Yield-to-maturity

Balance sheet 12/31/XX Debt, M After-tax yield to maturity, % After-tax weighted average cost, %... 

Each debt item in M divided by the total debt times the after-tax yield to maturity equals the after-tax weighted average cost contributing to the cost of capital. 

The general rule of corporate bonds is that they are priced at a spread to the government yield curve. In absolute terms, the yield spread is the difference between the yield to maturity of a corporate bond and the benchmark, generally a yield to maturity of a govermnent bond with the same maturity. Corporate bonds include a yield spread on a risk-free rate in order to compensate two main factors, liquidity premium and credit spread. The yield of a corporate bond can be assumed as the sum of parts of the elements as shown in Figure 8.1, in which the yield spread relative to a default-free bond is given by the sum of default premium (credit spread) and liquidity premium. 

Figure 8.2 shows the Bloomberg YAS page for Tesco bond SVi% 2019, as at October 9, 2014. The bond has a price of 109.345 and yield to maturity of 3.46%. On the date, the yield spread over a government bond benchmark UK 41 % Treasury 2019 is 200 basis points. The G-spread over an interpolated government bond is 181.5 basis points. Conventionally, the difference between these two spreads is narrow. We see also that the asset-swap spread is 173.6 basis points and Z-spread is 166.3 basis points. 

As explained in the introduction, the value of a convertible bond is the sum of two main components, the option-free bond and a call option on underlying security. The value of the option-free bond, or bond floor, is determined as the sum of future payments (coupon and principal at maturity). Therefore, the bond component is influenced by three main parameters, that is the maturity, the coupon percentage on par value and the yield to maturity (discount rate). Differently, the value of a call option can be found mainly through two option pricing models, Black Scholes model and binomial tree model. 

Bonds with embedded options are debt instruments that give the right to redeem the bond before maturity. As we know, the yield to maturity represents the key measure of bond s return (although, of course, it is an anticipated return that is seldom realised in practice). The calculation of the return is particularly easy for conventional bonds because the redemption date is known with certainty, as their value. In contrast, for callable bonds, but also for other bonds such as putable and sinking fund bonds, the redemption date is not known with certainty because the bonds can be redeemed before maturity. If we want to calculate... 

Yield to maturity This measure assumes that the bond is not called until the maturity date. Therefore, it is calculated as the yield of a straight bond ... 

Yield to worst This represents the most conservative yield measure. This is the minimum between the yield to maturity and yield to call for any date. 

The duration shows the bond s price sensitivity to its yield to maturity. The change in bond s price is plotted in a curve in which the duration represents the slope of the tangent at any point of the curve. Conversely, the effective duration, or also known as curve duration, shows the price sensitivity to the change of the benchmark yield curve or market yield curve. This duration is more suitable than Macaulay or modified duration for bonds with embedded options because the latter ones have not a well-defined yield to maturity. The effective duration is given by (11.1) ... 

The interest rate was not chosen arbitrarily the 5-year bond s yield to maturity (discussed shortly) is 2.975%. 

There are several yield measures commonly quoted by dealers and traders in the bond market. Among the more prominent are current yield, yield to maturity, yield to call, yield to worst, and cash flow yield. In this section, we will demonstrate how to compute various yield measures for a bond given its price. We will also highlight their limitations as measures of potential return. 

The most common measure of yield in the bond market is the yield to maturity. The yield to maturity is simply a bond s internal rate of return. Specifically, the yield to maturity is the interest rate that will make the present value of the bond s cash flows equal to its market price plus accrued interest (i.e., the full price). To find the yield to maturity, we must first determine the bond s expected future cash flows. Then we search by trial and error for the interest rate that will make the present value of the bond s cash flows equal to the market price plus accrued interest. 

At first blush, the yield to maturity appears to be an informative measure of a bond s potential return. It considers not only the coupon income but any capital gain or loss that will be realized by holding the bond to maturity. The yield to maturity recognizes the timing of the cash flows. It also considers the third source of euro return that we dis-... 

Consider a hypothetical 10-year bond selling at par ( 100) with a coupon rate of 7%. Assume the bond delivers coupon payments aimually. The yield to maturity for this bond is 7%. Suppose an investor buys this bond, holds it to maturity, and receives the maturity value of 100. In addition, the investor receives 10 annual coupon payments of 7 and can reinvest them every year that they received at an annual rate of 7%. What are the total future euros assuming a 7% reinvestment rate As demonstrated above, an investment of 100 must generate 196.72 in order to generate a yield of 7% compounded semiannually. Alternatively, the bond investment of 100 must deliver a total euro return of 96.72. 

This assumes that the bond in question pays semiannual cash flows. If the bond pays annual cash flows, the cash flows must be reinvested at the annual yield to maturity. 

Clearly, the investor will only realize the yield to maturity that is computed at the time of purchase if the following two assumptions hold ... 

Assumption 1 The coupon payments can be reinvested at the yield to maturity. 

With respect to the first assumption, the risk that an investor faces is that future interest rates will be less than the yield to maturity at the time the bond is purchased. This risk is called reinvestment risk. As for the second assumption, if the bond is not held to maturity, it may have to be sold for less than its purchase price, resulting in a return that is less than the yield to maturity. This risk is called interest rate risk. 

There are two characteristics of a bond that affect the degree of reinvestment risk. First, for a given yield to maturity and a given nonzero coupon rate, the longer the maturity the more the bond s total return is dependent on reinvestment income to realize the yield to maturity at the time of purchase. The implication is that the yield to maturity measure for long-term coupon bonds tells us little about the potential return an investor may real-... 

For callable bonds, the market convention is to calculate a yield to call in addition to a yield to maturity. A callable bond may be called at more than one price and these prices are specified in a call price schedule. The yield to call assumes that the issuer will call the bond at some call date and the call price is then specified in the call schedule... 

A yield can be calculated for every possible call date. Additionally, a yield to maturity can be calculated. The lowest of all these possible yields is called the yield to worst. 

Although it is commonly quoted by market participants, the cash flow yield suffers from limitations similar to the yield to maturity. These shortcomings include (1) the projected cash flows assume that the prepayment speed will be realized (2) the projected cash flows are assumed to be reinvested at the cash flow yield and (3) the mortgage-backed or asset-backed security is assumed to be held until the final payoff of all the loans in the pool based on some prepayment assumption. If the cash flows are reinvested at rate lower than the cash flow yield (i.e., reinvestment risk) or if actual prepayments differ from those projected, then the cash flow yield will not be realized. Mortgage-backed and asset-backed securities are particularly sensitive to reinvestment risk since payments are usually monthly and include principal repayments as well as interest. 

PVCF = present value of the cash flow in period t discounted at the yield to maturity where t = 1,2,..., n... 

Issues are initially priced and sold at a fixed spread over the reference rate. The price of an FRN can fluctuate considerably during the life of the issue, mainly depending on trends in the issuer s credit quality. The frequent resets in the reference rate means that changes in market interest levels have a minimal impact on an FRN s price. For investors, movements in an FRN s price are reflected in changes in the discount rate. The discount rate is effectively the yield needed to discount the future cash flows on the security to its current price. It thus functions in the same way as the yield to maturity for a fixed-rate instrument. And like a fixed-rate bond, the market convention is to use a constant spread... 

Taking as a base the example in Rule 1 above the theoretical increase in the bond s price is approximately 3.8% ( [97 - 17/93 - 30] -1 X 100) assuming a yield to maturity of 10.91%. If, on the other hand, the bond s yield were to rise 100 bps to 12.91%, the accompanying fall in the bond s price would be 3.5%. This is due to the nonlinear relationship that exists between a bond s price and its yield. 

A numerical example will help to clarify the method. The data in Exhibit 16.8 are daily observations, drawn from Bloomberg, on the Euro-Bund Futures quotes and CTD yield-to-maturity over a period of 12 days. Columns (4) and (5) display the changes in futures quotes and yields, respectively, that have taken place from one day to the next. Using the data in columns (4) and (5) equation (16.10) can be estimated using least squares regression. ... 

Yield to maturity Risk-free security Risky security... 

In the past bond analysis was frequently limited to calculating gross redemption yield, or yield to maturity. Today basic bond math involves different concepts and calculations. These are described in several of the references for chapter 3, such as Ingersoll (1987), Shiller (1990), Neftci (1996), Jarrow (1996), Van Deventer (1997), and Sundaresan (1997). This chapter reviews the basic elements. Bond pricing, together with the academic approach to it and a review of the term structure of interest rates, are discussed in depth in chapter 3. 

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