Zero Coupon Bonds. Municipal bonds may include zero-coupon bonds. Zero coupon bonds are securities that are sold at a discount to par value and do not pay interest during the life of the security. The discount approximates the total amount of interest the security will accrue and compound over the period until maturity at a rate of interest reflecting the market rate of the security at the time of issuance. Upon maturity, the holder of a zero coupon bond is entitled to receive the par value of the security. While interest payments are not made on such securities, holders of such securities are deemed to have received income ("phantom income") annually, notwithstanding that cash may not be received currently. The effect of owning instruments that do not make current interest payments is that a fixed yield is earned not only on the original investment but also, in effect, on all discount accretion during the life of the obligations. This implicit reinvestment of earnings at a fixed rate eliminates the risk of being unable to invest distributions at a rate as high as the implicit yield on the zero coupon bond, but at the same time eliminates the holder's ability to reinvest at higher rates in the future. For this reason, some of these securities may be subject to substantially greater price fluctuations during periods of changing market interest rates than are comparable securities that pay interest currently. Longer term zero coupon bonds are more exposed to interest rate risk than shorter term zero coupon bonds. These investments benefit the issuer by mitigating its need for cash to meet debt service, but also require a higher rate of return to attract investors who are willing to defer receipt of cash. The Fund accrues income with respect to these securities for U.S. federal income tax and accounting purposes prior to the receipt of cash payments. Zero coupon bonds may be subject to greater fluctuation in value and less liquidity in the event of adverse market conditions than comparably rated securities that pay cash interest at regular intervals. Further, to maintain its qualification for pass-through treatment under the federal tax laws, the Fund is required to distribute income to its shareholders and, consequently, may have to dispose of other, more liquid portfolio securities under disadvantageous circumstances or may have to leverage itself by borrowing in order to generate the cash to satisfy these distributions. The required distributions may result in an increase in...
Zero Coupon Bonds. A zero coupon bond (or discount bond) for maturity T is an instrument which pays $1 T years from now. We denote its market value by P (0, T ) > 0. It is thus the present value (abbreviated PV) of $1 guaranteed to be paid at time T . The market does not contain enough information in order to determine the prices of zero coupon bonds for all values of T , and arbitrary choices have to be made. Later in this lecture we will discuss how to do this in ways that are consistent with all the available information. In the meantime, we will be using these prices in order to calculate present values of future cash flows (both guaranteed and contingent), and refer to P (0, T ) as the discount factor for time T . Consider a forward contract on a zero coupon bond: at some future time t < T , we deliver to the counterparty $1 of a zero coupon bond of final maturity T . What is the fair price P (t, T ) paid at delivery? We calculate it using the following no arbitrage argument which provides a risk-free replication of the forward trade in terms of spot trades.
