Professor Ian Giddy's Foundations of Finance
Bonds and Yields: Highlights
- Fixed-income securities are distinguished by their promise to pay a fixed or specified stream of income to their holders. The coupon bond is a typical fixed-income security. Treasury notes and bonds have original maturities greater than one year. They are issued at or near par value, with their prices quoted net of accrued interest. Some T-bonds may be callable during their last five years of life.
- When bonds are subject to potential default, the stated yield to maturity is the maximum possible yield to maturity that can be realized by the bondholder. In the event of default, however, that promised yield will not be realized. To compensate bond investors for default risk, bonds must offer default premiums, that is, promised yields in excess of those offered by default-free government securities. If the firm remains healthy, its bonds will provide higher returns than government bonds. Otherwise the returns may be lower.
- Bond safety is often measured using financial ratio analysis. Bond indentures are another safeguard to protect the claims of bondholders. Common indentures specify sinking fund requirements, collateralization of the loan, dividend restrictions, and subordination of future debt.
- Callable bonds should offer higher promised yields to maturity to compensate investors for the fact that they will not realize full capital gains should the interest rate fall and the bonds be called away from them at the stipulated call price. Bonds often are issued with a period of call protection. In addition, discount bonds selling significantly below their call price offer implicit call protection.
- Put bonds give the bondholder rather than the issuer the option to terminate or extend the life of the bond.
- Convertible bonds may be exchanged, at the bondholder's discretion, for a specified number of shares of stock. Convertible bondholders "pay" for this option by accepting a lower coupon rate on the security.
- Floating-rate bonds pay a fixed premium over a reference short-term interest rate. Risk is limited because the rate paid is tied to current market conditions.
- Treasury bills are U.S. govemment-issued zero-coupon bonds with original maturities of up to one year. Prices of zero-coupon bonds rise exponentially over time, providing a rate of appreciation equal to the interest rate. The US IRS treats this price appreciation as imputed taxable interest income to the investor.
- Current yield is the coupon rate divided by price. It ignores capital gains or losses, so is a poor measure of the total return on a bond.
- The yield to maturity (or simply "yield") is the single interest rate that equates the present value of a security's cash flows to its price. Bond prices and yields are inversely related. For premium bonds, the coupon rate is greater than the current yield, which is greater than the yield to maturity. The order of these inequalities is reversed for discount bonds.
- The yield to maturity is often interpreted as an estimate of the average rate of return to an investor who purchases a bond and holds it until maturity. This interpretation is subject to error, however. Related measures are yield to call, realized compound yield, and expected (versus promised) yield to maturity.
Better Bond Pricing with Zero's
- Yield to maturity is often a poor measure of what a bond's giving you because it assumes one can reinvest coupons at the yield. Also, it measures a bond's price by discounting all cash flows (every coupon and the final principal) at the same rate, even when the yield curve is not flat.
- A better way to price bonds is to discount all their cash flows to the present using the appropriate zero-coupon rate for the cash flow's maturity. These zero-coupon rates can be obtained from two places:
- The market for Treasury "strips," which are zero-coupon bonds created by stripping conventional bonds into their component cash flows.
- By "bootstrapping," that is, finding by iteration the series of zero-coupon rates that best explain the prices of conventional coupon bonds.
Forward Interest Rates
- Implied forward rates are the rates that equate shorter-term rates, reinvested at the forward rate, with longer-term rates.
- According to the expectations theory of the term structure of interest rates, the forward rate is an unbiased estimator of the expected future short-term rate.
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