Bond Returns and Valuation PDF

Bond Returns and Valuation ► Long term fixed income securities ► Government bonds and corporate bonds ► Callable Bonds ► Convertible Bonds ► Zero Coupon Bonds ► Bond valuation V/S Stock valuation Bond Returns ► Coupon Rate: Nominal rate of interest fixed and printed on the bo...

Bond Returns and Valuation ► Long term fixed income securities ► Government bonds and corporate bonds ► Callable Bonds ► Convertible Bonds ► Zero Coupon Bonds ► Bond valuation V/S Stock valuation Bond Returns ► Coupon Rate: Nominal rate of interest fixed and printed on the bond certificate. It’s usually calculated on the face value of the bond. It is the rate at which interest is payable by the issuer annually/semi-annually till maturity ► ► ► ► Yield to Maturity: Compounded rate of return an investor is expected to receive from a bond purchased at the current market price and held till maturity ► YTM depends upon the current market price of the bond as well as the cash inflows from the bond including the future interest payments and the terminal principal payment ► ► ► The investor has to hold the bond till maturity ► All the coupon payments should be reinvested immediately at the same rate as that of YTM. Otherwise the actual or realised rate of interest will be different from the expected return ► Yield to Call: YTC is computed on the assumption that the bond’s cash inflows are terminated at the call date with redemption of the bond at specified call price ► YTC is that discount rate which makes the PV of cash flows to call equal to the bond’s current market price ► Bond Theorem- Burton G. Malkiel ► At the time of issue, coupon rate is generally equal to the prevailing market interest rates ► With the passage of time these market interest rates change but the coupon rate remains unchanged ► If current market rate rises above the coupon rate, bond provides a lower return and becomes less attractive and falls below its FV ► If current market rate falls below the coupon rate, bond provides a higher return and becomes more attractive and rises above its FV ► Malkiel provided an explanation on the relationship between bond prices, coupon rate, years to maturity and YTM in the form of five theorems, commonly known as Bond Theorems ► These theorems are “ceteris paribus” ► Theorem 1: ► Bond prices will move inversely to market interest rates ► If coupon rate and maturity are same, bonds with lower price will have higher YTM and vice versa  Particulars Bond A Bond B Par value 1000 1000 Coupon rate 10% 10% Maturity 2 years 2 years Market price 874 1035 YTM of Bond A= [100+126/2]/[(1000+874)/2] = 173/937 = 0.1846 = 18.46% YTM of Bond 2= [100+35/2]/[(1000+1035)/2] =117.5/1017.5=0.1155= 11.55% ► Theorem 2: ► The longer the maturity of a bond, the more sensitive is it’s price to a change in interest rates ► If the yield remains the same over the time, the discount or premium will depend upon time to maturity ► Bonds with lower term to maturity will sell at a lower discount as compared to a bond with higher term to maturity  Particulars Bond A Bond B Par value 1000 1000 Coupon rate 10% 10% Yield 15% 15% Maturity 2 years 4 years Calculate the Market price of both the bonds and find discount / premium as applicable ► Theorem 3: ► The price sensitivity of any bond increases with it’s maturity, but the increase occurs at a decreasing rate ► If yield is constant, discount or premium will decrease at an increasing rate  ►A 10-year bond is much more sensitive to changes in yield than a 1-year bond. However, a 30-year bond is only slightly more sensitive than a 20-year bond ► Theorem 4: ► The lower the coupon rate on a bond, the more sensitive is it’s price to a change in interest rates ► Iftwo bonds with different coupon rates have the same maturity, then the value of the one with the lower coupon is proportionately more dependent on the FV to be received at maturity ► Put another way, the bond with the higher coupon has a larger cash flow early in its life, so its value is less sensitive to changes in the discount rate  ► As a result, all other things being equal, the value of lower coupon bonds will fluctuate more as interest rates change ► Theorem 5: ► For a given absolute change in a bond’s yield to maturity, the magnitude of the price increase caused by a decrease in yield is greater than the price decrease caused by an increase in yield ► Price changes resulting from equal absolute change in market rates are not symmetrical ► For a given maturity, a decrease in market rate causes a price rise that is larger than the price decline resulting from an equal increase in market interest rate  Bond Risks ► Default Risk ► Foreign Exchange ► Callability Risk Risk ► Marketability Risk ► Interest Rate Risk ► Event Risk a) Reinvestment Risk ► Sovereign Risk b) Price Risk Bond Duration- Macauley duration ► The reinvestment risk and price risk derived from a change in the market interest rate have an opposite effect on bond returns ► For any bond there is a holding period at which these two risks have equal but opposite effects and hence they exactly balance each other ► What is lost on reinvestment is exactly compensated by a capital gain on sale of bond and vice versa ► For this particular holding period, there is no interest rate risk ► This holding period, where interest rate risk disappears, is known as the duration of the bond ► If the desired holding period is significantly different from the duration of the bond, the bond is subject to interest rate risk ► Mathematically, duration is the weighted average measure of a bond’s life and consists of setting out the series of cash flows, discounting them and multiplying each discounted cash flow by the time period in which it occurs ► Modified Duration ► Modified duration measures the average cash-weighted term to maturity of a bond ► Modified duration is an extension of the Macauley duration, which allows investors to measure the sensitivity of a bond to changes in interest rates ► ► A bond has a three-year maturity, pays a 10% coupon annually, and interest rates are 5% ► Duration ► Modified Duration ► This Modified duration tells how much would the bond price move inversely for a 1% change in interest rates Duration Principles ► As maturity increases, duration increases and the bond becomes more volatile ► As a bond's coupon increases, its duration decreases and the bond becomes less volatile ► As interest rates increase, duration decreases and the bond's sensitivity to further interest rate increases goes down