YIELD MEASURED, SPOT RATES, AND FORWARD RATES Pertemuan 5 - mupo -

2. YIELD MEASURED, SPOT RATES, AND FORWARD RATESPertemuan 5-mupo- Mata kuliah : F0922 - Pengantar Analisis Pendapatan Tetap Dan Ekuitas Tahun : 2010

3. YIELD MEASURED SPOT RATE AND FORWARD RATES Materi: Traditional yield measured Spot rates Forward rates

4. Traditional yield measured Yield measures cite in the bond market include Current Yield, Yield to Maturity, Yield to Call, Yield to Put, Yield to Worst and Cash flow Yield. 1.1 Current Yield. Current Yield = annual dollar coupon interest Price Example: the Current Yield for 7% 8-year bond whose price is $ 94.17 is 7.43% as show bellow: annual dollar coupon interest = 0.07 x $ 100 = $ 7 price = $94.17 Current Yield = $ 7 = 0.0743 = 7.43% $94.17 The Current Yield will be greater than the coupon rate when the bond sells at a discount; the reverse is true for a bond selling at a premium. For a bond selling at par, the Current Yield will be equql to the coupon rate.

5. 1.2 Yield to Maturity The most popular measure of yield in the bond market is the yield to maturity. The yield to maturity is the interest rate that will make the present value of bond’s cash flow equal to its market price plus accrued interest. Example: consider a 7% 8 years bond selling for $ 94.17. The cash flows for this bond are (1) 16 payments every 6 months of $ 3.50 and (2) a payment sixteen 6 month period from now of $ 100. The present value using various semiannual discount (interest) rates is: Semiannual interest rate 3.5% 3.6% 3.7% 3.8% 3.9% 4% Present value 100.00 98.80 97.62 96.45 95.30 94.17 When a 4% interest rate is used, the present value of cash flow is equal to $ 94.17, which is the price of bond. Hence, 4.0% is the semiannual yield to maturity

6. The relationship between the price of bond, coupon rate, current yield, and yield to maturity: Bond selling atRelationship par coupon rate = current yield = yield to maturity discount coupon rate < current yield < yield to maturity premium coupon rate > current yield > yield to maturity 1.3 Yield to call. When a bond is callable, the practise has been to calculate a yield to call as well as a yield to maturity. A callable bond may have a call schedule. The yield to call assumes the issuer will call a bond on on some assumed call date and that the call price is the price specified in the call schedule. Typically, investors calculate a yield to first call, a yield to first par call, and a yield to refunding. The yield to first call is computed for an issue that is not currently callable, while the yield to next call is computed for an issue that is currently callable.

7. 1.4 Yield to Put When a bond is putable, the yield to the first put date is calculated. The yield to put is the the interest rate that will make the present value of the cash flows to the first put date equal to the price plus accrued interest. Example: Suppose a 6,2% coupon bond maturing in 8 years is putable at par in 3 years. The price of this bond is $ 102.19. The cash flows for this bond if it is put in three years are: (1) a total of 6 coupon payment of $ 3.10 each paid every 6 months (2) the $ 100 put price in 6 month period from now The semiannual interest rate that will make the present value of each cashflows equal to the price of $ 102.19 is 2.7%. Therefor, 2.7% is semiannual yield to put and 5.4% is the yield to put on a bond equivalen basis 1.5 Yield to worst A yield can be calculated for every possible call date. In addition, a yield to matury can be calculated. The lowest of all these possible yields is called the yield to worst.

8. Example: suppose that there are only 4 possible call dates for a callable bond, that the yield to call assuming each possible call date is 6%, 6,2%, 5.8% and 5.7%, and that the yield to maturity in 7.5%. Then the yield to worst is the minimum of this yields, 5.7% 1.6 Cash flow yield Mortgagebacked securities and assets backed securities are backed by a pool of laoans or receivables. The cash flow for these securities include priciple payment as well as interest. The complication that arises is that the individual borrowers whose loans make up the pool typically can prepay their loan in whole or in part prior to scheduled principal payment dates. Because of pricipal prepayments, in order to project cash flows it is necessary to make an assumption about the rate at which which principal prepayments will accur. This rate is called prepayment rate or prepayment speed.

9. 2. Spot rate The theoritical spot rate for Treasury securities represent the appropriate set of interst rates that should be used to value default free cash flows. A default free theoretical spot rate can be constracted from the observed Treasury yield curve. There are several approaches that are used in practice. 2.1 Bootstrapping. Bootstrapping begins with the yield for the on the run Treasury issues because there is no credit risk and no liquidity risk. 2.2 Yield spread measures relative to a spot rate curve. Traditional analysis of the yield spread for a non Treasury involes calculating the difference between the bond’s yield and the yield to maturity of a benchmark Treasury coupon security. The latter is obtained from the Treasury yield curve