The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition

ARBITRAGE-FREE BOND VALUATION

The traditional approach to valuation is to discount every cash flow of a bond using the same interest rate. This approach to valuation was described in Chapter 17. The fundamental flaw of this approach is that it views each security as the same package of cash flows. For example, consider a five-year U.S. Treasury note with a 6% coupon rate. The cash flows per $100 of par value would be nine payments of $3 every six months and then payments of $103 for 10 six-month periods. The traditional practice would discount every cash flow using the same discount rate regardless of when the cash flows are delivered in time and the shape of the yield curve. Finance theory tells us that any security should be thought of as a package or portfolio of zero-coupon bonds.

The proper way to view the five-year 6% coupon Treasury note is as a package of zero-coupon instruments whose maturity value is the amount of the cash flow and whose maturity date coincides with the date the cash flow is to be received. Thus, the five-year 6% coupon Treasury issue should be viewed as a package of 10 zero-coupon instruments that mature every six months for the next five years. This approach to valuation does not allow a market participant to realize an arbitrage profit by breaking apart or “stripping” a bond and selling the individual cash flows (i.e., stripped securities) at a higher aggregate value than it would cost to purchase the security in the market. Simply put, arbitrage ...