10/29/08

Negative Bond Yields

I received a great question from a reader. He noted that a few weeks ago, news articles about the financial panic stated that short term Treasury Bills had negative yields for a brief time. He could not quite understand this, and thought perhaps that it was a mistake. Take a dividend paying stock, he said. The yield you get on it is the annualized dividend payment divided by the purchase price. The lowest it can be is zero, and that's when the stock doesn't pay dividends. A negative yield means you're paying someone else money, and that just doesn't make sense.

The reader is absolutely right about stock dividend yields. They cannot be lower than zero (ok, so this isn't necessarily true either. Example: you own a business. It gets into some trouble and is sued. The court rules against you, but your business doesn't have enough capital to pay the judgment. In certain cases--when the judge is angry, basically--the court can "pierce the corporate veil." The shareholders can be held liable and be forced to pay up. I doubt this would ever happen with a stock you buy on one of the major exchanges. Another example is just a vocabulary distinction--it depends on what you mean by yield. I discuss this below.) With bonds, on the other hand, yields can be negative and you end up losing money, even when you hold to maturity.

There are two types of bonds, those that have a coupon and those that don't. The coupon is the interest the bond pays. The face value of the bond is the sum the bond holder will receive when the bond matures. So, for example, when a bond with the face value of $1,000 matures, the debtor will pay the bond holder $1,000.

Bonds without coupons are typically sold below face value. For example, a bond with the face value of $1,000 is sold for $900. When the bond matures, the bond holder receives $1,000. He gets a return of $100, or an 11.11% gain. The yield on this bond, we can say, is 11.11% (if you factor in time in years when calculating the yield, you may get a different answer. Suppose you get that 11.11% gain in a month. Your annualized, non-compounded return is actually 133.32%. Or say you get that return over two years. Your yield on that bond is 5.55%).

But suppose the bond is in great demand (because of its safety, etc) and investors are willing to pay more than $1,000 for it. When it matures, they get $1,000. Since they paid more, then end up losing money, and the bond has a negative yield. Suppose they paid $1,100 for it. The yield is negative 10% (for a holding period of a year).

The short term Treasury Bills (maturities range from a few days to one year), or T Bills, have no coupon and usually sell below face value. Their return, upon maturity, is the difference between purchase price and face value. Panic striken investors were willing to pay slightly more than face value, recently. They preferred losing a known amount of money in the safety of Treasury Bills than possibly lose everything if the financial system suddenly collapsed. The newspapers were not in error when they reported that yields on short term Treasuries were slightly negative.

Bonds that have coupons, that is, bonds that pay interest in installments, can also have a negative yield. Suppose a bond with a face value of $1,000 will pay $60 in interest before it matures. If you buy that bond for $1,000, you'll get a yield of 6%. But if you pay more than $1,060, you'll get a negative yield if you are unable to sell it for more than you paid and end up holding it until maturity. That's because when the bond matures, you'll be paid $1,000.

As this may be confusing, it might be helpful to distinguish between the different types of gains and losses you can get with a bond, and thus different types of yields. The above makes no distinctions.

Bonds can produce capital gains and losses. If you sell a bond for higher than you bought it, you get a capital gain. If you sell a bond for lower than you paid for it, you get a capital loss.

Bonds can also produce income gains and losses. These are the interest payments bond holders receive. While it is possible that investors might be willing to pay the bond issuer interest payments, this is highly unlikely. So, generally speaking, bond income can only be positive. If you take "yield" to mean interest payments paid before the bond matures, then a bond's yield cannot be negative. We can call this "current yield." It is distinct from what we can call "yield to maturity," which is face value minus purchase price plus interest payments.

But didn't I just say that yields can be negative, as in the example of short term Treasuries? Yes. I guess it's only a vocabulary distinction. On T Bills, the yield is the difference between face value and purchase price. That is to say, current yield and yield to maturity are conflated when short term Treasuries are discussed. Perhaps we can think of our returns on them as short term (less than one year) capital gains or losses. This is the same as ordinary income. So it makes sense to say that the yields on these bonds can be negative.

Please email me or leave a comment for further questions or to point out any mistakes above.