1．A three-year bond with a 10 percent annual coupon has cash flows of $100 at Year 1, $100 at Year 2, and pays the final coupon and the principal for a cash flow of $1100 at year 3. The spot rate for Year 1 is 5 percent, the spot rate for year 2 is 6 percent, and the spot rate for Year 3 is 6.5 percent. What is the arbitrage-free value of the bond?

A)   $975.84.

B)   $1,094.87.

C)   $962.38.

D)   $1050.62.

2．The arbitrage-free bond valuation approach can best be described as the:

A)   use of a single discount factor.

B)   use of a series of spot interest rates that reflect the current term structure.

C)   arithmetic average of the spot interest rates.

D)   geometric average of the spot interest rates.

3．Which of the following packages of securities is equivalent to a three-year 8 percent coupon bond with semi-annual coupon payments and a par value of 100? A three-year zero-coupon bond:

A)   with a par value of 150 and six 8% coupon bonds with a maturity equal to the time to each coupon payment of the above bond.

B)   with a par of 100 and three zero-coupon bonds with a par value of 4 and maturities equal to the time to each coupon payment of the coupon bond.

C)   with a par of 100 and six zero-coupon bonds with a par value of 4 and maturities equal to the time to each coupon payment of the coupon bond.

D)   with a par of 100 and six zero-coupon bonds with a par value of 8 and maturities equal to the time to each coupon payment of the coupon bond.

4．An investor gathers the following information about three U.S. Treasury annual coupon bonds:

If bond price converge to their arbitrage-free value, what should happen to the price of Bond #3?

A)   Selling pressure should decrease its value.

B)   Buying pressure should increase its value.

C)   Selling pressure should increase its value.

D)   Buying pressure should decrease its value.

5．Which of the following statements concerning the arbitrage-free valuation of non-Treasury securities is TRUE? The credit spread is:

A)   only a function of the bond's default risk.

B)   only a function of the bond's term to maturity.

C)   only a function of the volatility of past interest rates.

D)   a function of default risk and the term to maturity.

答案和详解如下：

1．A three-year bond with a 10 percent annual coupon has cash flows of $100 at Year 1, $100 at Year 2, and pays the final coupon and the principal for a cash flow of $1100 at year 3. The spot rate for Year 1 is 5 percent, the spot rate for year 2 is 6 percent, and the spot rate for Year 3 is 6.5 percent. What is the arbitrage-free value of the bond?

A)   $975.84.

B)   $1,094.87.

C)   $962.38.

D)   $1050.62.

The correct answer was 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. To find the arbitrage-free value:

Bond value = [$100/(1.05)] + [$100/(1.06)²] + [$1100/(1.065)³]

= $95.24 + $89.00 + $910.63 = $1094.87

2．The arbitrage-free bond valuation approach can best be described as the:

A)   use of a single discount factor.

B)   use of a series of spot interest rates that reflect the current term structure.

C)   arithmetic average of the spot interest rates.

D)   geometric average of the spot interest rates.

The correct answer was B)

The use of multiple discount rates (i.e., a series of spot rates that reflect the current term structure) will result in more accurate bond pricing and in so doing, will eliminate any meaningful arbitrage opportunities. That is why the use of a series of spot rates to discount bond cash flows is considered to be an arbitrage-free valuation procedure.

3．Which of the following packages of securities is equivalent to a three-year 8 percent coupon bond with semi-annual coupon payments and a par value of 100? A three-year zero-coupon bond:

A)   with a par value of 150 and six 8% coupon bonds with a maturity equal to the time to each coupon payment of the above bond.

B)   with a par of 100 and three zero-coupon bonds with a par value of 4 and maturities equal to the time to each coupon payment of the coupon bond.

C)   with a par of 100 and six zero-coupon bonds with a par value of 4 and maturities equal to the time to each coupon payment of the coupon bond.

D)   with a par of 100 and six zero-coupon bonds with a par value of 8 and maturities equal to the time to each coupon payment of the coupon bond.

The correct answer was C)

This combination of zero-coupon bonds has exactly the same cash flows as the above coupon bond and therefore it is equivalent to it.

4．An investor gathers the following information about three U.S. Treasury annual coupon bonds:

	Bond #1	Bond #2	Bond #3
Maturity	2-year	1-year	2-year
Price	$10,000	$476.19	$9,500
Coupon	5%	0%	0%
Par Value	$10,000	$500	$10,500
Misvaluation	$0	$0	?

If bond price converge to their arbitrage-free value, what should happen to the price of Bond #3?

A)   Selling pressure should decrease its value.

B)   Buying pressure should increase its value.

C)   Selling pressure should increase its value.

D)   Buying pressure should decrease its value.

The correct answer was B)

Currently, an arbitrage opportunity exists with the three bonds. An investor could purchase Bonds #2 and #3 and sell Bond #1 for an arbitrage-free profit of $23.81 (10,000 + -476.19 + -9,500). This action will result in positive income today in return for no future obligation – an arbitrage opportunity. Hence, buying pressure on Bond #3 should increase its value to the point where the arbitrage opportunity would cease to exist.

5．Which of the following statements concerning the arbitrage-free valuation of non-Treasury securities is TRUE? The credit spread is:

A)   only a function of the bond's default risk.

B)   only a function of the bond's term to maturity.

C)   only a function of the volatility of past interest rates.

D)   a function of default risk and the term to maturity.

The correct answer was D)

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.