Bond Features债券的特点

Bond Features债券的特点 Bond Features , Bond - evidence of debt issued by a corporation or a governmental body. A bond represents a loan made by investors to the issuer. In return for his/her money, the investor receives a legaI claim on future cash flows of the borrower. The issuer promises to: Make regular coupon payments every period until the bond matures, and pay the face value(or par value) of the bond when it matures. Coupon: the interest payment made on a bond Face value: the principal amount of a bond that is repaid at the end of the term Maturity: specified date on which the principal amount of a bond is paid , Bond pricing Bond price =Coupon (PVIFA r%,t) + Face value (PVIF r%,t) , If a bond has five years to maturity, an $80 annual coupon, and a $1000 face value, its cash flows would look like this: Time 0 1 2 3 4 5 $80 Coupons $80 $80 $80 $80 Face Value $ 1000 How much is this bond worth? It depends on the level of current market interest rates. If the market rate on bonds like this one is 8%, then this bond is worth; B = 80(PVIFA 8%,5) +1000(PVIF 8%,5) =80*3.9927 + 1000*0.6806 = 319.4+680.6 =$1,000 , What if market interest rate changes after issue? Suppose market rate increases to 10% two years from issue. B = 80(PVIFA 10%,3) +1000(PVIF 10%,3) = 80(2.4869) +1000(0.7513) =198.95+751.3= 950.25 , What if market interest rate decreases to 6% two years from issue? B = 80(PVIFA 6%,3) +1000(PVIF 6%,3) =80*2.6730 + 1000*0.8396 = 213.84 + 839.6 =$1,053.44 1. YTM > coupon (Discount bonds) , The coupon payments alone will not provide investors as high a return as they could earn elsewhere in the market. , To receive a fair return on such an investment, investors also need to earn price appreciation on their bonds. Thus, the bonds would have to sell below par value to provide a “built-in” capital gain on the investment 2. YTM < coupon (Premium bonds) , If the coupon rate exceeds the market interest rate, the interest income by itself is greater than that available elsewhere in the market. , Investors will bid up the price of these bonds above their par values. , The resulting capital losses offset the large coupon payments so that the bondholder receives only a fair rate of return. 3. YTM = coupon: Bonds with a price equal to par value; Par bonds Yields , Coupon rate or coupon yield: a bond’s annual coupon divided by its par value. , Current yield: a bond’s annual coupon divided by the bond price , Yield to maturity The market interest rate for bonds with similar features. This is the discount rate that equates a bond’s price with the present value of is future cash flows. , 3. The yield to maturity (or “YTM”) is the interest rate required in the market on a bond. In other words, YTM is the rate that makes the price of the bond just equal to the present value of its future cash flows. , Suppose the current bond price is $930. Annual coupon rate is 7%, maturity is 10 years from now, and face value is $1000. Find YTM. , $930 = $70(PVIFA r%, 10) + $1000(PVIF r%,10) Given a bond value, coupon, time to maturity, and face value, it is possible to find the implicit discount rate, or yield to maturity, by trial and error only. To do this, try different discount rates until the calculated bond value equals the given bond value. Remember that increasing the rate decreases the bond value. , The only way to find the YTM is trial and error: But, we know that this bond is discounted. So, r should be higher than coupon rate. The coupon rate is 70/1000 = 7% and B = 930. a. Try 10%: $70 (PVIFA 10%,10)+ $1000(PVIF 10%,10)= $816 b. Try 9%: $70 (PVIFA 9%,10)+ $1000(PVIF 9%,10) = $872 c. Try 8%: $70 (PVIFA 8%,10)+ $1000(PVIF 8%,10)= $933 Therefore, YTM is between 8% and 9 %. Interest Rate Risk and Time to Maturity , Issued 11 year bonds one year ago. , t= 10 years Coupon rate= 8.25% YTM = 8% (not 7.1%) Semiannual payments Assume face value = $1,000 Convert annual units into semiannual units , t = 20 Coupon rate/ 6months = 8.25 / 2 = 4.125% per 6 months YTM = 8% / 2 = 4% B = 41.25 (PVIFA 4%,20) + 1000 (PVIF 4%,20) = 41.25*13.5903 + 1000*0.4564 = 560.6 + 456.4 = $1,017 Callable bonds • Bonds that may be repurchased by the issuer at a specified call price during the call period • A call usually occurs after a fall in market interest rates that allows issuers to refinance outstanding debt with new bonds. • Generally, the call price is above the bond’s face value. The difference between the call price and the face value is the call premium • Bonds are not usually callable during the first few years of a bond’s life. During this period the bond is said to be call-protected. • Decreasing yields cause bond prices to rise, but long-term bonds increase more than short-term. Similarly, increasing yields cause long-term bonds to decrease in price more than short-term bonds. Malkiel’s Theorems Summarizes the relationship between bond prices, yields, coupons, and maturity: all theorems are ceteris paribus: 1) Bond prices move inversely with interest rates. 2) The longer the maturity of a bond, the more sensitive is it’s price to a change in interest rates. 3) The price sensitivity of any bond increases with it’s maturity, but the increase occurs at a decreasing 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 . 4) The lower the coupon rate on a bond, the more sensitive is it’s price to a change in interest rates. • If two 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 face amount to be received at maturity. • As a result, all other things being equal, the value of lower coupon bonds will fluctuate more as interest rates change. • 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 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 Malkiel’s Theorems (#3) Bond Prices and Yields (8% bond) Malkiel’s Theorems (#4) 20-Year Bond Prices and Yields Malkiel’s Theorems (#5) 8% coupon, 20 year bond Duration • Price sensitivity tends to increase with time to maturity • Need to deal with the ambiguity of the “maturity” of a bond making many payments. • Duration measures a bond’s sensitivity to interest rate changes. • More specifically, duration is a weighted average of individual maturities of all the bond’s separate cash flows. • The weight is the present value of the payment divided by the bond price. • Calculate a duration for a bond with three years until maturity. 8% of Coupon rate and yield. Calculating Par Value Bond Duration To calculating Macaulay’s Duration for any other bond: C = annual coupon rate M = maturity (years) Assume you have a bond with 9% coupon, 8% YTM, and 15 years to maturity. Calculate Macaulay’s Duration. Price Change & Duration Calculating Price Change Price Change & Duration • Zero coupon bond: duration = maturity • Duration Properties • Longer maturity, longer duration • Duration increases at a decreasing rate as maturity lengthens • Lower coupon, longer duration • Higher yield, shorter duration YTM = 10.498% Now calculate the Macaulay’s duration. Solution: