LOS f, (Part 1): Explain the arbitrage-free valuation approach and the market process that forces the price of a bond toward its arbitrage-free value.

Q1. 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%. You have determined that the spot rate for year 1 is 5.2%, the spot rate for year two is 5.5%, and the spot rate for year three is 5.7%. What would you be willing to pay for the bond now?

A)   $937.66.

B)   $995.06.

C)   $1,000.00.

Q2. A 3-year option-free bond (par value of $1,000) has an annual coupon of 9%. An investor determines that the spot rate of year 1 is 6%, the year 2 spot rate is 12%, and the year 3 spot rate is 13%. Using the arbitrage-free valuation approach, the bond price is closest to:

A)   $912.

B)   $1,080.

C)   $968.

Q3. A 2-year option-free bond (par value of $1,000) has an annual coupon of 6%. An investor determines that the spot rate of year 1 is 5% and the year 2 spot rate is 8%. Using the arbitrage-free valuation approach, the bond price is closest to:

A)   $992.

B)   $1,039.

C)   $966.

Q4. A 2-year option-free bond (par value of $10,000) has an annual coupon of 15%. An investor determines that the spot rate of year 1 is 16% and the year 2 spot rate is 17%. Using the arbitrage-free valuation approach, the bond price is closest to:

A)   $9,694.

B)   $8,401.

C)   $11,122.

Q5. 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, 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.

B)   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.

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.

Q6. Which of the following statements concerning arbitrage-free bond prices is FALSE?

A)   Credit spreads are affected by time to maturity.

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.

Q7. Which of the following statements concerning the arbitrage-free valuation of non-Treasury securities is TRUE? The credit spread is:

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

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

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

Q8. The arbitrage-free bond valuation approach can best be described as the:

A)   use of a single discount factor.

B)   geometric average of the spot interest rates.

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

Q9. A three-year bond with a 10% 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 $1,100 at year 3. The spot rate for year 1 is 5%, the spot rate for year 2 is 6%, and the spot rate for year 3 is 6.5%. What is the arbitrage-free value of the bond?

A)   $1,094.87.

B)   $1,050.62.

C)   $975.84.

Q10. 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)   Buying pressure should increase its value.

B)   Buying pressure should decrease its value.

C)   Selling pressure should decrease its value.

Q11. Which of the following packages of securities is equivalent to a three-year 8% coupon bond with semi-annual coupon payments and a par value of 100? A three-year zero-coupon bond:

A)   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.

B)   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.

C)   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.

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