BONDS

A bond's price reacts conversely to the movement in interest rates. As rates move up, the value of a bond tends to move down. As interest rates go down- say to spur on economic conditions, values on already issued bonds will go up. This assumes normal bonds with the primary caveat being GNMA's.

The stated, nominal or coupon rate of a bond is what is the stated return on the bond. For example, if the coupon rate is stated as 6% and the bond has a par value of $1,000, the bond will pay $60 per year.

Current Yield is the interest being returned on a bond divided by the current price. If interest rates in the economy had gone down, the value of a bond would go up. If the price was quoted at 120, it means that the actual price was 1200. But the bond would continue to pay its stated coupon rate, which we will say was 8%. The current yield would therefore equal the yield divided by the current price. $80/1200 = 6.67%. If interest rates had gone up, the value of bonds decreases. An 8% bond priced at 83 would have a current yield of $80/830 = 9.64%.

Yield to Maturity considers not only the interest being generated, but also any gain or loss that will be experienced by a bond if it is held to maturity.

Assume a 10% bond, 15 year bond is quoted at 95. You need to use a financial calculator

YTM= 10.68%

Yield to Call is measured in a similar way as yield to maturity but obviously uses a shorter hold period due to the projected call on the bond. When quoting a bond, you must always uses the lowest of the three quotes. Otherwise the quote may be considered deceptive.

Tax equivalent yields when you want to compare a municipal/non taxable return with that of a taxable bond. To do that, take the municipal bond yield and divide it by 1 minus the taxpayers tax bracket

6% municipal yield

30% investor tax bracket

.06/1-.30= .06/.7= 8.57% That means, everything else being equal (it never is, though) that it would make no difference to an investor buying either a 6% tax free bond or a taxable 8.57% bond since they would both produce the same net return. (I have not addressed other issues of risk, however.)

Maturity As stated, a bond reacts conversely to interest rates movements, but a further distinction to that is that the longer the maturity of the bond, the greater the impact on price, all other factors remaining equal.

Coupon A similar relationship also exists with the amount of the yield on the bond. All other factors being equal, the lower the coupon rate, the more volatile the bond will be due to changes in the economic rates.

A most interesting note is the fact that since municipal bonds universally carry lower rates than corporate bonds, they tend to be more volatile overall. But the computations show that tax free bonds fall more when interest rates rise than the go up in value when interest rates drop.

Short term tax free bonds tend to sell at about 70% of taxable issues. Long term municipals tend to sell at 80% of the taxable rate. Therefore, it the gap lessens even more, municipals are highly desired.

Quality The lower the quality of the bond, the more volatility it will experience.

Duration Stocks are usually measured by their betas. This is based on historic figures that may change at any time. Bonds can be better analyzed one against the other through duration since duration is a measure of a bond's price sensitivity to changes in interest rates. It is a measure of market risk.

From basic texts, the definition of Macaulay duration is the weighted average of the time periods over which cash flows accrue to bondholders using the percentage of the present values of the cash flows which occur at each payment time as the weighting scheme.

Convexity is approximately the weighted average of the square of the time periods over which the cash flows accrue to the bondholders using the same weighting scheme.

How do these work given in practice? Consider a 10% coupon, 5 year bond priced at 95.75 that has a modified duration of 3.94 and a convexity of 19.42. What is the effect on price if interest rates rise by 1% or drop by 1%.

Multiply duration (always a negative number) by the interest rate change and add 1/2 times convexity times the interest rate change squared

If rates rose: -3..94 (.01) + 1/2 (19.42) (.01) SQ = -0.394 + .000971= -3.8429%

If rates dropped: -3.94 (-.01) + 1/2 (19.42) (-.01) SQ = 0.394 + .000971 = 4.0371%

For all intents and purposes, if the change in interest rates is small, convexity may simply be ignored.

Price change: If a interest rates would change by one basis point, what would be the price impact on a 7%, 8 year bond priced at 101 with a modified duration of 2.79?

Multiply .0001 (101)(2.79) = $.02818

This means that a one basis point change in interest rates would cause the price of this bond to change by $.02818 in the OPPOSITE direction of the interest rate change (since duration is always a negative number.)

More concise properties of duration are

For example, if Bond A comprised 60% of a portfolio with a duration of 2.97 and Bond B comprised 40% and had a duration of 3.33, then the duration of the portfolio would be

.60(2.97) + .40(3.33) = 1.78 + 1.33 = 3.11 years.

For investment purposes, if you expect interest rates to rise, reduce the duration of the portfolio. If one expects interest rates to fall, increase the duration of the portfolio. It is similar to varying the maturities of a bond but with the added condition of yield.

Resulting Duration with Alternative Bond characteristics
Coupon 8% 8% 8% 8% 10% 6% 8% 10%
Maturity (years) 10 10 10 8 10 10 12 10
Par 1000 1000 1000 1000 1000 1000 1000 1000
Yield 10 12 14 12 12 12 12 10
Durations 6.725 6.49 6.24 5.695 6.185 7.01 7.10 10



After all said and done, unless you buy a bond(s) for a particular duration and intend to hold them to maturity, you may want to consider mutual funds. Most individuals cannot buy enough bonds for proper diversification and some analysts say that you must have $400,000 or even more. Probably the issue for concern is if you had to sell the bonds prior to maturity. Stocks have relatively liquid markets and a sale can usually take place quickly. But bonds do not have such a liquid market and a few bonds will demand a potentially severe discount.

BOND PRICING: (1999) (NY TIMES) "Last Tuesday, someone bought one or more Los Angeles County pension bonds due in June 2007. The bonds were of the zero-coupon variety, and the buyer paid dearly -- $613.23 for every $1,000 in face amount. Another buyer, the very same day, paid just $568.23 for the same bond. As a result, the first investor will get a yield to maturity of 5.79 percent while the second will get a yield of 6.71 percent." Why the difference? Because the first investor didn't know what he/she was doing. Why's that? Because bonds and bond pricing are far from the liquid, open and market of most equities.

"Unlike the stock market, where investors can scarcely avoid learning the latest prices, the municipal bond arena has long been cloaked in such mystery that just to ask about the detailed terms of an issue can be akin to breaking a fraternal taboo. And some brokers have used this secrecy to mark up muni bonds by big amounts."

"There's this perception that bonds are more risky than stocks" because so little specific information about issuers and the trading markets reaches the investing public."

Bond Index Funds (Indexfundsonline) (2000) bond index funds consistently beat actively managed funds by 0.7% or 0.8% annually. In large part this is because bond fund managers have great difficulty beating the indexes, even more so than do stock fund managers. Unlike stock funds, bond funds vary little in their gross returns. Once an investor has chosen a level of credit quality and average maturity, most bond funds will have a similar gross yield-the yield before expenses. It is really expenses more than anything that differentiates bond funds, and it is index funds that are the leaders in keeping expenses down. "The investment-grade bond area, with high-quality, highly liquid securities, is an ideal place for index investing. There's very little a manager can do. There's no surer way to outperform among high-quality bond funds than to have smaller expenses." Indexing also lends itself especially well to shorter-term corporate and U.S. government bonds, where active managers have still fewer opportunities to outperform the indexes. Also, bond index funds are frequently more diversified than actively-managed bond funds.

Bond index funds are probably not the best investment vehicles for wealthy individual investors. In general, tax-exempt municipal bonds are probably best for those whose combined federal and state tax bracket is over 28%.

Advantages of Bond Index Funds Over Buying Bonds Directly: (Indexfundsonline 2000)

Bigger is better in Bonds: There are numerous benefits to being very well-capitalized when buying bonds, including volume discounts and invitations to closed auctions. Ordinary investors can rarely take advantage of these benefits.

Lower Investment Amounts: The minimum investment for an individual bond can be as high as $10k. Realistically it probably takes about $50k to build a diversified and cost-effective portfolio of bonds. On the other hand, the minimum investment in a bond index fund is usually $500 or $1000. And a mutual fund investor can often buy addition fund shares in increments as low as about $10.

Regular Monthly Income:  Most bond index funds distribute dividends monthly. Investors may choose to receive them as cash or have them automatically reinvested. Individual bonds usually pay interest only every six months and these payments cannot be reinvested automatically. This is often an important consideration, especially for retirees.

Even "passive" bond index funds enjoy the benefits of fixed-income analysts; Vanguard has six such analysts who decide which bonds to buy and sell for their index funds and actively-managed funds. These analysts are important because few investors have the time or the expertise to manage their personal investments or to investigate all the different bonds on the market.  And investors often underestimate the complexity of global fixed-income securities markets.

Lower Commissions in Most Cases: When an investor buys individual bonds through a broker, he pays a commission that's usually hidden; the quoted bond price includes a substantial commission. The smaller the investment, the greater the commission. On a $1000 bond the commission can be 5%. Sometimes the hidden costs for these bonds appear quite cryptic. Jason Zweig of Money Magazine said, "if you have $100k you're better off buying a bond fund than individual bonds because most bond brokers take an 'invisible spread' which lowers yield."

Daily Liquidity :Investors may buy and sell shares in a bond index fund on any business day. And the market for shares in many bond index funds is highly liquid. Also, most bond index funds offer options such as check writing and telephone redemption to make bond investing more convenient.

Bond index funds Outperform Inflation-indexed Bonds in a Low-inflation Environment : According to Morningstar, when inflation is low the principal of the inflation-indexed bond would remain the same and the yield would decrease. Simultaneously the net asset value (NAV) of the bond index fund would increase, but the yield would decrease. This scenario favors bond index funds.

Bond statistics 2001:

Bond Sector

Last 1-year return, %

7-year ann. return, %

7-year ann. std. dev., %¹

Government bonds

12.3 7.5 3.8

Investment-grade corporate bonds

12.4

7.7

4.7

Mortgage-backed securities

12.6

7.8

3.1

High-yield bonds

2.5

6.7

5.8

Emerging market bonds

8.4

12.5

15.9

Non-U.S. dollar bonds

-5.4 3.6 8.2

¹A statistical measure of the variability of securities returns. The higher the standard deviation, the riskier the security.

CREDIT RATINGS

CREDIT RISK

Moody's

Standard & Poor's

Fitch

Duff & Phelps

INVESTMENT GRADE

Highest quality

Aaa

AAA

AAA

AAA

High quality (very strong)

Aa

AA

AA

AA

Upper medium grade (strong)

A

A

A

A

Medium grade

Baa

BBB

BBB

BBB

NOT INVESTMENT GRADE

Lower medium grade (somewhat speculative)

Ba

BB

BB

BB

Low grade (speculative)

B

B

B

B

Poor quality (may default)

Caa

CCC

CCC

CCC

Most speculative

Ca

CC

CC

CC

No interest being paid or bankruptcy petition filed

C

C

C

C

In default

C

D

D

D

10-year annualized return

10-year annualized std. deviation³

Short-term U.S. Government Bonds¹

6.44%

1.64%

Long-term U.S. Government Bonds²

9.99%

7.68%

¹Represented by the Lehman Brothers 1-3 Year U.S. Treasury Index, with a 1.65-year average duration.
²Represented by the Lehman Brothers Long-term U.S. Government Index, with a 10.94-year average duration.
³A statistical measure of the variability of securities returns. The higher the standard deviation, the riskier the security.

Consider a bond with a yield to maturity of 4% and duration of 5.8 under three hypothetical scenarios: (2004)

Interest rates decline. If interest rates decline by one percentage point a year over the next two years from 4% to 2%, bond prices would get a significant boost. In the next 12 months, the combination of the bond's interest income and rising price would produce a total return of 8.8%. Over time, however, as the bond's interest payments are reinvested at 2%, the bond's long-term return would decline. After seven years, the bond would have produced an annualized return of 3.8%.

Interest rates remain unchanged. If interest rates remain at 4% throughout the holding period, the bond would produce an annual total return of 4%, whether the security is held for one year or ten.

Interest rates rise. If interest rates rise from 4% to 6% by one percentage point per year, bond prices would decline. In the next 12 months, the bond's total return—price change plus reinvested income—would be –0.8%. As the coupons are reinvested at higher yields, however, long-term returns would rise. After seven years, the bond would have produced an annualized return of 4.2%, outpacing the returns earned in both the unchanged and falling-rate environments.

HOLDING PERIOD RETURNS: (2004)

CONVENTIONAL TREASURIES VS. INFLATION-PROTECTED BONDS

  Inflation rate                  Nominal Return                                                   Real Return

                                      Traditional bond Inflation-Protected Bond     Traditional Bond   Inflation-Protected Bond

10                                 4.8                                     12.1                       (5.2)                   2.1

6                                   4.8                                       8.1                       (1.2)                     2.1

5                                   4.8                                       7.1                       (0.2)                    2.1

4                                   4.8                                       6.1                        0.8                      2.1

3                                  4.8                                        5.1                       1.8                        2.1

2                                  4.8                                        4.1                       2.8                        2.1

1                                  4.8                                        3.1                        3.8                        2.1

0                                 4.8                                         2.1                       4.8                         2.1

-1                               4.8                                         1.1                        5.8                         2.1

-2                              4.8                                           0.1                       6.8                           2.1

Source: adapted from "Inflation-Protection Bonds"

BOND VOLATILITY LINK: Excess Sensitivity and Volatility of Long Interest Rates: The Role of Limited Information in Bond Markets (Beechey, Meredith, Department of Economics, University of California, Berkeley PDF)

Empirical work shows that forward rates up to 15 years ahead respond to today's news about inflation and output and exhibit as much volatility at long horizons as at short.

Against the benchmark predictions of a macroeconomic model with time-invariant parameters and fully informed agents, these behaviours are puzzling. Models incorporating backward-looking behaviour still have difficulty reproducing the lengthy response of long rates.

Revision of long-run inflation expectations prompted by the revelation of such information seems a likely candidate for explaining the behaviour described above. This view is supported by findings in the empirical finance literature that much of the variation in the term structure is due to changes in expected inflation.

Volatility of Bond Returns

Table shows the variance of quarterly changes in constant maturity bonds in the United States from 1981 to 2004. The volatility of bond returns declined substantially in the 1990s.

Table 2: Volatility of returns on U.S. Treasuries, 1981Q1 to 2004Q3

Maturity (years) 1981Q1 - 2004Q3 1981Q1 - 1989Q4 1990Q1 - 2004Q3

1                        0:74                       1:51                         0:27

2                        0:72                       1:35                         0:34

5                        0:61                       1:06                          0:33

10                      0:46                        0:82                        0:24

30                      0:37                        0:67                        0:15

Notes: Volatility is calculated as the variance of the quarter-to-quarter change in the reported bond yield. Data are end quarter observations March, June, September, December. Missing data March 2002 to end of sample. Source: Board of Governors

Bond defaults: (2005) The historic default rate for Aaa-rated securities is very low. The average default rate from 1970- 2000 for Aaa-rated securities over a 10-year period was only 0.67%, well under 1%. However, as one descends the rating scale into the speculative-grade section, the default rate increases dramatically. For B-rated securities, the 10-year probability of default is 44.57%.

Survivor's Option or Death Put Bonds (as of June 2005)

Issuer                            Survivor's Option Eligibility Annual Put Limits (Greater of)            Individual Put Limits (annual)

Federal Home Loan Mortgage Corp 12 mos. After issuance date $1MM or1% of outstanding aggregate $200,000

Caterpillar Power Notes 12 mos. After issuance date $1MM or 1% of outstanding aggregate $200,000

UPS Notes 12 mos. After issuance date $1MM or 1% of outstanding aggregate $200,000

TVA Electronotes 12 mos. After issuance date $1MM or 1% of outstanding aggregate $200,000

Lasalle Notes 12 mos. After issuance date $1MM or 1% of outstanding aggregate $200,000

Marshall & Illsley Notes 12 mos. After issuance date $1MM or 1% of outstanding aggregate $200,000

John Hancock Signature Notes 12 mos. After issuance date $1MM or 1% of outstanding aggregate $200,000

AGF income Notes 12 mos. After issuance date $1MM or 1% of outstanding aggregate $200,000

ILFC Notes 12 mos. After issuance date $1MM or 1% of outstanding aggregate $200,000

IBM Notes 12 mos. After issuance date $1MM or 1% of outstanding aggregate $200,000

Bank of America Internotes Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate $250,000

Daimler Chrysler Internotes Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate $250,000

Boeing Capital Corp Internotes Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate $250,000

Dow Internotes Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate $250,000

PHH Internotes Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate $250,000

CIT Internotes Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate $250,000

Merrill Lynch CoreNotes Owned by decedant/estate 6 mos. prior to request $5MM or 5% of outstanding aggregate $500,000

Gillette CoreNotes Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate $250,000

Bank of New York CoreNotes Owned by decedant/estate 6 mos. prior to request $5MM or 5% of outstanding aggregate $500,000

General Mills CoreNotes  Owned by decedant/estate 6 mos. prior to request $5MM or 5% of outstanding aggregate $500,000

GE Capital Internotes Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate $250,000

Household Internotes (issued after 5/29/02) Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate

                                                                                                                                                                    $250,000

Sears Roebuck Accpt Corp Internotes Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate

                                                                                                                                                                                                                     $250,000

Wells Fargo & Co CoreNotes Owned by decedant/estate 6 mos. prior to request $5MM or 5% of outstanding aggregate $500,000

Principal Life CoreNotes Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate $250,000

Protective Life Internotes Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate $250,000

Prudential Internotes Owned by decedant/estate 6 mos. prior to request $2MM or 2% of outstanding aggregate $250,000

Ford Motor Credit Co. Owned by the decedant for 6 mos. $2MM or 2% of outstanding aggregate $250,000

Diageo Notes Owned by the decedant for 12 months $2MM or 2% of outstanding aggregate $250,000

GMAC Smart Notes Anytime after date of issuance $1MM or 1% of outstanding aggregate $200,000