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The relative pricing of securities with fixed cash flows

  • Wiley Global Finance WILEY GLOBAL FINANCE
  • Bonds
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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.

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.

While the interest rates discussed provide excellent intuition with respect to the time value of money embedded in market prices, other quantities provide intuition with respect to the returns offer by individual securities. Spreads describe the pricing of particular securities relative to benchmark government bond or swap curves and yields are the widely used, although sometimes misunderstood, internal rates of return on individual securities.

Given the central role of benchmarks for relative pricing, 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 historically most liquid markets, that is, from government bond markets. Recently, however, the benchmark has shifted significantly to swap curves. European markets, on the other hand, have for some time relied predominantly on interest rate swap markets for benchmarks because their swap markets have been, on average across the maturity spectrum, more liquid than government bond markets.

It is not hard to understand why government bond and interest rate swap markets are the preferred choices for use as benchmarks. First, they are the most liquid markets, consistently providing prices at which market participants can execute trades in reasonable size. Second, they incorporate information about interest rates that is common to all fixed income markets. The value of a corporate bond, for example, depends on the interest rate information embedded in the government bond or swap curve in addition to depending on the credit characteristics of the individual corporate issuer.

But what about the choice between government bond and swap curves as benchmarks? Historically, government bonds were the only choice because swaps did not exist until the early 1980s and it took some time for their liquidity to become adequate. But bond markets have a significant disadvantage when used as a benchmark, namely that an individual bond issue is not a commodity in the sense of being a fungible collection of cash flows: bond issues are in fixed supply and have idiosyncratic characteristics. The best-known examples of nonfungibility are on-the-run U.S. Treasury bonds that trade at a premium relative to other government bonds because of their superior liquidity and financing characteristics. Put another way, pricing with a curve that is constructed from “similar” bonds, which are not on-the-run bonds, will underestimate the prevailing prices of on-the-runs. By contrast, an interest rate swap is really a commodity, that is, a fungible collection of cash flows. A 10-year, 4% interest rate swap cannot possibly be in short supply because any willing buyer and seller can create a new contract with exactly those terms. In fact, market practice bears out this distinction between bonds and swaps. While bond traders set prices for each and every bond they trade (although they certainly may use heuristics relating various prices to each other or to related futures markets), swap traders strike a curve that is then used to price their entire book of swaps automatically.

In short, global fixed income markets currently use interest rate swaps as benchmarks or base curves and build other curves from spreads or spread curves on top of swap curves. Even in the liquid U.S. Treasury market, strategists assess relative value using spreads of individual Treasury issues against the USD swap curve.


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Article copyright 2011 by Bruce Tuckman and Angel Serrat. Reprinted and adapted from Fixed Income Securities: Tools for Today’s Markets, 3rd Edition with permission from John Wiley & Sons. The statements and opinions expressed in this article are those of the author. Fidelity Investments® cannot guarantee the accuracy or completeness of any statements or data. This reprint and the materials delivered with it should not be construed as an offer to sell or a solicitation of an offer to buy shares of any funds mentioned in this reprint.
The data and analysis contained herein are provided "as is" and without warranty of any kind, either expressed or implied. Fidelity is not adopting, making a recommendation for or endorsing any trading or investment strategy or particular security. All opinions expressed herein are subject to change without notice, and you should always obtain current information and perform due diligence before trading. Consider that the provider may modify the methods it uses to evaluate investment opportunities from time to time, that model results may not impute or show the compounded adverse effect of transaction costs or management fees or reflect actual investment results, and that investment models are necessarily constructed with the benefit of hindsight. For this and for many other reasons, model results are not a guarantee of future results. The securities mentioned in this document may not be eligible for sale in some states or countries, nor be suitable for all types of investors; their value and the income they produce may fluctuate and/or be adversely affected by exchange rates, interest rates or other factors.

In general, the bond market is volatile, and fixed income securities carry interest rate risk. (As interest rates rise, bond prices usually fall, and vice versa. This effect is usually more pronounced for longer-term securities). Fixed income securities also carry inflation risk, liquidity risk, call risk and credit and default risks for both issuers and counterparties. Lower-quality fixed income securities involve greater risk of default or price changes due to potential changes in the credit quality of the issuer. Foreign investments involve greater risks than U.S. investments, and can decline significantly in response to adverse issuer, political, regulatory, market, and economic risks. Any fixed-income security sold or redeemed prior to maturity may be subject to loss.

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