# SOME USES OF YIELD-TO-MATURITY STATISTICS I

I can think of four uses of (street convention) yields to maturity. First, yields can be used to price bonds. That means there is a one-to-one mapping, given the schedule of coupon and principal cash flows, between the price of a bond (including accrued interest, which we get to soon) and the yield to maturity. If you know the yield, you can unambiguously get the price, and vice versa. Therefore, bonds can trade on either a yield basis or a price basis. In practice, dealers usually quote just bid-and-ask prices and perhaps provide bid-and-ask yields for reference. An example of trading on a yield basis is the when-issued market before Treasury note and bond auctions. The outcome of the auction determines the particular coupon rate, so buying and selling on a when-issued basis sets the yield for the transaction. The corresponding price is calculated later once the results of the auction are known and the coupon rate is set.

Second, yields to maturity can be used to compare bonds for relative value, either as investments or as sources of borrowed funds. For this purpose, it is essential to convert securities having varying coupon payment frequencies to a common periodicity, usually a semiannual bond basis, before comparison. Issuers also should include the financing costs in their analysis to assess the all-in cost of funds. If the bonds that are being compared contain call or put options, their respective yields to maturity no longer matter – they are data but not information. Then additional work is needed to value those embedded options to arrive at option-adjusted yields and option-adjusted spreads (over the benchmark Treasuries).

Third, yields to maturity can be used to project the future value of investments – hopefully with careful attention to assumptions. Suppose a wealthy investor buys our 4-year, 4% corporate bond yielding 4.182% for a par value of \$10,000,000, paying \$9,934,200. This investment will grow to a total return of \$11,703,200 – if there is no default by the issuer and if each annual \$400,000 interest payment is reinvested at 4.182%. But suppose the yield curve is projected to be stable and upwardly sloped over the next few years. Then how reasonable is that reinvestment assumption? Shouldn't you assume lower reinvestment rates as you slide down the yield curve and the time to maturity shortens? Suppose you are not so wealthy and are only able to buy bonds for a par value of \$10,000 so that you receive just \$400 in coupon interest each year. Will you be able to reinvest that amount at 4.182% if the minimum denomination for a bond is \$1,000? In that case, maybe you should assume a lower, more conservative reinvestment rate, such as that available on money market securities.

Fourth, street convention yields to maturity often are used to calculate risk statistics for the bond. These risk statistics – duration and convexity in their various forms – aim to measure the sensitivity of the bond price to changes in market interest rates. This is a very important topic, which we go into in detail in Chapter 6.