Bond crash. Course.

I have decided I need to educate myself about bonds, with the goal of understanding what the h*ll John Jansen is talking about more often. I have a hunch this will be important, and possibly soon. We shall see how far I get.

I will hold myself up for ridicule by keeping my notes here on the blog. If I humiliate myself, I figure I can always erase the evidence later. Or pick a new pseudonym.

Right, here goes. I will start in my comfort zone and move further and further afield in later posts. Terms being defined are emphasized.

A bond is an instrument that gives its owner small payments at regular intervals for some amount of time, followed by a final large payment. The final large payment is the face value. The small periodic payments are the interest. The total time over which the payments are made is the maturity (not the “duration”, because that is something else entirely). The currency of the payments is the denomination. The entity promising to make the payments is the issuer.

The size of the interest payments is always described as a fraction (percentage) of the face value on a per-year basis. This percentage is called the coupon (not the “yield”, because that is something else entirely).

For example, a bond that pays you $200 every six months and then $10,000 at the end of 10 years would be described as a “dollar-denominated bond with $10,000 face value, 10-year maturity, and a 4% coupon payable semi-annually”.

All of these properties are specified at the time the bond is created. All of them are constants. (This is a simplification / lie. The coupon can be “variable-rate” instead of “fixed-rate”; the bond can be “callable”; and so forth. But I have to start somewhere.) You need to know all of them to know what the bond is. Bond traders sometimes (<-- MASSIVE UNDERSTATEMENT) abbreviate or omit pieces, but all of them are always stated either explicitly or implicitly for any bond. How much money you want to exchange for such a gadget depends on how soon you need that money, what your other options are for that money, how much money itself will be worth in the future, and, very importantly, how much you trust the promises of the issuer. Bonds trade in a market not unlike the stock market, but vastly larger and populated by smarter people. The price at which a bond trades is simply called its price, but nobody ever thinks about that, at least not directly. Instead, they take the current market price and ask themselves, “If I were to pay this price for that bond right now and hold it until maturity, what annual interest rate would a savings account have to offer me to provide the same return?” This hypothetical rate is called the bond’s yield, or to be precise, its yield to maturity.

For example, suppose you are looking at a zero-coupon bond with 10 year maturity and $10,000 face value. In other words, it pays no interest and then dumps $10,000 in your lap after ten years. If you were to pay $9,000 for that bond today, what would be your yield? Answer: 1.06%, because that is the annual rate a savings account would have to pay to turn $9000 into $10000 over ten years.

You can do this calculation yourself; for zero-coupon bonds, you learned the necessary math by seventh grade (unless you live in India or China, in which case it was second or third grade). A savings account paying interest rate y will multiply its balance by 1+y every year. Since we want to grow 9000 to 10000 over ten years, we need to solve 10000 = 9000*(1+y)^10. So divide through by 9000, take the 10th-root, subtract 1, and bam. If the bond had a non-zero coupon, the math would have no nice closed form, and you would use a bond calculator (or the IRR function on your spreadsheet).

Or you wouldn’t bother, because when people want to talk about bond prices, they almost always talk about yields to maturity instead.

I think that is enough for a first post. Next: price, yield, and duration.