FINC462/662 - Fixed Income Seccurities: Lecture 05 Quiz

Question 1

How is the dirty (full) price of a bond conceptually determined?

It is the quoted clean price plus a market-convention adjustment unrelated to future cash flows. It is the present value of all future coupon and principal cash flows discounted at the appropriate interest rates. It is the sum of all future coupon payments without discounting, plus par value. It is defined purely by supply and demand and has no relationship to discounted cash flows.

Question 2

A Treasury bond has a face value of $100 and an annual coupon rate of 4%, paid semi-annually. What is each semi-annual coupon payment?

$0.04 $2.00 $4.00 $8.00

Question 3

Consider a 3-year Treasury note with a 4.0% annual coupon rate (paid semi-annually) and a par value of $100. Which description of the bond’s cash flows is correct?

Three coupon payments of $4.0 (one at the end of each year) and a separate $100 principal repayment at year 3. Six coupon payments of $2.0 every six months, and on the final coupon date at year 3 the investor also receives the $100 principal, for a total of $102.0 at maturity. Six equal total payments of $2.0, and the $100 principal is repaid one period after the last coupon payment. One coupon payment of $4.0 at year 3 and a $100 principal repayment at year 5.

Question 4

When is it appropriate to use the annuity formula as a shortcut to price a coupon bond?

When coupon payments are identical through time and a single interest rate is used to discount all cash flows. When the coupon rate changes every year but the face value is fixed. Only for bonds with embedded call or put options. Only for semi-annual coupon bonds.

Question 5

Which of the following best describes a zero-coupon bond?

A bond that pays no coupons and a single principal cash flow at maturity. A bond that pays small coupons each period and a large coupon at maturity instead of principal. A bond that pays coupons only for the first half of its life and nothing at maturity. A perpetuity that pays coupons forever and never matures.

Question 6

What does the discount factor D(T) represent?

The future value at time T of $1 invested today. The present value today of $1 to be received at time T. The annual coupon rate of the bond. The difference between clean and dirty prices.

Question 7

Assuming a positive interest-rate environment, which statement about discount factors D(T) is usually true?

D(T) is always greater than 1 and increases as T increases. D(T) is always equal to the bond’s coupon rate. D(T) is less than or equal to 1 and generally decreases as T increases. D(T) must be exactly zero for all positive T.

Question 8

How is a Treasury bond conceptually related to zero-coupon bonds?

It is equivalent to a single zero-coupon bond maturing on the first coupon date. It is a bundle (portfolio) of zero-coupon bonds with different maturities, one for each cash flow. It has no relationship to zero-coupon bonds. It is identical to a perpetuity plus a zero-coupon bond.

Question 9

To price a coupon bond using discount factors D(T), what should you do with the bond's cash flows?

Discount only the final principal payment and ignore the coupon cash flows. Multiply each cash flow at time T by the corresponding D(T) and sum the results. Multiply all cash flows by a single discount factor, regardless of their timing. Average the discount factors and multiply by the bond’s face value only.

Question 10

Suppose you observe the full set of discount factors D(T) for all maturities up to 30 years, where each D(T) is the price today of a $1 zero-coupon bond maturing at time T. Ignoring credit risk, what additional interest-rate information is required to compute the arbitrage-free price of any fixed-coupon Treasury bond with maturity at or below 30 years?

You must also assume a yield-to-maturity specific to that bond. No further term-structure information is needed; the discount factors and the bond’s cash-flow schedule are sufficient. You must know the future reinvestment rate for each coupon payment. You must know the credit spread term structure, even for default-free Treasuries.

FINC409/609 - Fixed Income Securities

Prof. Matt Fleckenstein

Lecture 5 - Quiz

Bond Pricing & Discount Factors Quiz