高顿网校 财经讲堂 2013 年 CFA 一级考试难点解析. 全球财经证书培训领导品牌 Fixed Income (1) Embedded Options. Fixed Income (1) Example: Embedded Options

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1 高顿网校 财经讲堂 2013 年 CFA 一级考试难点解析 高顿教育旗下品牌 : 高顿网校 Fixed Income (1) Embedded Options Option Type Benefits the Yield Price Call Issuer/Borrower Higher Lower Prepayment Issuer/Borrower Higher Lower Put Buyer Lower Higher Conversion Buyer Lower Higher Caps Issuer/Borrower Higher Lower Floors Buyer Lower Higher Example: Embedded Options Fixed Income (1) Would the following embedded options increase or decrease the price of an otherwise option-free bond? Prepayment Cap A Increase Increase B Increase Decrease C Decrease Decrease

2 Example: Embedded Options Fixed Income (1) Answer: C The prepayment option (in particular with mortgage backed securities) gives the issuer the right to pay principal back to the holder early. The Cap sets a maximum on coupon rate for floating rate bond. Both options benefit the issuer, and therefore decrease the price. Fixed Income (2) Factors Affecting Interest Rate Risk Longer maturity higher interest rate risk Higher coupon lower interest rate risk Higher yield lower interest rate risk Call option lower interest rate risk Put option lower interest rate risk Fixed Income (2) Example: Factors Affecting Interest Rate Risk Which of the following statements concerning the price volatility of bonds is most accurate? A) Bonds with higher coupons have lower interest rate risk. B) Bonds with longer maturities have lower interest rate risk. C) As the yield on callable bonds approaches the coupon rate, the bond's price will approach a "floor" value.

3 Fixed Income (2) Example: Factors Affecting Interest Rate Risk Answer: A Bonds with higher coupons have lower interest rate risk. Note that the other statements are false. Bonds with longer maturities have higher interest rate risk. Callable bonds have a ceiling value as yields decline. Fixed Income (3) Factors Affecting Reinvestment Risk Reinvestment risk is higher when: 1. Coupon is higher 2. Bond has a call feature 3. A security is amortizing 4. A security contains a prepayment option Fixed Income (3) Example: Factors Affecting Reinvestment Risk Which of the following statements is CORRECT? A) A bond with high reinvestment risk also has high price, or interest rate risk. B) The prepayment option on a mortgage loan benefits the issuer. C) Mortgage backed and asset backed securities have lower reinvestment risk than straight coupon bonds.

4 Fixed Income (3) Example: Factors Affecting Reinvestment Risk Answer: B In the case of a mortgage, the issuer is the borrower and is the party that benefits from the prepayment option. Mortgage backed and other asset backed securities have high reinvestment (or prepayment) risk because in addition to cash flows from periodic interest payments (like bond coupons), these securities have repayment of principal. Fixed Income (4) Forms of Credit Risk Default risk: Probability of default; Downgrade risk: Probability of ratings decrease; Credit spread risk: Risk of increase in spread to treasuries to compensate for given default risk (bond rating). Fixed Income (4) Example: Forms of Credit Risk Credit risk is measured in several ways. The yield differential above the return on a benchmark security measures the: A) default risk. B) recovery rate. C) credit spread risk

5 Fixed Income (4) Example: Forms of Credit Risk Answer: C The yield differential above the return on a benchmark security measures the credit spread risk. Credit spread risk is also known as the risk premium or spread. Fixed Income (5) Treasury Inflation Protected Securities (TIPS) Coupon rate is fixed; Par value is adjusted for inflation; Real rate of return; semiannual payment = ½ coupon rate inflation adjusted par value Fixed Income (5) Example: TIPS U.S. Treasury Inflation Protection Securities (TIPS): A) make annual inflation adjustments. B) will be repaid at maturity for less than their initial face value if deflation has occurred. C) have coupon rates that are fixed for the life of the issue.

6 Fixed Income (5) Example: TIPS Answer: C The coupon rate is fixed for a TIPS. The principal adjusts semi-annually and then the fixed coupon is multiplied by the new principal value to get the inflation adjusted interest payment. If deflation occurs over the life of a TIPS, the Treasury will redeem the security for its initial face value of $1,000 at maturity. Yield Curve Shapes & Shifts Fixed Income (6)? What if time passes away? (Cross-section data) Yield Curve Shapes & Shifts Fixed Income (6) Change in the level of interest rate: Y= a + bx level

7 Yield Curve Shapes & Shifts Fixed Income (6) Change in the slope of the yield curve: Y= a + bx slope Yield Curve Shapes & Shifts Fixed Income (6) curvature curvature Change in the curvature of the yield curve: Y= a + bx + cx 2 curvature Fixed Income (6) Term Structure Theory 1. Pure Expectations Theory Yield curve shape determined by expectations about future short-term rates 2. Liquidity Preference (Premium) Theory Greater premium (yield) required for longer maturities 3. Market Segmentation Theory Supply and demand for specific maturity ranges determines interest rates; any shape Yield curve shapes Term structure theory

8 Fixed Income (6) Example: Term Structure Theory The concept of spot and forward rates is most closely associated with which of the following explanations of the term structure of interest rates? A) Segmented market theory. B) Liquidity premium theory. C) Expectations hypothesis. Fixed Income (6) Example: Term Structure Theory Answer: C The pure expectations theory purports that forward rates are solely a function of expected future spot rates. In other words, long-term interest rates equal the mean of future expected short-term rates. The implications for the shape of the yield curve under the pure expectations ti theory are: If the yield-curve is upward sloping, short-term rates are expected to rise. If the curve is downward sloping, short-term rates are expected to fall. A flat yield curve implies that the market expects short-term rates to remain constant. Fixed Income (7) Price Change as Maturity Approaches 1, A premium bond (e.g., a 8% bond trading at YTM of 3%) 1, A par value bond (e.g., a 8% bond trading at YTM of 8%) A discount bond (e.g., a 8% bond trading at YTM of 12%) M Time 3 years

9 Fixed Income (7) Example: Price Change as Maturity Approaches Consider a 10%, 10-year bond sold to yield 8%. One year passes and interest rates remained unchanged (8%). What will have happened to the bond's price during this period? A) It will have increased. B) It will have remained constant. C) It will have decreased. Fixed Income (7) Example: Price Change as Maturity Approaches Answer: C The bond is sold at a premium, as time passes the bond s price will move toward par. Thus it will fall. N = 10; FV = 1,000; PMT = 100; I = 8; CPT PV = 1, N = 9; FV = 1,000; PMT = 100; I = 8; CPT PV = 1,125 Fixed Income (8) Arbitrage Arbitrage: riskless return with no initial investment. Dealers can strip a T-bond into its individual cash flows or combine the individual cash flows into a bond. The present value of the bond s cash flows (pieces) calculated with spot rates is the arbitrage-free value If the bond is priced less than the arbitrage free value: Buy the bond, sell the pieces. If the bond is priced higher than the arbitrage-free value: Buy the pieces, make a bond, sell the bond.

10 Fixed Income (8) Example: Arbitrage Current spot rates are as follows: 1-Year: 6.5%; 2-Year: 7.0%; 3-Year: 9.2%. Which of the following is CORRECT A) For a 3-year annual pay coupon bond, all cash flows can be discounted at 9.2% to find the bond's arbitrage-free value. B) For a 3-year annual pay coupon bond, the first coupon can be discounted at 6.5%, the second coupon can be discounted at 7.0%, and the third coupon plus maturity value can be discounted at 9.2% to find the bond's arbitrage-free value. C) The yield to maturity for 3-year annual pay coupon bond can be found by taking the geometric average of the 3 spot rates. Fixed Income (8) Example: Arbitrage Answer: B Spot interest rates can be used to price coupon bonds by taking each individual cash flow and discounting it at the appropriate spot rate for that year s payment. Note that the yield to maturity is the bond s internal rate of return that t equates all cash flows to the bond s price. Current spot rates have nothing to do with the bond s yield to maturity. Fixed Income (9) Z spread and option-adjusted spread Nominal spreads are just differences in YTMs; Zero-volatility (Z) spreads are the (parallel) spread to Treasury spot-rate curve to get PV = market price; Equal amounts added to each spot rate to get PV = market price. Option-adjusted spreads (OAS) are spreads that take out the effect of embedded options on yield. Option cost in yield% = ZV spread% OAS% Option cost > 0 for callable, < 0 for putable Must use OAS for debt with embedded options!

11 Fixed Income (9) An investor purchases a bond that is putable at the option of the holder. The option has value. He has calculated the Z- spread as 223 basis points. The option-adjusted spread will be: A. equal to 223 basis points. B. less than 223 basis points. C. greater than 223 basis points. Fixed Income (9) Answer: C Z-spread(223 bps) = OAS + option cost in percent(<0) Because option cost for putable bond is less than zero, OAS will be greater than 223 basis points. Fixed Income (10) Spot Rates and Forward Rates Forward rates are N-period rates for borrowing/lending at some date in the future. ( 1+S ) 3 3 = (1 + S 1)(1+ 1F 1)(1+ 1F 2) 3 2 ( 1+S 3) = (1 + S 1)(1+ 2F 1) 3 2 ( 1+S ) = (1 + S ) (1+ F )

12 Fixed Income (10) The six-year spot rate is 7% and the five-year spot rate is 6%. The implied one-year forward rate five years from now is closest to: A) 6.5%. B) 5.0%. C)12.0%. Fixed Income (10) Answer: C 1R 5 = [(1 + R 6 ) 6 / (1 + R 5 ) 5 ] - 1 = [(1.07) 6 /(1.06) 5 ] 1 = [1.5 / 1.338] - 1 = 0.12 Fixed Income (11) Duration Macaulay duration is in years Duration of a 5-yr. zero-coupon bond is 5 1% change in yield, 5% change in price Modified d duration adjusts Macaulay duration for market yield, yield up duration down Effective duration allows for cash flow changes as yield changes, must be used for bonds with embedded options

13 Duration Interpretation Fixed Income (11) 1. PV-weighted average of the number of years until coupon and principal cash flows are to be received 2. Slope of the price-yield curve (i.e., first derivative of the price yield function with respect to yield) 3. Approximate percentage price change for a 1% change in YTM: The best interpretation! Fixed Income (11) Which of the following statements about duration is NOT correct? A) Effective duration is the exact change in price due to a 100 basis point change in rates. B) For aspecific bond, the effective duration formula results in a value of 8.8. For a 50 basis point change in yield, the approximate change in price of the bond would be 4.4%. C) The numerator of the effective duration formula assumes that market rates increase and decrease by the same number of basis points. Fixed Income (11) Answer: A Effective duration is an approximation because the duration calculation ignores the curvature in the price/yield graph.

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