Deck 11: The Term Structure of Interest Rates

Question 1

A Treasury bill is a zero-coupon instrument. Therefore, its annualized yield is equal to the spot rate. Similarly, for the one-year Treasury, its cited yield is the one-year spot rate. Given these two spot rates, we can compute the spot rate for ________.

A) a theoretical 0.5-year zero-coupon Treasury.
B) a theoretical 1.0-year zero-coupon Treasury.
C) a theoretical 1.5-year zero-coupon Treasury.
D) a theoretical 2.0-year zero-coupon Treasury.

Answer 1

C

Question 2

As quoted on a bond equivalent basis, what is the forward rate (f) for if the six-month spot rate is 3.50% and the one-year spot rate is 6.55%?

A) 9.65%
B) 8.12%
C) 6.28%
D) 4.83%

Answer 2

A

Question 3

The convention in the marketplace is to refer to a Treasury positively sloped yield curve whose maturity spread (measured by the six month and 30-year yields) as a ________ when the spread is 300 basis points or less.

A) maturity yield curve
B) positively sloped yield curve
C) normal yield curve
D) negatively sloped yield curve

Answer 3

C

Question 4

Market participants have tended to construct yield curves from observations of prices and yields in the Treasury market. Two reasons account for this tendency. Which of the below is ONE of these reasons?

A) The smallest and most inactive bond market, the Treasury market offers the fewest problems of illiquidity or frequent trading
B) Treasury securities have a small amounts of default risk, and differences in creditworthiness do affect yield estimates.
C) The largest and most active bond market, the Treasury market offers the fewest problems of illiquidity or infrequent trading.
D) Treasury securities are full of default risk, and differences in creditworthiness do not affect yield estimates.

Question 5

Consider the following two investment alternatives for an investor who has a one-year investment horizon. For Alternative 1, the investor buys a one-year instrument. For alternative 2, the investor buys a six-month instrument and when it matures in six months the investor buys another six-month instrument. Which of the below statements is FALSE?

A) Given the one-year spot rate, there is some rate on a six-month instrument one year from now that will make the investor indifferent between the two alternatives.
B) With Alternative 1, the investor will realize the one-year spot rate and that rate is known with certainty.
C) With Alternative 2, the investor will realize the six-month spot rate, but the six-month rate six months from now is unknown.
D) For Alternative 2, the rate that will be earned over one year is not known with certainty.

Question 6

Suppose that the six-month spot rate is 4.00% and one-year spot rate is 8.10%. Additionally, suppose that you can look into a crystal ball and know for sure that six months from now that the six-month rate will be 3.60%. Finally, suppose that there is an investor who expects that six months from now, the six month rate will be 4.10%. That is, the investor expects that the six-month rate will be higher than its current level of 4.00%. How would you advise an investor who wants to buy a six-month instrument and when it matures in six months buy another six-month instrument?

A) You would advise the investor to buy at the six-month spot rate and then in six months buy another six-month instrument because the investor will make 41.6 cents more this way for every $100 invested.
B) It really does not matter because you will break even either way.
C) You would advise the investor not to buy at the current rate and reinvest six month later by buying another six-month instrument because the investor will lose money compared to investing at the one-year spot rate.
D) Using the formula for "f" we can show that the investor is correct in their assessment and thus it does not matter what the six-month spot rate will be in six months.

Question 7

With an upward-sloping yield curve, the yield rises steadily as the ________.

A) maturity premium falls.
B) default premium falls.
C) maturity decreases.
D) maturity increases.

Question 8

There have not been many instances in the recent history of the U.S. Treasury market where the yield curve exhibited ________.

A) a downward-sloping.
B) a normal sloping yield curve.
C) a reverted yield curve.
D) an upward-sloping yield curve.

Question 9

Which of the below statements is FALSE?

A) To determine the value of each zero-coupon instrument, it is necessary to know the yield on a zero-coupon Treasury with that same maturity ─ this yield is called the forward rate.
B) Each zero-coupon instrument in the package has a maturity equal to its coupon payment date or, in the case of the principal, the maturity date.
C) The value of the bond should equal the value of all the component zero-coupon instruments.
D) the graphical depiction of the relationship between the spot rate and its maturity is called the spot rate curve.

Question 10

Because of the different cash flow patterns, it is not appropriate to use ________ to discount all cash flows because each cash flow should be discounted at ________ that is appropriate for the time period in which the cash flow will be received.

A) the same interest rate; a different interest rate
B) the same interest rate; a unique interest rate
C) a different interest rate; a common interest rate
D) a different interest rate; a unique interest rate

Question 11

The market prices its expectations of future interest rates into the rates offered ________.

A) on investments with the same maturity date.
B) on investments with two different maturity dates.
C) on investments with different maturities.
D) None of these

Question 12

More recently market participants have come to realize that the traditionally constructed Treasury yield curve is ________ measure of the relation between required yield and maturity with the key reason is that securities with the same maturity may actually provide ________.

A) an unsatisfactory; different yields
B) an unsatisfactory; very similar yields
C) a satisfactory; different yields
D) a satisfactory; very similar yields

Question 13

What is the forward rate (f) for if the six-month spot rate is 5% and the one-year spot rate is 9%?

A) 6.00%
B) 6.12%
C) 6.31%
D) 6.54%

Question 14

The correct way to think about bonds A and B is not as bonds but as packages of ________.

A) coupon payments.
B) separate bond instruments.
C) zero-coupons without payments.
D) zero-coupon instruments.

Question 15

Suppose an investor purchases a five-year, zero-coupon Treasury security for $58.48 with a maturity value of $100. The investor could instead buy a six-month Treasury bill and reinvest the proceeds every six months for five years. The number of dollars that will be realized will ________.

A) be independent of spot and forward rates.
B) not depend on the six-month forward rates.
C) depend solely on the six-month spot rate today.
D) depend on the six-month forward rates.

Question 16

What is the forward rate (f) for a six-month security if z₁ is 2.00% and z₂ is 3.50%?

A) 5.00%
B) 5.02%
C) 5.04%
D) 5.06%

Question 17

It is important to remember that the basic principle underlying bootstrapping is that the value of the Treasury coupon security should be equal to the value of the package of ________ that duplicates the ________.

A) coupon paying T-Bills; coupon bond's cash flow
B) zero-coupon Treasury securities; coupon bond's cash flow
C) coupon paying T-Bills; discount bond's cash flow
D) zero-coupon Treasury securities; discount bond's cash flow

Question 18

Which of the below equations give the forward rate (f) for a six-month security if z₁ is the six-month spot rate and z₂ is the one-year spot rate?

A) f =
B) f =
C) f =
D) f =

Question 19

As quoted on a bond equivalent basis, what is the forward rate (f) for a six-month security if z₁ is 2.00% and z₂ is 4.50%?

A) 7.06%
B) 9.02%
C) 14.12%
D) 15.06%

Question 20

The slope of a yield curve is commonly measured in terms of ________, which is the difference between long-term and short-term yields.

A) the yield curve spread
B) the maturity spread
C) the default spread
D) the interest rate spread

Question 21

Ilmanen investigated the effect of the behavior of ________ using historical average returns on U.S. Treasury securities.

A) the bond risk premium
B) the convexity bias
C) market's expectations
D) different maturities

Question 22

Which of the below statements about the pure expectations theory is FALSE.

A) According to the pure expectations theory, the forward rates exclusively represent the expected future rates.
B) The entire term structure at a given time reflects the market's current expectations of the family of future short-term rates.
C) A rising term structure must indicate that the market expects short-term rates to rise throughout the relevant future.
D) A flat term structure reflects an expectation that future short-term rates will always be constant, while a falling term structure must reflect an expectation that future short rates will decline rapidly.

Question 23

Given the spot rates, the theoretical value of a bond can be calculated.

Question 24

For a flat yield curve, the yields are identical for each maturity.

Question 25

If the implied forward rates are realized, an investor that buys a six-month Treasury bill (and reinvests the proceeds every six months for five years) will produce the same number of dollars as an investment in a zero-coupon Treasury security at the five-year spot rate.

Question 26

According to the ________, the forward rates exclusively represent the expected future rates.

A) preferred habitat theory
B) pure expectations theory
C) market segmentation theory
D) pure liquidity theory

Question 27

Comprehensive research on the main influences of the shape of the Treasury yield curve was done by Antti Ilmanen in a series of papers. He finds that there are three main influences. Which of the below is NOT one of these main influences?

A) One influence concerns the market's expectations of future rate can changes (in a way predicted by the pure expectations theory).
B) One influence concerns bond risk premiums.
C) One influence concerns convexity bias.
D) One influence concerns convexity premiums (in a way predicted by the preferred habitat theory).

Question 28

Ilmanen argues that the ________ is the least well known of the three main influences.

A) duration impact
B) basis point influence
C) maturity premium impact
D) convexity bias influence

Question 29

By convention, when the maturity spread for a Treasury security is more than 100 basis points, the yield curve is said to be a steep yield curve.

Question 30

Which of the below statements is FALSE?

A) One interpretation of the Pure Expectations Theory suggests that the return will vary dramatically over a short-term investment horizon starting today.
B) According to the liquidity theory of the term structure, the implicit forward rates will not be an unbiased estimate of the market's expectations of future interest rates because they embody a liquidity premium.
C) The preferred habitat theory adopts the view that the term structure reflects the expectation of the future path of interest rates as well as a risk premium and at the same time rejects the assertion that the risk premium must rise uniformly with maturity.
D) The market segmentation theory differs from the preferred habitat theory in that it assumes that neither investors nor borrowers are willing to shift from one maturity sector to another to take advantage of opportunities arising from differences between expectations and forward rates.

Question 31

If we assume an initially flat term structure followed by economic news that subsequently leads market participants to expect interest rates to rise, which of the below statements is FALSE if the pure expectations theory holds?

A) Market participants interested in a long-term investment would not want to buy long-term bonds because they would expect the yield structure to rise sooner or later, resulting in a price decline for the bonds and a capital loss on the long-term bonds purchased.
B) Any response from borrower or lender would tend either to lower the net demand for, or to increase the supply of, long-maturity bonds, and two responses would increase demand for long-term debt obligations.
C) Speculators expecting rising rates would anticipate a decline in the price of long-term bonds and, therefore, would want to sell any long-term bonds they own and possibly to "short sell" some they do not now own.
D) Borrowers wishing to acquire long-term funds would be pulled toward borrowing now, in the long end of the market, by the expectation that borrowing at a later time would be more expensive.

Question 32

Two major theories have evolved to account for these observed shapes of the yield curve: ________.

A) the expectations theory and the market segmentation theory.
B) the pure expectations theory and the liquidity theory.
C) the expectations theory and the liquidity theory.
D) the liquidity theory and the preferred habitat theory.

Question 33

Market participants refer to forward rates as being hedgeable rates. For example, by buying the one-year security, the investor is able to hedge the six-month rate that will occur six months from now.

Question 34

The preferred habitat theory asserts that, to the extent that the demand and supply of funds in a given maturity range does not match, some lenders and borrowers will be induced to shift to maturities showing the opposite imbalances.

Question 35

There are risks that cause uncertainty about the return over some investment horizon. Which of the below is ONE of these risks?

A) The uncertainty about the coupon payment at the end of the investment horizon if the bond does not default and has not been called or converted.
B) The risk that the price of the bond will be higher than currently expected at the end of the investment horizon.
C) One of these risks involves the uncertainty about the rate at which the proceeds from a bond that matures prior to the maturity date can be reinvested until the maturity date.
D) This risk associated with reinvesting at a known rate of return.

Question 36

For the liquidity theory, the shape of the yield curve is determined by supply of and demand for securities within each maturity sector.

Question 37

Which of the below statements is TRUE?

A) The pure expectations theory pays attention to the risks inherent in investing in bonds and like instruments.
B) In regards to the uncertainty about the return over some investment horizon, one risk involves the uncertainty about the price of the bond at the beginning of the investment horizon.
C) An investor who plans to invest for five years would not consider the alternative of investing in a 30-year bond and selling it at the end of five years.
D) The risk that the price of the bond will be lower than currently expected at the end of the investment horizon is called price risk.

Question 38

To determine the value of each zero-coupon instrument, it is necessary to know the yield on a corporate bond with that same maturity.

Question 39

Studies have demonstrated that forward rates do a good job in predicting future interest rates.

Question 40

The concept of ________ suggests that when interest rates change by a large number of basis points, a Treasury security's price change will not be the same for an increase and decrease in interest rates.

A) inversion
B) maturity premium
C) convexity
D) expectations

Question 41

Name and comment on two of the three main influences on the shape of the Treasury yield curve as suggested by empirical research.

Question 42

What is the basic principle underlying bootstrapping? Explain how to compute the spot rate for a theoretical 1.5-year zero-coupon Treasury.

Question 43

Convexity biases are the expected return differentials across Treasury securities of different maturities.

Question 44

Describe the three generic shapes that have appeared for the U.S. Treasury yield curve with some frequency over time.

Question 45

The empirical evidence suggests that at the front end of the yield curve (i.e., up to a duration of 3), bond risk premiums increase steeply with duration.

Question 46

Explain through an example as to why borrowers (like investors) need to understand the mean of a forward rate.

Question 47

There is a drawback to the pure expectations theory in that it does not consider the risks associated with investing in bonds. Nonetheless, there is risk in holding a long-term bond for one period, and that risk increases with the bond's maturity because maturity and price volatility are directly related. Given this uncertainty, and the reasonable consideration that investors typically do not like uncertainty, some economists and financial analysts have suggested a different theory. What is this theory and explain its relevance including its suggestions about implicit forward rates and yield curve.