Lecture Notes in Fixed Income Fundamentals

The following sections are included:

• Preface
• Contents
• About the Author

One of the most basic concepts of finance is “time value of money”. Dollars, like quantities in physics, also have a measure of units other than the magnitude measure. This unit measure is the time at which the magnitude of money is available to you to be used. Financial markets offer investors the opportunity to invest their money rather than “keeping it idle”. If you have a certain amount of money, for example $1000, that you do not need now but only in a year, this money can be invested for a year. In most of this book we are concerned with risk-less investments, which means that there are no uncertainties about the return of the investment. It is fixed at the time the investment is made, and the likelihood that it will not be realized as promised is zero. While we shall touch on the meaning of “risk-free” investment in the next section, for now let us just take it for granted. The existence of such risk-free investment possibilities introduces the second dimension (unit) of monies, which is time. Assume that one can get r for each dollar invested for a year. If r for example is 10%, then $1000 today will grow to be 1000(1.10) or in general to 1000+1000r. Therefore $1000 today is not equivalent to $1000 a year from today. If one needs $1000 in a year, one only needs to have 1000(1+r)⁻¹. Given 1000(1+r)⁻¹ today and investing it for a year generates [1000(1+r)⁻¹](1+r) = 1000 which is the required amount. We see therefore that $X in a year is equivalent to today. is termed the present value of X. Similarly Y dollars today is equivalent to Y(1+r) in a year and the latter is termed the future value of Y. The conversion of dollars of a year from now to dollars of today is done by multiplying by (1+r)⁻¹, which is termed a discount factor. It is usually denoted by d with a sub index of the time. It is a discount factor for a year from now and will be denoted by d₁. The future value of a dollar in a year can thus be written also as .

In Chapter 1 we revisited the concept of time value of money and its relation to opportunity cost, but over a one period model. We did touch upon multi period models but only under the assumption that the interest rate from period to period is the same: a phenomena referred to as a flat term structure of interest rate.

In the last chapter we investigated the meaning of the discount factors and their relation to the NA condition, and valuing future cash flows utilizing the present value concept. Some financial instruments, that also fall into the class of derivative securities, are valued based on risk-free discount factors. The valuation concept of these instruments is induced by the noarbitrage condition. These securities are valued either by replication or by applying to their cash flow the discount factors.

This lecture is dedicated to the study of the sensitivity of the price of bonds and portfolios of bonds to the changes in the interest rates. A measure of the sensitivity of bond prices to changes in interest rates, called Duration, was first suggested by Macaulay in 1938. The field of fixed income securities has evolved tremendously since that time and the academic literature now criticizes this measure. As we proceed with the development and understanding of this measure we will also gain an insight into this critique.

In Chapter 1 we introduced the concepts of forward contracts in the realm of a one period model. The current chapter investigates contracts that depend on the term structure of interest rates in the framework of a multiperiod model. In this framework the chapter takes a second and more realistic look at forwards and introduces futures and Eurodollar contracts.

We have already been introduced to swaps in Chapter 1 where they were investigated in the framework of a one-period model. Here we take a second look at swaps in a more realistic multiperiod setting for which we have a continuum of states of nature in each period. This setting allows the investigation of one of the most common forms of swaps that could not been analyzed in Chapter 1. It will be followed by revisiting currency and equity swaps in a multiperiod setting. As before, the risk of default by the parties is ignored.

The following section is included:

• Index