coupon on November 1 and settlement on February 14 (29 remaining days in November, 30 days in December, 30 days in January, and 14 days in February). There are assumed to be 180 days in the 6-month coupon period. The sum of the flat price and the accrued interest, $1,346,051.81, is the full (or dirty) price.
The street convention yield-to-maturity statistic for this bond is shown to be 2.322082%. That it is so much lower than the coupon rate of 8.375% explains why it is trading at such a high premium over par value. This IBM
FIGURE 3.5 Bloomberg Yield and Spread Analysis Page for the IBM 8 3/8% Bond Due 11/01/2019
Used with permission of Bloomberg.com © 2014. All rights reserved.
bond was issued in 1989 at a time of much higher market interest rates. This yield can be confirmed using the YIELD financial function in Excel, as shown here:
The entered items are the settlement date, maturity date, annual coupon rate as a decimal, flat price, par value, periodicity, and the code for a 30/360 day-count. The Excel program solves for the accrued interest and then the internal rate of return on the total cash flows.
Another way of confirming the yield to maturity is to substitute into equation 3.11 and solve for y by trial and error. The semiannual coupon payment (PMT) is 4.1875 per 100 of par value: 8.375%/2 * 100 = 4.1875. There are 12 semiannual periods (N) between the last coupon payment on November 1, 2013, and maturity on November 1, 2019. The fraction of the period gone by is 103/180 (t/T). The left side of the equation is the full price; the right side is the present value of the coupon and principal cash flows discounted at the yield per semiannual period (y).
The solution for y turns out to be 0.0116104083. Multiply that by two to annualize and round to six digits to obtain the street convention yield to maturity of 2.322082%.
Shown next is a periodicity conversion. The street convention yield of 2.322082% is on a semiannual bond basis; it converts to 2.335562% for one compounding period per year, that is, an effective annual rate.
The true yield for this bond is 2.321916%, a bit lower than the street convention yield because three coupon dates fall on weekends (November 1, 2014, November 1, 2015, and May 1, 2016) and the payments are deferred until the following Monday. The U.S. Government and Japanese simple yields are not displayed but can be found by pulling down the menu. They are 2.324031% and 2.069000%, respectively. The former can be verified by solving this equation:
The only change from the equation for street convention is to switch the day-count on the right side from 103/180 to 105/181 to reflect the actual/actual convention used on Treasuries. Here y is 0.011620153; that gives 2.324031% when annualized and rounded. I won't bother confirming the Japanese simple yield calculation – it's just a datum that I hope you never use in making a decision. The same is true for the current yield, shown to be 6.334667%. It is the sum of the coupon payments over the year divided by the flat price but how you'll use that statistic I really don't know.
The after-tax rate of return, shown at the bottom of the page to be 1.314666%, is discussed in Chapter 4 on bond taxation. You will see that I have a problem with how Bloomberg reports after-tax yields on some bonds trading at a discount. This IBM bond is priced at a premium, and its after-tax rate is fine.
Now look at the spread calculation in the top left side of the page. The street convention yield on the IBM bond is compared to the yield on the on-the-run (i.e., most recently issued) 5-year Treasury note. Its coupon rate is 1.5% and it matures on January 31, 2019. Its flat price is shown to be 99-26% for settlement on February 12, 2014. Treasuries are quoted in 32nds, so that price means 99 + 26.75/32 = 99.8359375 per 100 of par value. Note that this Bloomberg page was taken on February 11, indicating that Treasuries settle “T+l” and corporate bonds “T+3.”
The street convention yield for this T-note is 1.534396%. The same result is obtained using the YIELD function in Excel.
Note that the last entry item of 1 is the code for actual/actual day-count convention. The spread over this particular Treasury note for the IBM bond is 78.77 basis points: 2.322082% – 1.534396% = 0.787686%. This is not exactly an “apple-to-apple” comparison because the settlement dates and day-counts differ. The U.S. Government Equivalent yield could be used to account for the second difference, which would give a spread of 78.96 basis points: 2.324031% – 1.534396% = 0.789635%. That this is not done in practice (at least by Bloomberg) suggests that U.S. Government yields for corporate bonds are data, not information.
Several other spreads are shown in the lower left side of the Bloomberg page. The G-Spread is the street convention yield minus the yield on an interpolated Treasury curve. The idea is to find the point on the government bond yield curve that best matches the maturity on the IBM bond because there is no Treasury maturing on 11/01/19. I-spread is similar in that it is the bond yield minus the yield on an interpolated interest rate swap curve – more on swaps in Chapter 8. The Basis relates the bond spread to prices on credit default swaps – a great topic but one not covered in this book (sorry).
The Z-spread is the uniform increment over a benchmark spot (i.e., zero- coupon) curve that obtains the full price of the bond. This calculation is shown in Chapter 5. The asset swap spread (ASW) is the difference between the bond's coupon rate and a corresponding fixed rate on an interest rate swap. Finally, the option-adjusted spread (OAS) “corrects” the bond spread for the presence of embedded options. This is addressed in Chapter 6.
The duration and convexity calculations in the Risk section on the top right side of the page are very important to the study of bond math, but we have to wait until Chapter 6 for that discussion.
Owning or issuing a standard semiannual payment coupon bond entails dealing with many cash flows. A yield-to-maturity statistic is a way of summarizing these many cash flows into just one number. Of the many yield statistics that are out there, the street convention yield is probably the most informative and the most useful in making decisions. It is information and not just more data. At least it is a decent starting place to think about future coupon reinvestment rates and the probability of default. It does, however, neglect the inevitability of taxation. That no longer can be avoided.