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Part One
The Relative Pricing of Securities with Fixed Cash Flows
Consumers and businesses are willing to pay more than $1 in the future in exchange for $1 today. A newly independent adult borrows money to buy a car today, agreeing to repay the loan price plus interest over time; a family takes a mortgage to purchase a new home today, assuming the obligation to make principal and interest payments for years; and a business, which believes it can transform $1 of investment into $1.10 or $1.20, chooses to take on debt and pay the prevailing market rate of interest. At the same time, this willingness of potential borrowers to pay interest attracts lenders and investors to make consumer loans, mortgage loans, and business loans. This fundamental fact of financial markets, that receiving $1 today is better than receiving $1 in the future, or, equivalently, that borrowers pay lenders for the use of their funds, is known as the time value of money.
Borrowers and lenders meet in fixed income markets to trade funds across time. They do so in very many forms: from one-month U.S. Treasury bills that are almost certain to return principal and interest to the long-term debt of companies that have already filed for bankruptcy; from assets with a simple dependence on rates, like Eurodollar futures, to callable bonds and swaptions; from assets whose value depends only on rates, like interest rate swaps, to mortgage-backed securities or inflation-protected securities; and from fully taxable private-sector debt to partially or fully tax-exempt issues of governments and municipalities.
To cope with the challenge of pricing the vast number of existing and potential fixed income securities, market professionals often focus on a limited set of benchmark securities, for which prices are most consistently and reliably available, and then price all similar assets relative to those benchmarks. Sometimes, as when pricing a UK government bond in terms of other UK government bonds, or when pricing an EUR swap in terms of other EUR swaps, relative prices can be determined rigorously and for the most part accurately by arbitrage pricing. This methodology is developed in Chapter 1, where it is also shown that discounting, i.e., calculating present values with discount factors, is really just shorthand for arbitrage pricing.
While discount factors in many ways solve the relative pricing problem, they are not very intuitive for understanding the time value of money that is embedded in market prices. For this purpose, markets rely on spot, forward, and par rates. Chapter 2 introduces these rates and derives the relationships linking them to each other and to discount factors. The trading case study in Chapter 2, inspired by an abnormally shaped EUR forward swap curve, illustrates how fixed income analytics, market technicals (due to institutional factors described in the Overview), and a macroeconomic setting all contribute to a trade idea.
While the interest rates of Chapter 2 provide excellent intuition with respect to the time value of money embedded in market prices, other quantities provide intuition with respect to the returns offered by individual securities. The first half of Chapter 3 defines returns, spreads, and yields. Spreads describe the pricing of particular securities relative to benchmark government bond or swap curves and yields are the widely used, although somtimes misunderstood, internal rates of return on individual securities. The second half of Chapter 3 breaks down a security's return into several component parts. First, how does the security perform if rates and spreads stay the same? Second, how does the security perform if rates change? Third, how does the security perform if spreads change?
Given the central role of benchmarks in Part One, it is worth describing which securities are used as benchmarks and why. Until relatively recently, benchmark curves in U.S. and Japanese markets were derived from the histori...
