Returns from Bonds and How Change in Interest Rates Affects Them - Essay Example

Running Head: RETURNS FROM BONDS Returns from Bonds and How Change in Interest Rates Affect Them Name Course Instructor Date RETURNS FROM BONDS Introduction Investors go to the bond market with the intention of making money and it is important for them to have a way of determining how much they are likely to make from that investment. The bond market is reputed as being one of the safest ways to invest as the investor cannot lose the principal invested. This reputation supposes that an investor intends to hold the bond to its maturity. However recent observations show that this stodgy reputation is a carryover from the past, when investors who bought bonds were contented with the coupons while waiting out the term of the bond; that was then. According to the American Association of Individual Investors (2007) today the average holding period of a thirty year US treasury bond is thirty days with the vast majority of bond holders seeking to make money on changes in bond prices. Therefore, while calculation of the yield to maturity is still a very important indicator of how this bond is likely to do in the market, an understanding of how prices change during the life of the bond has gained more and more currency over the years as more and more speculators get into bond markets the world over. One of the key indicators of the direction bond prices will take is the interest rates, thus the keenness with which players in the market observe it. Types of bond yields Yield to maturity Fabozzi (2007) describes this as the rate of return obtained by buying a bond at the current market rate and holding it to its maturity. This yield is normally calculated at the time the bond is issued and it is one of the important aspects of the bond reported alongside its reference number maturity date and coupon dates. YTM assumes that there will be no default whatsoever, RETURNS FROM BONDS if some of the expected payments are not paid, the actual yield is less than projected. There is a relationship between Yield to Maturity and the Holding Period Returns this is because when the initial value of Yield to Maturity does not change, the HPR will be equal to the YTM. There however are differences between the two in that YTM depends on values that can be seen even at the time when the bond is being issued, these include; the current price, the coupon rate and the bond’s face value. Holding Period Returns shows the yield over a period of investment which is not necessarily the bond’s full term and therefore depends on the bond’s market price at the end of that investment period. This price cannot be determined at the bond’s issuing. The popular understanding is that in order for YTM to be arrived at, all the coupon payments received have to be reinvested at the same rate as the rate at which the bond was issued. However, some observers have disagreed with the assertion. This alternative school of thought argues that since interest is not compounded and future values are not used in YTM calculation there should be no assumption of coupon reinvestment. If, for instance, a person purchases a four year note with a coupon rate of 5% at par, he receives $50 interest every year for the four years duration and then at maturity he is paid at face value. In this case, the 5% may be described as the bond’s Yield to Maturity with the discount rate making the present coupon value and the bond’s face value to be equivalent to the bond’s price (Shawn et al, 2008). Calculating YTM An approximate YTM is attained by finding the average of the bond’s purchase price and that of the redemption price at par (Brown & Patrick, 1998). The formula for this calculation is:- Income from interest + Yearly price change x 100 (Purchase price +100)/2 RETURNS FROM BONDS Example A $5000 bond purchased at $92 maturing after eight years and has a rate of 10%. The first step is to find the annual interest rate based on $100 par i.e. $100 x 10% Then find how much the price will change annually, considering that par value is $100 since the bond was purchased at $92 and it will mature at $100, it will increase by $8 before maturity and because its life is 8 years, it will change by $1 per year. Then find the average price; this is equal to purchase price plus price at maturity divided by two. In this case: ($92 + $100)/2 = $96. The approximate YTM for this bond is therefore $10.00 +$1.00 x 100 ($92 +$ 100)/2 =$11.00 x 100 = 11.46% $96 Current Yield Thau (2002) describes current yield as income from the bond per year; it is expressed as a percentage of the market price. The calculation of this yield is applied to an individual bond. It is equal to the annual coupon payout divided by the price at which the bond was purchased. Current yield gives the rate of income to be received through considering the bond’s purchase price. This yield does not put into account what the effects of compounding would be should the investor decide to reinvest the coupons received at the same rate. It also does not consider the effects of the bond being sold prior to maturity, whether the effect of that sale is a profit or a loss. RETURNS FROM BONDS It although this measure leaves out many important considerations during its calculation, it is important for comparing bond yields from yield from other investments. Its biggest limitation is that it changes daily depending on the price of the bond on that day, it, therefore, cannot be used by an investor whose intention is to hold bonds to maturity. Comparison between YTM and current yield is an important way of determining whether the bond is likely to return a price appreciation or not. If the yield to maturity is greater than the current yield, the bond offers a possibility of price appreciation and vice versa (Johnson et al, 2002). Current Yield =Coupon rate (%) x 100 Clean price Example: If a bond whose coupon rate is 10% is bought at $900 par value its current yield will be found by: Finding 10% of the clean price i.e. $900 I.e. 10/100 x 900 = 90 Then divide the 10% found by 1000. 90/1000 = 0.9/10 This is then multiplied this by 100 to get the percentage which is how the yield should be reported. 0.9/10 x 100 = 9% therefore the current yield of the above described bond is 9%. RETURNS FROM BONDS Simple yield is basically the current yield when it factors in the interest rates. It is calculated based on the assumption that the interest rates accrue in a linear fashion during the bond’s life, it however, does not allow for interest to be compounded and it uses clean price in calculation hence the lack of consideration of accrued interest. It is calculated using the following formula. Simple Yield = [Coupon Rate + (100 - clean price) x 100] x clean price Years to maturity (United Kingdom Debt Management Office, 1998) Yield to call According to Fabozzi (2007) some bonds are said to have the call feature, this means that the company issuing them is allowed to call the bond from the market forcing investors who have already invested in it to relinquish it. Callable bonds may be disadvantageous to the investor since the rates may fall as the bond is called. If that happens, the investor receives the call price and then the proceeds will have to be reinvested at lower interests as compared to the YTM of the original bond. When this happens, what the bond issuer saves in interest rates, the bond holder will lose. To compensate for this possible loss to the investor, a callable bond is expected to offer higher yield to maturity. Mostly, investors take up this bond offer if its price reflects the possibility of the bond being called because of the higher promised yield. If interest rates fall increasing the possibility of call, bond holders consider the bond mature and they are then paid off at the call date, if the interest rates increase the bond payment must be on the maturity date. It might be argued that because the holder of a callable bond receives the principal plus a premium if the bond is called then he receives a better deal (Brown & Patrick, 1998). However, since the RETURNS FROM BONDS bond issuer is only likely to call the bond when the interest rates are low it makes it a bad deal for the investor who seeks to reinvest because the reinvestment will be done at a lower rate. It might seem that Yield to Call is mostly profitable to the short term speculator whose interests are only in the short term. Example The Yield to Call for a bond with twenty year maturity, five year call period and it is priced at $1098.96 implied Yield to maturity of 8% and a 9% coupon rate. Formula 40 P=∑ 45 + 1,000 t=1 (1+ 0.04) (1+0.04)40 10 1,098.96 = ∑ 45 + 1,050 t=1 (1+r) t (1+r) 10 Yield to Call: r =3.72% R BEY = 7.44% There are other types of yields including yield to put, this comes into play when a bond, at issue allows the bond holder to give up the bond at certain preset dates before maturity. It is used to show the gain an investor might expect if they decide to give up the bond at any of the put dates. Bonds with this provision are referred to as puttable bonds. Yield to worst is a determination of the worst possible return an investor can receive, short of default on the part of the bond issuer. It considers all the factors likely to make the bond a bad investment as a way of showing the RETURNS FROM BONDS investor the worst possible case scenario and thus help him in making the decision to invest (Thau, 2002). The yield curve This is a graphical representation of different interest rates of bonds with equal credit quality but different maturity rates at different points in time. There are three different types of curves, normal, inverted and humped. In a normal curve, longer maturity bonds have higher yields than the shorter maturity ones. An inverted curve shows the shorter maturity bonds having higher yields which may indicate a future recession. A humped or flat yield curve shows shorter and longer term yields being almost similar and shows the possibility of transition between normal and inverted yield curve (Eckett 2009). Normal Yield Curve Flat Yield Curve RETURNS FROM BONDS Inverted Yield Curve Effects of Interest Rates on bond prices When interest rates rise an when the interest rates fall the price of bonds already held by investors increases. To illustrate, if a government issues a bond at a time when the market interest rates are 8% a bond with $1000 face value during the time of issue would pay $80 dollars in two $40 installments. If market interest rates increase to 10% the bond would become less attractive and to make the bond attractive to buyers, it would be necessary to reduce the bond’s market price to a level where the $80 it earns in interest annually would be equivalent to the prevailing 10% in this case the bond will be quoted at $800. If the interest rates fall to 6% it would mean that the bond should have its price adjusted to $1,333.33. The bond would still be redeemed at face value, so if the buyer who bought the bond at $800 or $1,333.33 depending on whether the interest rates rose or fell will get a return of $1000 in principal. This means that the buyer who bought when interest rates were high gets a capital gain while the one who buys when they are low makes a capital loss; the issue of capital gain or loss is put to consideration during calculation of the Yield to Maturity (Fabozzi, 2007). References American Association of Individual Investors (2007). “The Investor Professor”, The American Association of Individual Investor’s Journal, July, 14-16. Brown, Patrick, J (1998). Bond Markets: Structures and Yield Calculations. Gilmour Drummond Publishing in association with ISMA. ISBN: 1901912027 Eckett, S (2009). Online Investing: 200 essential Q & s for the internet investor. Hampshire: Harriman House Limited. Fabozzi, F 2007 Bond Markets: Analysis and Strategies. 6th edn. Upper Saddle River, NJ: Prentice Hall. Johnston, Ken, Forbes, S and Hatem, J (2002). “Reinvestment Rate Assumptions in Capital Budgeting: A Note”, Journal of Economics and Finance Education, Volume1, Number 2, Winter, 28-29. Shawn, M, Forbes, Hatem, J, and Paul, C (2008) Yield-to-Maturity and the Reinvestment of Coupon Payment. Journal of Economics and finance education • Volume 7 • Number 1 Thau, A (2002). “Bond Basics: An Investor’s Guide.” The American Association of Individual Investors’ Journal, January, 24-27. United Kingdom Debt Management Office (1998). Formulae for Calculating Gilt Prices From Yields. Read More