Fixed Income Securities: Valuation, Risk, and Risk Management

CHAPTER 2

BASICS OF FIXED INCOME SECURITIES

2.1   DISCOUNT FACTORS

Receiving a dollar today is not the same as receiving it in a month or in a year. There are numerous reasons why people would like to have money today rather than in the future. For one, money today can be put in a safe place (a bank or under the mattress) until tomorrow, while the opposite is not easily doable. That is, money in hands gives its holder the option to use it however he or she desires, including transferring it to the future through a deposit or an investment. This option has a value on its own. If we agree that households and investors value $1 today more than $1 in the future the question is then how much $1 in the future is worth in today’s money. The value of what $1 in the future would be in today’s money is called the discount factor. The notion of discount factors is at the heart of fixed income securities.

It is easiest to introduce the concept by looking at a concrete example. The U.S. government, as with most governments, needs to borrow money from investors to finance its expenses. As discussed in Chapter 1, the government issues a number of securities, such as Treasury bills, notes, and bonds, to investors, receiving money today in exchange for money in the future. The U.S. Treasury is extremely unlikely to default on its obligations, and thus the relation between purchase price and payoff of U.S. Treasury securities reveals the market time value of money, that is, the exchange rate between ...