Chapter 2

Fixed Income Securities

What's past is prologue.

—William Shakespeare, The Tempest

A security is a financial asset that yields a measurable payoff, which may be state dependent (for example, it pays $1 if it rains and zero otherwise). The return to the security is the percentage change in the security's value over some well-defined period of time. That return is fixed if payoffs do not vary over the life of the asset. Bonds are securities paying fixed payoffs (coupons). U.S. Treasuries are the least risky bonds because they have the smallest relative likelihood of defaulting on their payoffs. Corporate and municipal bonds are generally riskier because they do not have the power of the federal government (the taxpayer) to guarantee that bondholders will receive the promised payoffs. Bond market participants will therefore pay close attention to bond rating agencies like Standard & Poor's, Moody's, and Fitch when pricing the present value of future coupon streams. Credit risk is covered in more detail in Chapter 11.

In general, a bond is a loan; the holder of the bond is a creditor and the original seller of the bond is the borrower. In the case of government bonds, creditors have a claim on taxpayers (unless the government defaults on its debt). In the case of the corporate bond, the bondholder (creditor) has a claim to the assets of the firm and their claims generally are senior to shareholders (holders of equity, or stock). Thus, there are risks that cash flows like coupons or principal will not be paid and, as a result, bondholders may seek to insure their claims by holding credit default swaps. Credit default swaps are similar to insurance policies. Buying and selling credit default swaps is commonly referred to as buying and selling protection. If the borrower defaults, then the creditor collects on the credit default swap, which allows them to partially or fully hedge their loss. The CDS market is large and generally unregulated, which was partly responsible for the collapse of credit markets in 2008 (for example, the insurance giant AIG defaulted on billions of dollars in CDS contracts that they underwrote for bondholders).

We can categorize fixed income securities into the following categories:

Savings deposits (demand deposits, time deposits, and CDs), which earn a fixed interest payment.

Money market instruments, which are short-term securities of maturity less than a year. These include commercial paper (unsecured corporate borrowing) and to a lesser extent, bankers’ acceptances as well as Eurodollars (dollar-denominated deposits in European banks).

U.S. government securities, which we discuss further on.

Mortgages, which are a fixed income security to the lender—the monthly mortgage payment performs in much the same way as a coupon payment.

Other miscellaneous bonds such as municipals and corporate bonds.

Annuities (consols in Great Britain), which pay a perpetual (infinite) coupon.

We will learn how to price these securities.

Let's concentrate first on U.S. government securities, which are issued through the U.S. Treasury to finance government expenditures (for example, if Congress appropriates $100 billion in expenditures in a fiscal year, but collects only $50 billion in tax revenues, then they must borrow $50 billion. They do this through their agent, the U.S. Treasury). Treasuries (U.S. government securities), come in two basic types: those that mature in one year or less and pay only the face value (but no coupon), and those that mature in more than one year that pay face value at maturity in addition to periodic coupon payments. The former are referred to as Treasury bills while the latter are either Treasury notes (10 years maturity or less) or Treasury bonds. Only bills pay no coupons. These are therefore referred to as zero coupon bonds, or, for short, just zeros. They are sold at discount (through Treasury auctions) and perhaps later through secondary bond markets. Let's do these first, since they are easiest.

First, a word on notation: Let P be the price, C the cash flow to the holder, and r, the interest rate—the bond's yield to maturity. Consider then the simple case in which the government desires to borrow $100 for one year. That is, suppose the Treasury prints up a bond certificate with a face value of $100 to be paid to the holder in one year at maturity. This is the principal. Suppose that the outcome of a sealed bid auction is that someone will agree to purchase this paper for $90 now and in one year, will redeem it for its face value at maturity ($100).

Then that person has bought this zero at discount for 90 and earns:

Thus, the return on this bond, if held to maturity, is 11 percent. This is also called the yield on the bond. If the market price were $95 instead, then this would generate a yield of about 5.26 percent. Notice that the bond's price and return are inversely related. This means that, in general, if the Treasury borrows more, the supply of bonds rises, driving down their market prices, which increases their yields.

Looked at differently,

Here, we see that the market price of the bond is the discounted present value of C; P represents the price bid to receive $100 one year from now. In equilibrium, market forces price this bond at $90 because the investor could alternatively have lent out her $90 at a rate of 11 percent, earning $100 in one year on an investment of equivalent risk. So, a willingness to buy this bond for more than $90 is irrational because the investor is earning a relatively lower rate of return.