The Different Measures of Yield - Coursework Example

Bond Yield Measures Name Course Lecturer Date Affiliation Using bond yield measures, an investor can be informed of the rate of return on their bond. However, this is under a number of assumptions. The changes in the rates of interest significantly affect the bond prices. Having an investment in bonds ensures that the investor gets return from three different sources. The first is from the issuer payments of coupons. The second is from the capital gain after the bond matures and is sold. The profits of the investor are the difference between the buying price and the selling price. Lastly, the investor receives earnings from the reinvestment of the interim cash flows. This paper looks at the bond yield measures and to what extent the changes in interest rates can have an effect on the bond prices. Comcept of Yield on Investment The yield on investment is a concept in reference to the interest rate that will ventually turn the present value of the cash flows from the said investment be equal to the total price of the investment. This concept is represented in a formula the as in the following equation. In this, CFt represents the cash flow in year t, N is the number of years while P represents the price of the investment made. The result of this calculation (the yield), is also referred to as the internal rate of return. The yield that is detremined is the yield for that particular time frame. For instance, if the cash flows are computed in an annual format, the yield will be an annual yield. If the computaton is done on the basis of months, the same rules and procedures apply and the resulting yield will be monthly. For one to be able to calculate/ compute the simple annual interest rate, a different step has to be applied. In this case, the yield for the specific period is put under multiplication by the number of periods that have been availed in the said year. Example This is the formula that will be applied in the case of an investment which is composd of one future cash flow. . Process of yield annualization The formula that is used to obtain an effective annual yield is as follows. The yield that is derived is associated with a periodic interest rate. Effective annual yield = (1 + periodic interest rate)m – 1 In the equation, m is the representative of frequency of payments that have been made per year. For instance, the periodic interest rate is 8% and the interest is paid quarterly, Which implies 8%  4 = 2%, As a result the effective annual yield is shown below (1.02)4 – 1 = 1.0824 – 1 = 0.0824 This is equivalent to 8.24%. Getting the Current Yield The current yield has a direct relatationship with the annual coupon interest to the market price. As such, the computation is done as follows: Current yield = the annual $ coupon interest  by price. In this equation of current yield calculation, the time value is not put into consideration. However, the coupon interest rate is taken into account. Yield to Maturity The present calculated value of the cash flows that are equal to the price divided by the total investments are the yield to maturity rates. For example, the yield to maturity in a semiannual pay bond is derived by first computing the periodic interest rate. This is the element y, which is supposed to satisfy the following relationship: In this, P represents the price of the bond, M is equal to maturity value (in $), C is the representative of the semiannual coupon interest (in $), while n shows the number of periods. In the case of a semiannual pay bond, to get the yield to maturity one simply doubles the periodic interest rate. However, one can also double the discount rate (y). This does understate the effective annual yield. When the yield to maturity is derived by computing the variables on the basis of this market convention it is referred to as the bond-equivalent yield. Yield to maturity for a zero-coupon bond is computed using the following . Yield to Call The call price refers to the price at which one may call the bond. This is expressed as follows In the above equation, M* represents the call price (in $) while the value n* is the representative of the number of periods until the assumed call date. It is usually derived from the number of years multiplied by 2. For the yield to call bond equivalent basis, a semiannual pay bond is used. The derivation is obtained by doubling the periodic interest rate (y). Yield to Put A putable issue simply means that the bondholder can at anytime (at their pleasure) force the issuer to purchase the issue at his / her own said price. An issue is regarded by specialists as putable only when the yield to put is completely ready for calculation. The yield to put is a term in reference to the interest rate that is applied to make the current values of the cash flows to be assumed put date. Additionally, the price of put on the specific date as set forth in the put schedule will be an equivalent to the bond’s price. As such, the formula that is used will be the same as for the yield to call. However, there will be slight variations. The value M* is now regarded as the put price and n* will now represent the number of periods that will be involved until the assumed put date is arrived at. Accordingly, the procedure that will be used will be exactly the same as the ones used in calculating the yield to maturity and yield to call. Yield to Worst As one of the most used practices in the bond industry, an investor is expected to accurately calculate the yield to maturity. Not only this but also the yield to every possible call date which is followed by the yield to every possibility of a put date. As such, the minimum of all of these factors and yields is called the yield to worst. Yield for a Portfolio This is also considered to be the Internal Rate of Return. Normally the yield for a portfolio of bonds is not put across represented by the total weighted average of the yield to maturity. This is in regard to the individual bond issues in the portfolio in question. The determination of constant cash flows is the main mode for the computation of yield for a portfolio of bonds. The other factor that plays a major role is the speculative determination of the interest rate. The result of the above is the equal status of the current value of the portfolios in the market and present value of the cash flows. Yield Spread Measures for Floating-Rate Securities Being based on the coupon reset formula, the coupon rate for a floating-rate security keeps on changing. For this to work, this formula is made up of the quoted margin and the reference rate. Since it is a known fact that the future value for the reference rate is unknown, it is virtually impossible to determine the cash flows that will be experienced. This only means that the quantity yield to maturity cannot be calculated. For this reason, there are several conventional measures which are critically used as margin or technical spread measures that are cited by market participants for floaters instead. These measures include the spread for life which is also known as simple margin, the adjusted simple margin, discount margin and the adjusted total margin. Depending on used, he most popular of these measures is discount margin. This measure is used to directly estimate the average margin. This is over the reference rate which the investor can expect to earn over the life of his or her security. Interest-On-Interest Dollar Return determination. A substantial portion of the potential return of the bond can be represented by the interest-on-interest component in the bond yield process. As such, the coupon interest together with the interest on interest can be derived from the application of the following equation. In the above equation, r represents the rate of semiannual reinvestment. For one to establish the total $ amount of coupon interest, one has to multiply the semiannual coupon interest by the number of periods As such, the total coupon interest = nC Adding the difference between the coupon interest + interest on interest and the total $ coupon interest gives the interest-on-interest component. This is represented in the following equation. Yield to Maturity and Risk of Reinvestment. Yield to maturity can only be realized by the investor at the time of purchase of the bond. Therefore, this will only occur when the bond is held to maturity. The coupon payments are reinvested at the computed yield to maturity. In this case, there are risks that the investor experiences. One of these risks is reinvestment risk. In this risk, the future reinvestment rates are significantly lower compared to the yield to maturity. This will happen at the time that the bond is purchased. The critical importance of the interest-on- interest component and the degree of reinvestment risk are determined by two characteristics of a bond. These are the coupon and maturity. This works in the following way, for a specific coupon rate and yield to maturity, the longer the maturity the greater the risk of reinvestment that will be experienced. If the maturity is long, bond’s total dollar return is more dependent on the interest-on-interest component. For the realization of the yield to maturity at the time of purchase this process has to take place. Risk of Reinvestment and Cash Flow Yield The reinvestment risk is greater for amortizing securities compared to non amortizing securities. This is because the investor has to reinvest the periodic principal repayments. This is in addition to the periodic payments of the coupon interest. As such, the total return is derived as a measure of yield. This measure incorporates a specific assumption about the rate of reinvestment. Total Return for a Bond computation. First, a particular investment rate is assumed. This is in order to compute the total future dollars from the investment one makes in a bond. The computation of the total return is calculated as the interest rate. This is what will determine the growth of the initial investment in the bond. This will turn out to be the computed total future dollars. Yield changes The measurement of the absolute yield change is strictly based on points. The absolute/ exact value of the difference that results from the two yields is calculated as shown below. In order to get the percentage change, the ratio of the change is computed as the natural logarithm. This is done as follows. % Change yield = 100 x ln (new yield / initial yield). Example of a Current Yield Mufasa has a ten-year bond. This bond has a rate of 5% while at the same time the market price in 98. Answer The valuation of the annual dollar coupon interest is as follows = .05 * $100 = 5$ As such, the Current Yield = $5 / 98 = .05102= 5.1% As illustrated, a change in the rate of interest results to a change in the bond yield. References Alliance consulting (2010), Bond Yields & Duration Analysis. Alliance Consulting. Charles P. Jones (2009), Investments: Analysis and Management. John Wiley & Sons. Frank J. Fabozzi (2007), Yield Measures, Spot Rates, and Forward Rates. John Wiley & Sons. H. Kent Baker, Gary Powell (2009), Understanding Financial Management: A Practical Guide. Wiley. Kapil Sheeba (2010), Financial Management. Pearson Education India. Moorad Choudhry (2002), The Repo Handbook. 1st ed. Butterworth-Heinemann. Prashant Shah (2010), Bond Yield Measures – Current Yield and Yield to Maturity. Vikranth Publishers. Richard C. Wilson, Frank J. Fabozz (1995), Corporate Bonds: Structure and Analysis. Wiley. Sunil Parameswaran (2007), Bond Valuation, Yield Measures and the Term Structure. Mc Grow Hill. Read More