CFA Level I：Fixed Income - Yield Measures, Spot Rates, and Forward Rates 习题精选 帝国

cityboy

1. Consider a $1,000 par value bond, with an annual paid coupon of 7%, maturing in 10 years. If the bond is currently selling for $980.74, the YTM is closest to: A. 8.28% B. 7.28% C. 6.28%

Ans: B; Use the calculator to calculate YTM: N=10, PMT=70, FV=1000, PV=-980.74 CPT -> 1/Y=7.28

cityboy

2. Consider the three bonds in the following table. Which of the three bonds is most likely to have the greatest reinvestment risk? Bond YTM Time to Maturity Current Price A 8% 15 $980 B 8% 15 $1,000 C 8% 15 $1,098 A. Bond A B. Bond B C. Bond C

Ans: C; The yield to maturity assumes the coupon payments are reinvested at the yield to maturity and the bond will be held until maturity. The bond selling at a premium has the highest coupon rate and thus is expected to earn the most reinvestment income. If the reinvestment rate falls, this bond will suffer the greatest loss. Therefore Bond C, which is currently selling at premium, is most likely to have the greatest reinvestment risk.

cityboy

3. Using the U.S. Treasury forward provided in the following table, the value of a 2 year, 100 par value Treasury bond with a 4% coupon rate is closes to: Period Years Forward Rate 1 0.5 1.1% 2 1.0 1.7% 3 1.5 2.2% 4 2.0 2.5% A. $104.20 B. $100 C. $98.74

Ans: A; According to the definition of the forward rate, the value of the bond= +++ =$104.20

cityboy

4. Using the BEY (bond-equivalent yield) spot rates for U.S. Treasury yields provided in the following table, the 6-month forward rate one year from now on a bond-equivalent yield basis is closest to: Period Years Spot Rate 1 0.5 1.40% 2 1.0 2.30 % 3 1.5 3.00% 4 2.0 3.50% A. 4.41% B. 2.20% C. 2.30%

Ans: A; Assume: xfy represents x-period forward rate y-period from now; Z x+y represents (x+y)-period spot rate; Z y represents y-period spot rate. We have (1+Z x+y)x+y=(1+Zy)y (1+xfy)x 6-month forward rate one year from now in this case is 1 period forward rate 2-period from now. All spot rates are given on a BEY basis and must be divided by 2 in the calculation: (1+1f 2)1 (1+0.023/2)2=(1+0.03/2)3 1f 2=0.022038 On a BEY basis, the forward rate is 0.022038*2=4.41%

cityboy

5. Elaine Wong has purchased an 8% coupon bond for $1,034.88 with 3 years to maturity. At what rate must the coupon payments be reinvested to produce a 5% yield-to-maturity rate? A. 8% B. 6.5% C. 5%

Ans: C; C is correct. Yield-to-maturity measure assumes that the coupon payments can be reinvested at the yield-to-maturity. In this case, it’s 5%. C is the correct answer.

cityboy

6. The yield of a 3-year bond issue quoted on an annual-pay basis is 7.84%. The yield-to-maturity on a bond-equivalent basis is closest to: A. 3.85% B. 7.69% C. 7.84%

Ans: B; (1+bond-equivalent yield/2) 2 =1+annual-pay yield In this case, (1+bond-equivalent yield/2) 2 =1+0.0784 Therefore, bond-equivalent yield=7.69% B is the correct answer.

cityboy

7. The U.S. Treasury spot rates are provided in the following table: Period Years Spot Rate 1 0.5 2.20% 2 1.0 2.50 % 3 1.5 2.70% 4 2.0 3.20% Given a consistent corporate spread of 0.50%, what will be the most likely price of a 4% coupon corporate bond with 2 years to maturity? A. $100.61 B. $102.96 C. $98.92

Ans: A; The current price should be calculated using cash flows discounted at appropriate spot rate plus corporate spread: Current Price = +++ =+ ++ =$100.61

cityboy

8. Tina Mo, a fixed income analyst, is asked to value a single, default-free cash flow of $60,000. She is given the information in the following table: Period Years Annual Par Yield to Maturity BEY Theoretical Spot Rate BEY 6-month Forward Rates BEY 1 0.5 2.00% 2.00% 2.00% 2 1.0 2.40 % 2.40% 2.71% 3 1.5 2.70% 2.71% 3.12% 4 2.0 3.20% 3.23% 4.55% The value of this single cash flow at the end of Period 4 is closest to: A. $56,427 B. $56,309 C. $56,276

Ans: C; The theoretical spot rate for Treasury securities represent the appropriate set of interest rates that should be used to value single, default-free cash flows. Therefore: $60,000/(1+0.0323/2)4=$56,276

cityboy

9. The zero-volatility spread is a measure of the spread off: A. one point on the Treasury yield curve. B. all points on the Treasury yield curve. C. all points on the Treasury spot curve.

Ans: C; Instead of measuring the spread to YTM, the zero-volatility spread measures the spread to Treasury spot rates necessary to produce a spot rate curve that correctly prices a risky bond. Therefore B is incorrect. The zero-volatility spread is the equal amount that we must add to each rate on the Treasury spot yield curve in order to make the present value of the risky bond’s cash flow equal to its market price. Therefore A is incorrect.

cityboy

10. The U.S. Treasury spot rates are provided in the following table: Period Years Spot Rate 1 1 4.000% 2 2 8.167 % 3 3 12.377% Consider a 3-year, 9% annual coupon corporate bond currently trading at $89.464. Given the YTM of a 3-year Treasury is 12%, the Z- spread of the corporate bond is closest to: A. 1.50%. B. 1.67%. C. 1.76%.

Ans: B; The Z- spread is the equal amount that we must add to each rate on the Treasury spot yield curve in order to make the present value of the risky bond’s cash flow equal to its market price. To compute the Z-spread, set the present value of the bond’s cash flows equal to today’s market price. Discount each cash flow at the appropriate zero-coupon bond spot rate plus a fixed spread named ZS. 89.464 = + + Solve for ZS. Note that ZS can be found by replacing Choice A, B and C into the equation to see which is the correct answer. ZS=1.67%