Ever since the late 1970s, the public has been sensitive to interest rates and very much aware of fixed-income securities. All of a sudden, interest rates were double digit, and bonds were offering higher returns than equities.

The only trouble was, inflation was sometimes higher than the interest rates on bonds, which meant that an investor was receiving a negative total return (interest income less price depreciation) on the investment.

But interest rates rose through 1979 and into the early 1980s until the 1981-1982 recession broke the spiraling growth of inflation. Interest rates have fallen from their peak levels of January 1982, but the inflation rate has fallen even more.

Consequently, we now have a real interest rate (the nominal interest rate minus the inflation rate) of 7 1/2 percent or more, which is close to a historic high. This means that the returns on bonds are extremely attractive and that bonds definitely should be considered for investment.

A bond is a fixed-income security that represents debt. A corporation or a government may borrow money for a certain period of time (maturity). For the use of that money, a set, or fixed, fee (interest) is paid to the lender periodically over the life of the loan. When the loan expires, the borrower repays the amount borrowed (principal) plus any outstanding interest to the lender.

The amount of interest paid, or received, depends on three factors: the principal amount of money on which the interest is computed, the rate of interest that is charged and the length of time over which the interest will be calculated.

There are basically two major types of interest: One is simple interest, where the rate is always computed on an original principal. A type of simple interest is ordinary interest, which is computed on a 360-day year based on twelve 30-day months. Also under this type would be exact interest, where the rate is computed on a 365-day year or 366 days in leap year. Exact interest is used in computing the interest on U.S. Treasury notes and bonds. Simple interest is used in computing the interest on corporate, agency and municipal bonds.

The other major type of interest is compound interest, where the interest is computed and added to the principal periodically. When the interest is added to the principal, it becomes part of the principal. Future interest then is computed on this larger amount. Compound interest also may be computed on a 360-day or an exact 365/366-day basis.

To appreciate the real power of compounding, consider these facts: If the interest on a sum of money is compounded at the same rate every six months, that sum of money will double every 11.7 years if the interest rate is 6 percent, every 8.8 years at 8 percent and every 7.1 years if the interest rate is 10 percent. The compounding of interest is the key to U.S. Savings Bonds -- Series EE and also the zero-coupon bonds (which will be covered in a later article).

The market value of a bond is expressed as a percentage of $1,000. If a bond is quoted at 90, its value is $900. If it is selling at 105, the value will be $1,050. Should the bond be selling at par or 100, the price would be $1,000.

In looking at fixed-income securities, there is a confusing principle to understand; namely, that yields and prices move inversely.

The yield is the effective rate of return on the investment. A simple formula will help explain the relationship of price to yield.


P=the dollar price or value of a bond.

A=annual fixed income (coupon).

Y=yield or market rate of return (on a percentage basis) at a given time.

Therefore, if we have a bond with a 9 percent coupon returning a yield of 9 percent we see that the dollar price or value of the bond is expressed thusly: P=$90.00/.09.

If the market rate of return is 8 percent, the dollar value or the bond will be P=$90.00/.08=$1,125 (112 1/2).

And if the market rate is 10 percent, the dollar value is P=$90.00/.10=$900 (90).

We can conclude by saying that, if the dollar price goes up, the yield or rate of return will come down and, conversely, if the price goes down, the yield, or return, will rise. Actually, the price and yield changes are different aspects of the same phenomenon of an inverse mathematical relationship.

Two other important math concepts are current yield (CY) and yield to maturity (YTM). CY takes into account the coupon income received and the actual dollars invested. Consequently, if you pay $900 for a bond that has a 9 percent coupon, your current return is 10 percent:

$100=$90/$900, or 10 percent.

For the individual investor, current yield is probably the most important consideration, because most individuals are concerned about spendable income, and CY gives you that picture.

The bond tables carried in newspaper financial sections give this kind of information: ATT 10 3/8 90 10.5 98 7/8

Translated: an American Telephone & Telegraph bond with a coupon rate of 10 3/8 percent and a maturity of 1990 has a current yield of 10 1/2. The closing price was 98 7/8.

The yield expressed on common and preferred stocks is actually current yield. Quite simply in their case, it is the dividend divided by the cost per share. If you purchase a $20 stock that pays a $1.00 dividend, your yield, or current return, is 5.00 percent.

Yield to maturity considers the various aspects of the purchase price. YTM shows the effect of the capital gain on a bond when purchased at a discount from par ($1,000), or capital loss when a bond is purchased at a premium (above par). YTM takes into consideration the time to maturity, the price paid and the semiannual interest payments.

Consider a 20-year Treasury with a 9 percent coupon purchased at 90. The investor will receive $1,000 at maturity, which is $100 more than was paid. The appreciation between the purchase price and the par value (100) is called accumulation, or accretion, and is factored into the YTM.

Consider the same Treasury where the market value of the bond is 8 percent and the dollar value of the bond was $1,125.00. The premium ($125), or depreciation, must be taken into account when YTM is calculated, because the owners received $1,000 at maturity. This depreciation is called amortization.

By using bond tables or a computer, we arrive at the YTMs in our examples. First, the YTM of the 9 percent Treasury selling at 100 is 9 percent. Second, the YTM of the same bond selling at 90 (discount) is 10.8 percent, and when the same bond is selling at 112 1/2 (premium), the YTM is 7.76 percent.

Putting the CY & YTM in perspective, we see that, when a bond sells at a premium over the par value, the CY is the larger than the YTM because CY ignores the capital loss. When it sells at a discount from par value, the CY is smaller than the YTM because it ignores the capital gain. When purchased at par, both are the same.

Another aspect of YTM that is often overlooked is that YTM assumes that the coupon income is reinvested at the purchase yield semiannually and compounded over the life of the bond. Therefore, if investors are able to reinvest their coupon income and compound their return, YTM will be more important than current yield.

If the coupon income is reinvested at a higher yield than the purchase yield, then the YTM is greater than the original YTM. Conversely, if the future rates of reinvestment are made at yields lower than the purchase yield, the YTM will be less than the assumed YTM at the time of the original purchase.

Another point, as a method of measuring the amount of change in yield, basis points are used. A basis point is one one-hundredth of a percentage point.