Reading 67: Introduction to the Valuation of Fixed Income

答案和详解如下：

6．Which of the following statements concerning arbitrage-free bond prices is FALSE?

A)   The riskier the bond, the greater is its credit spread.

B)   It is not possible to strip coupons from U.S. Treasuries and resell them.

C)   The determination of spot rates is usually done using risk-free securities.

D)   Credit spreads are affected by time to maturity.

The correct answer was B)

It is possible to both strip coupons from U.S. Treasuries and resell them, as well as to aggregate stripped coupons and reconstitute them into U.S. Treasury coupon bonds. Therefore, arbitrage arguments ensure that U.S. Treasury securities sell at or very near their arbitrage free values. For valuing non-Treasury securities, a credit spread is added to each treasury spot yields. The credit spread is a function of default risk and the term to maturity.

7．Current spot rates are as follows:

1-Year: 6.5%
2-Year: 7.0%
3-Year: 9.2%

Which of the following is TRUE?

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)   The yield to maturity for 3-year annual pay coupon bond can be found by taking the arithmetic average of the 3 spot rates.

C)   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.

D)   The yield to maturity for 3-year annual pay coupon bond can be found by taking the geometric average of the 3 spot rates.

The correct answer was C)

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 equates all cash flows to the bond’s price. Current spot rates have nothing to do with the bond’s yield to maturity.

8．A 2-year option-free bond (par value of $10,000) has an annual coupon of 15 percent. An investor determines that the spot rate of year 1 is 16 percent and the year 2 spot rate is 17 percent. Using the arbitrage-free valuation approach, the bond price is closest to:

A)   $8,401.

B)   $10,000.

C)   $11,122.

D)   $9,694.

The correct answer was D)

We can calculate the price of the bond by discounting each of the annual payments by the appropriate spot rate and finding the sum of the present values. Price = [1,500/(1.16)] + [11,500/(1.17)²] = $9,694. Or, in keeping with the notion that each cash flow is a separate bond, sum the following transactions on your financial calculator:

N=1, I/Y=16.0, PMT=0, FV=1,500, CPT PV=1,293
N=2, I/Y=17.0, PMT=0, FV=11,500, CPT PV=8,401

Price = 1,293 + 8,401 = $9,694.

9．2-year option-free bond (par value of $1,000) has an annual coupon of 6 percent. An investor determines that the spot rate of year 1 is 5 percent and the year 2 spot rate is 8 percent. Using the arbitrage-free valuation approach, the bond price is closest to:

A)   $992.

B)   $966.

C)   $1,000.

D)   $1,039.

The correct answer was B)

The arbitrage free valuation approach is the process of valuing a fixed income instrument as a portfolio of zero coupon bonds. We can calculate the price of the bond by discounting each of the annual payments by the appropriate spot rate and finding the sum of the present values. Bond Price = [60/(1.05)] + [1,060/(1.08)²] = $966. Or, in keeping with the notion that each cash flow is a separate bond, sum the following transactions on your financial calculator:

N=1, I/Y=5.0, PMT=0, FV=60, CPT PV=57.14
N=2, I/Y=8.0, PMT=0, FV=1,060, CPT PV=908.78
Price = 57.14 + 908.78 = $966.

10．A 3-year option-free bond (par value of $1,000) has an annual coupon of 9 percent. An investor determines that the spot rate of year 1 is 6 percent, the year 2 spot rate is 12 percent, and the year 3 spot rate is 13 percent. Using the arbitrage-free valuation approach, the bond price is closest to:

A)   $968.

B)   $1,000.

C)   $912.

D)   $1,080.

The correct answer was C)

We can calculate the price of the bond by discounting each of the annual payments by the appropriate spot rate and finding the sum of the present values. Price = [90/(1.06)] + [90/(1.12)²] + [1,090/(1.13)³] = 912. Or, in keeping with the notion that each cash flow is a separate bond, sum the following transactions on your financial calculator:

N=1, I/Y=6.0, PMT=0, FV=90, CPT PV=84.91
N=2, I/Y=12.0, PMT=0, FV=90, CPT PV=71.75
N=3, I/Y=13.0, PMT=0, FV=1,090, CPT PV=755.42

Price = 84.91 + 71.75 + 755.42 = $912.08.

11．You are considering the purchase of a three-year annual coupon bond with a par value of $1,000 and a coupon rate of 5.5 percent. You have determined that the spot rate for year 1 is 5.2 percent, the spot rate for year two is 5.5 percent, and the spot rate for year three is 5.7 percent. What would you be willing to pay for the bond now?

A)   $937.66.

B)   $995.06.

C)   $1,000.00.

D)   $910.29.

The correct answer was B)

You need the find the present value of each cash flow using the spot rate that coincides with each cash flow.
The present value of cash flow 1 is: FV=$55, PMT=0, I/Y=5.2%, N=1, and compute PV=-$52.28.
The present value of cash flow 2 is: FV=$55, PMT=0, I/Y=5.5%, N=2, and compute PV= –$49.42.
The present value of cash flow 3 is: FV=$1,055, PMT=0, I/Y=5.7%, N=3, and compute PV= –$893.36.
The most you pay for the bond is the sum of: $52.28 + $49.42 + $893.36 = $995.06.