Bonds, Bond Prices and the Determination of Interest Rates - Example

Measures of Bond Yield Name: Institution: Date: Measures of Bond Yield When investing in bonds, an investor expects three sources of return on investment. These are: coupon payments to be made by the issuer; the capital gains realized when the bond is sold, matures or is called. This is the difference between the purchase price and the price realized when it is given up; and interest on interest, this is where the investor takes the interim cash flows before maturity and reinvests it to earn extra returns. The measure of any investment is interest rate. Interest rate measures the present value of the expected cash flow from the investment to its cost. I = Fc1 + Fc2 + Fc3 + ………….. + Fcn 1+r (1+r) 2 (1+r) 3 (1+r) n I = S Fct (1+r) t Where: FC is cash flow in a given period, I is the price of investment, n is the number of period and r is the interest rate. This calculated yield is also known as internal rate of return. In most cases calculation of yield is through trial and error method also known as iterative method Fabbozi (2010). Different measures of yield There are different measures of yield in bond market namely: Realized yield, yield to call, yield to maturity, current yield, and nominal yield. Realized yield measures the expected return if you sell the bond before maturity (Arthur & Sheffrin, 2003). This measure gives the portfolio manager an opportunity to estimate the performance of a bond based on the planned investment, future market yield and reinvestment rates Bruce (2012).The problem with this method is that the manager is forced to make assumptions concerning specified period, future investment and reinvestment rates. On the other hand the manager is able to evaluate performance under different interest rates. Current yield Current yield measures cash flow to market price i.e. dividing the annual interest is by the market value. Time value of money and capital gains or losses is not considered when using this method of yield calculation. This calculation only takes into account the coupon interest as the only source of income that will have an effect on an investor's yield. Current Yield = Annual bond interest Price Practical example: Apple Inc 10-year bond with an interest rate of 5% and a market price of 98 Answer: Price Figuring out the annual dollar bond interest = 0.05 * $ 100 = $5 Current yield = $5/98= 0. 5102 = 5.1% Current yield is lower when bond is selling at a premium and higher when it is selling at a discount. When both are equal, the bond is selling at par. The Apple Inc bond is selling at a discount. Yield to maturity (YTM) This is the rate that will make the current value of a coupon's cash flow to equal its market price plus all the accrued interest (Brigham & Joel, 2004). Calculation in this measure requires trial and error, after developing cash flows, to find the interest rate that makes the market price plus interest equal to the present value of cash flow. Yield to maturity takes into consideration the time value of money and capital gain or loss. Example: Using the Apple Inc bond above, the cash flows will consist of 20 payments of $ 2.50 each bi-annually and another payment, ten years from now, amounting to $100. Trial and error analysis of various discounts calculated semi-annually are: By use of the analysis above but semi annually: 2.5% gives $100 2.6% gives $99.5  2.7% gives $99.00 2.8% gives $98.5 2.9% gives $98.00 From the above sequence, the present value of cash flows equals $98 at an interest rate of 2.9%, making it the semi-annual rate of interest. To get the bond equivalent yield or market rate of the bond, the semi-annual rate is doubled. In the above example therefore, 5.8% would be the yield to maturity. I. When a bond selling at par value; Coupon Rate equals the Current Yield as well as the Yield to Maturity. II. When selling at a discount; Coupon Rate is less than the Current Yield, while the current yield is less than Yield to Maturity. III. When selling at a premium; Coupon Rate is larger than the Current Yield; the Current Yield is consequently larger than the Yield to Maturity. The yield to maturity however has a limitation in assuming that reinvestment of the nominal will be at the same interest rate as the Yield to Maturity (Schwab, 2009). Nominal yield On the other hand nominal yield is the coupon rate of a specific issue and is the best way of explaining coupon characteristics Fabbozi (2012). In this regard, nominal yield is mostly used by the portfolio managers compared to other measures. This is because it is very simple, easier to calculate and well understood by investors. Investor using this method always get good returns thus it is recommended. Yield to First Call This is calculated for a bond that is callable but is not currently callable. The computation is similar to that of the yield to maturity the only distinction being that in place of the stated maturity and par value, the first call date and the call price are used in working out the yield. Yield to First Par Call Yield to first par call follows the same procedure as the yield to first call, the only difference being that that the maturity date that will be used instead of the maturity date that is stated should be the first time the issuing entity can call on the bonds at face value. Yield to Refunding The calculation is exactly the same as the yield to maturity. This is applied when bonds presently callable but the source of funds to be used are in some restrictions. The earliest date on which the bond can be recalled using a lower cost debt is referred to as the refunding date (Yla Eason, 1983). Yield Spreads Spreads are usually discussed based on treasury securities which have the same maturity period. An investor can also talk about spreads between two bonds with the same maturity. Absolute Yield Spread This is the most common method of measuring spreads in the market. The spreads evaluates the variation in spread in two bonds by assessing the basis points.  Example In comparing a ten-year bond from Apple Inc with a coupon rate of 5% and a government ten-year bond with a yield of 4.5%. The absolute yield spread would be: Absolute Yield Spread = 5% - 4.5% = 0.5% or 50 basis points Relative Yield Spread The relative yield spread measures the yield spread comparative to a reference bond. The formula is: Relative yield spread = Yield of bond A – Yield of reference bond Yield of reference bond In the example above, we can use the government bond as the reference bond and therefore the formula will be: Relative yield spread = 5% - 4.5% = 0.11 = 11.11% 4.5% Yield Ratio This is basically the ratio between the yields of two bonds. The equation therefore would be: Yield on Bond A Yield on Bond B Using the above example, the yield ratio of the two bonds would be expressed as: Yield Ratio = 5% = 1.11 4.5% Which spreads are better? Relative spreads measure the extent of the entire yield spread and the way interest rates affect the yields. Absolute spreads on the other hand are preserved as the interest rates change. With this, relative spreads are a better measure in that they move relative to the levels of interest rates. Effects on bond when interest rate changes Bonds in the market tend to present an aspect of stability that compensates for some of the unpredictability of stocks. The largest threat to bond prices is the fluctuation of interest rates. However, all other factors held constant, if a bond is held to maturity, changes in interest rates do not affect the returns. Interest rates only affect bond prices when they are held for investment purposes, which is buying and selling of the bonds in the market. Bond prices are inversely related to interest rates. This is to say that when interest rates are rising, bond prices decline Jackson M S Staunton M (2001). Illustration: A 5 year bond is issued at a price of $10,000 with a coupon rate of 5%, paid semi-annually. Assume an increase in interest rates to 6%. This means that the bond is offering an interest rate of 1% below market rates i.e. 6% - 5%. This consequently means that offloading the bond will be impossible as no one will take a lower rate of investment than that offered in the market. Since the coupon rate cannot be altered, the only cause of action would be to sell the bond at a discounted rate. Annual payment ($10,000 * 5% = $500) should be equal to a 6% payment. Calculations show that a discounted price of $8,333 equals the $500 payment which is fixed. This would yield a payment equaling a 6% yield on investment for the buyer, this is expressed as $8,333 * 6% = $500. This in effect shows that the bond would be offered at a premium if the interest rates declined below the coupon rate. Prices change faster for long-term bonds If interest rates rise, prices of long term bonds fall a lot faster because the fixed coupon rate is held for a longer period of time because of the longer maturity period. This means that coupon payments will be received for a longer period of time which can fall above or below the prevailing market interest rates (Oswego State University, nd). Therefore, the bond may be more or less attractive to an investor in comparison to the options that are currently available. Long term bonds are more precarious than short term bonds because of the interest rate fluctuations. References: Arthur, O., & Sheffrin, S. M. (2003). Economics: Principles in action. New Jersey: Pearson Prentice Hall. Bruce T (2012) Fixed Income Securities: Tools for today’s Market, John wisely $ sons inc Brigham, E. F., & Joel, F. d. (2004). Fundamental of Financial Management. South-Western: Thomson. Fabbozi J, Man S (2010) Introduction to Fixed Income Analytics: Relative Value Analysis, Risk Measures, and Valuation, Second Edition John Wiley & Sons Jackson M Staunton M (2001) Advanced Modeling in Finance John wisely $ sons Inc Oswego State University. (nd). Bonds, Bond Prices and the Determination of Interest Rates, Part II. Retrieved November 23, 2012, from Oswegu education: http://www.oswego.edu/~edunne/340ch6part2.htm Schwab, C. (2009, Novemberr 25). Bonds Article. Retrieved November 23, 2012, from Schwab global: http://www.schwab-global.com/public/schwab-gcb-en/advice_and_research/market_insight/investing_strategies/bonds/impact_of_interest_rates_on_bond_investments.html Yla Eason. (1983). Final Surge in Bearer Bonds. New York: New York Times. Read More