6． investor gathers the following information about a 2-year, annual-pay bond:

§ Par value of $1,000

§ Coupon of 4%

§ 1-year spot interest rate is 2%

§ 2-year spot interest rate is 5%

Using the above spot rates, the current price of the bond is closest to:

A)   $1,000.

B)   $1,010.

C)   $990.

D)   $983.

7．investor gathers the following information about a 3-year, annual-pay bond:

§ Par value of $1,000

§ Coupon of 8%

§ Current price of $1,100

§ 1-year spot interest rate is 5%

§ 2-year spot interest rate is 6%

Using the above information, the 3-year spot rate is closest to:

A)   8.00%.

B)   8.20%.

C)   4.37%.

D)   4.27%.

8．ich of the following statements regarding zero-coupon bonds and spot interest rates is FALSE?

A)   Zero-coupon bonds have no coupons.

B)   Price appreciation creates all of the zero-coupon bond's return.

C)   Spot interest rates will never vary across the term structure.

D)   A graph of spot rates versus term to maturity is called the spot yield curve.

9．n spot interest rates be used to value a callable bond?

A)   No.

B)   Yes, however spot interest rates cannot be used to value a putable bond.

C)   Yes.

D)   It depends on the slope of the term structure.

答案和详解如下：

6． investor gathers the following information about a 2-year, annual-pay bond:

§ Par value of $1,000

§ Coupon of 4%

§ 1-year spot interest rate is 2%

§ 2-year spot interest rate is 5%

Using the above spot rates, the current price of the bond is closest to:

A)   $1,000.

B)   $1,010.

C)   $990.

D)   $983.

The correct answer was D)

The value of the bond is simply the present value of discounted future cash flows, using the appropriate spot rate as the discount rate for each cash flow. The coupon payment of the bond is $40 (0.04*1,000). The bond price = 40/(1.02) + 1,040/(1.05)² = $982.53.

7．investor gathers the following information about a 3-year, annual-pay bond:

§ Par value of $1,000

§ Coupon of 8%

§ Current price of $1,100

§ 1-year spot interest rate is 5%

§ 2-year spot interest rate is 6%

Using the above information, the 3-year spot rate is closest to:

A)   8.00%.

B)   8.20%.

C)   4.37%.

D)   4.27%.

The correct answer was D)

The value of the bond is simply the present value of discounted future cash flows, using the appropriate spot rate as the discount rate for each cash flow. The coupon payment of the bond is $80 (0.08*1,000) and the face value is $1,000. Hence, bond price of 1,100= 80/(1.05)+ 80/(1.06)² + 1,080/(1 + 3-year spot rate)³. Using the y^x key on our calculator, we can solve for the 3-year spot rate of 4.27%.

8．ich of the following statements regarding zero-coupon bonds and spot interest rates is FALSE?

A)   Zero-coupon bonds have no coupons.

B)   Price appreciation creates all of the zero-coupon bond's return.

C)   Spot interest rates will never vary across the term structure.

D)   A graph of spot rates versus term to maturity is called the spot yield curve.

The correct answer was C)

Zero-coupon bonds are quite special. Because zero-coupon bonds have no coupons (all of the bond’s return comes from price appreciation), investors have no uncertainty about the rate at which coupons will be invested. Spot rates are defined as interest rates used to discount a single cash flow to be received in the future. A graph of spot rates versus term to maturity is called the spot yield curve.

9．n spot interest rates be used to value a callable bond?

A)   No.

B)   Yes, however spot interest rates cannot be used to value a putable bond.

C)   Yes.

D)   It depends on the slope of the term structure.

The correct answer was C)

Any complex debt instruments (like callable bonds, putable bonds, and mortgage-backed securities) can be viewed as the sum of the present value of its individual cash flows where each of those cash flows are discounted at the appropriate zero-coupon bond spot rate. It should be noted that while the appropriate spot interest rate can be used to discount each cash flow, determining the actual pattern of cash flows is uncertain due to the possibility of the bond being called away.