Reading 56: LOS e ～ Q 5- 22

James uses a rounded day count of 0.5 years for each semi-annual period.

Following Wallace's first lecture he asks the trainees which of the following explains an upward sloping yield curve according to the (unbiased) pure expectations theory of the term structure of interest rates?

A)   There is a risk premium associated with more distant maturities.

B)   There is greater demand for long-term securities than for short-term securities.

C)   The market expects short-term rates to rise through the relevant future.

D)   There is greater demand for short-term securities than for long-term securities.

6.Wallace now poses a similar question regarding the liquidity preference theory. Which of the following could explain an upward sloping yield curve according to the liquidity preference theory of the term structure of interest rates?

A)   The market expects short-term rates to rise through the relevant future.

B)   There is greater demand for long-term securities than for short-term securities.

C)   There is greater demand for short-term securities than for long-term securities.

D)   There is a risk premium associated with more distant maturities.

7.Wallace explains to the class that the swap fixed rate is one where the values of the floating-rate and the fixed-rate are the same at the inception of the swap. Using the information in Table 1, he asks the class to compute the swap fixed rate for a one-year plain vanilla interest rate swap with semiannual payments. Which of the following is the closest to the correct answer?

A)   3.43%.

B)   7.25%.

C)   2.56%.

D)   5.18%.

8.Wallace finally asks the class about the market segmentation theory of the term structure of interest rates. Specifically, Wallace asks which of the following could explain an upward sloping yield curve according to the market segmentation theory?

A)   There is greater demand for short-term securities than for long-term securities.

B)   There is a risk premium associated with more distant maturities.

C)   The market expects short-term rates to rise through the relevant future.

D)   There is greater demand for long-term securities than for short-term securities.

9.Wallace presents the relationships between spot and forward rates according to the pure expectations theory. Which of the following is closest to the one-year implied forward rate one year from now?

A)   6.58%.

B)   6.48%.

C)   5.75%.

D)   6.25%.

10.Wallace completes his first lecture by tying the relationship between Treasury prices and the shape of the term structure. He is particularly interested in the implications of a steepening yield curve. Which of the following must be TRUE for a steepening yield curve?

A)   The price of short-term Treasury securities increases.

B)   The price of short-term Treasury securities increases relative to the price of long-term Treasury securities.

C)   The price of long-term Treasury securities increases.

D)   The price of long-term Treasury securities increases relative to the price of short-term Treasury securities.

11.The liquidity theory of the term structure of interest rates is a variation of the pure expectations theory that explains why:

A)   duration is an imprecise measure.

B)   convexity is an imprecise measure.

C)   the yield curve usually slopes downward.

D)   the yield curve usually slopes upward.

12.Which theory explains the shape of the yield curve by considering the relative demands for various maturities?

A)   The pure expectations theory.

B)   The segmentation theory.

C)   The liquidity premium theory.

D)   The relative strength theory.

13.If the liquidity preference hypothesis is true, what shape should the term structure curve have in a period where interest rates are expected to be constant?

A)   flat.

B)   upward sweeping.

C)   downward sweeping.

D)   hump-backed.

14.Assuming the pure expectations theory is correct, an upward sloping yield curve implies:

A)   interest rates are expected to increase in the future.

B)   longer-term bonds are riskier than short-term bonds.

C)   interest rates are expected to decline in the future.

D)   shorter-term bonds are less risky than longer-term bonds.

15.According to the pure expectations theory, how are forward rates interpreted? Forward rates are:

A)   equal to futures rates.

B)   expected future spot rates if the risk premium is equal to zero.

C)   expected future spot rates.

D)   the expected future difference between short and long-term rates.

16.According to the liquidity theory, how are forward rates interpreted? Forward rates are:

A)   expected future spot rates if the risk premium is equal to zero.

B)   equal to futures rates.

C)   expected future spot rates.

D)   the expected future difference between short and long-term rates.

17.Which of the following correctly explains the "locked-in-rate" interpretation of forward rates? The forward rate allows an investor to lock in:

A)   a coupon rate for the current period.

B)   an interest rate for the current period.

C)   a coupon rate for some future period.

D)   an interest rate for some future period.

18.The liquidity premium theory of the term structure of interest rates projects that the normal shape of the yield curve will be:

A)   downward sloping.

B)   flat.

C)   variable.

D)   upward sloping.

19.Which of the following is TRUE according to the pure expectations theory? Forward rates:

A)   always overestimate future spot rates.

B)   exclusively represent expected future spot rates.

C)   are biased estimates of market expectations.

D)   are always non-negative.

20.What are the implications for the shape of the yield curve according to the liquidity theory? The yield curve:

A)   is always flat.

B)   must be upward sloping.

C)   may have any shape.

D)   must be downward sloping.

21.A portfolio manager who believed in the liquidity premium theory would expect:

A)   long-term securities to offer higher returns than short-term securities.

B)   rational investors to pay a price premium for short-term securities.

C)   all of the choices are correct.

D)   long-term rates to be higher than investors’ expectations of future rates, because of the liquidity premium.

22.Which of the following correctly explains the "break-even-rate" interpretation of forward rates? The forward rate is the rate that will make an investor indifferent between investing:

A)   now or at a forward time.

B)   investing at the spot or forward interest rate.

C)   for the full investment horizon, or for part of it, and then rolling over the proceeds for the balance of the investment horizon at the forward rate.

D)   for the full investment horizon or for part of it.

James uses a rounded day count of 0.5 years for each semi-annual period.

Following Wallace's first lecture he asks the trainees which of the following explains an upward sloping yield curve according to the (unbiased) pure expectations theory of the term structure of interest rates?

A)   There is a risk premium associated with more distant maturities.

B)   There is greater demand for long-term securities than for short-term securities.

C)   The market expects short-term rates to rise through the relevant future.

D)   There is greater demand for short-term securities than for long-term securities.

The correct answer was C)

Under this theory, forward rates exclusively represent expected future spot rates. Thus the entire term structure at a given time reflects the market's expectations of future short term spot rates.

6.Wallace now poses a similar question regarding the liquidity preference theory. Which of the following could explain an upward sloping yield curve according to the liquidity preference theory of the term structure of interest rates?

A)   The market expects short-term rates to rise through the relevant future.

B)   There is greater demand for long-term securities than for short-term securities.

C)   There is greater demand for short-term securities than for long-term securities.

D)   There is a risk premium associated with more distant maturities.

The correct answer was D)

According to the liquidity preference theory, the pure expectations theory applies but is modified for a risk or term premium. The longer the maturity, the greater the risk of price fluctuation to the investor.

Short-term rates to rise through the relevant future could explain an upward sloping yield curve according to the pure expectations theory. Greater demand for long-term securities than for short-term securities would drive the yields on long-term securities down and would result in an inverted (downward sloping) yield curve. Greater demand for short-term securities than for long-term securities could explain an upward sloping yield curve according to the market segmentation theory. The market segmentation theory implies that the rate of interest for a particular maturity is determined solely by demand and supply for that maturity, with no reference to conditions for other maturities.

7.Wallace explains to the class that the swap fixed rate is one where the values of the floating-rate and the fixed-rate are the same at the inception of the swap. Using the information in Table 1, he asks the class to compute the swap fixed rate for a one-year plain vanilla interest rate swap with semiannual payments. Which of the following is the closest to the correct answer?

A)   3.43%.

B)   7.25%.

C)   2.56%.

D)   5.18%.

The correct answer was D)

First calculate the discount factors:

Z₁₈₀ = 1/[1+(.05x180/360)] = .9756

Z₃₆₀ = 1/[1+(.052498x360/360)] = .9501

The semi-annual fixed rate on the swap is:

(1-.9501)/(.9756 + .9501) = 2.59% x 2 = 5.18%

8.Wallace finally asks the class about the market segmentation theory of the term structure of interest rates. Specifically, Wallace asks which of the following could explain an upward sloping yield curve according to the market segmentation theory?

A)   There is greater demand for short-term securities than for long-term securities.

B)   There is a risk premium associated with more distant maturities.

C)   The market expects short-term rates to rise through the relevant future.

D)   There is greater demand for long-term securities than for short-term securities.

The correct answer was A)

This could explain an upward sloping yield curve according to the market segmentation theory. The market segmentation theory implies that the rate of interest for a particular maturity is determined solely by demand and supply for that maturity, with no reference to conditions for other maturities.

A risk premium associated with more distant maturities could explain an upward sloping yield curve according to the liquidity preference theory. The market expecting short-term rates to rise through the relevant future could explain an upward sloping yield curve according to the pure expectations theory. Greater demand for long-term securities than for short-term securities would drive the yields on long-term securities down and would result in an inverted (downward sloping) yield curve.

9.Wallace presents the relationships between spot and forward rates according to the pure expectations theory. Which of the following is closest to the one-year implied forward rate one year from now?

A)   6.58%.

B)   6.48%.

C)   5.75%.

D)   6.25%.

The correct answer was D)

The 2 year spot rate is 5.7492 meaning the return that should be earned after 2 years would be 5.7492 + 5.7492 = 11.498%.  The 1 year spot rate is 5.2498 therefore the 1 year forward rate 1 year from now must be the difference between the 11.498% earned over the 2 year spot rates and the 1 year spot rate.  Thus the 1 year forward rate 1 year from now is 11.498 - 5.2498 = 6.2486 or 6.25%.

10.Wallace completes his first lecture by tying the relationship between Treasury prices and the shape of the term structure. He is particularly interested in the implications of a steepening yield curve. Which of the following must be TRUE for a steepening yield curve?

A)   The price of short-term Treasury securities increases.

B)   The price of short-term Treasury securities increases relative to the price of long-term Treasury securities.

C)   The price of long-term Treasury securities increases.

D)   The price of long-term Treasury securities increases relative to the price of short-term Treasury securities.

The correct answer was B)

For a steepening of the yield curve to occur, in every case, the short-term yield has to decrease relative to the long-term yield. Therefore, the price of short-term Treasury securities increases relative to the price of long-term securities.

11.The liquidity theory of the term structure of interest rates is a variation of the pure expectations theory that explains why:

A)   duration is an imprecise measure.

B)   convexity is an imprecise measure.

C)   the yield curve usually slopes downward.

D)   the yield curve usually slopes upward.

The correct answer was D)

The pure expectations hypothesis says that the shape of the yield curve only reflects expectations of future short-term rates. Yet, the yield curve generally slopes upward. The liquidity theory says that the yield curve incorporates expectations of short-term rates; however, the tendency for the yield curve to slope upward reflects the demand for a higher return to compensate investors for the extra interest rate risk associated with bonds with longer maturities.

12.Which theory explains the shape of the yield curve by considering the relative demands for various maturities?

A)   The pure expectations theory.

B)   The segmentation theory.

C)   The liquidity premium theory.

D)   The relative strength theory.

The correct answer was B)

The market segmentation theory contends that lenders and borrowers have preferred maturity ranges, and that supply and demand forces in each maturity range determines yields. This theory relies on the idea that some investors have restrictions (either legal or practical) on their preferred maturity structure and that they are unwilling or unable to move out of their preferred ranges.

13.If the liquidity preference hypothesis is true, what shape should the term structure curve have in a period where interest rates are expected to be constant?

A)   flat.

B)   upward sweeping.

C)   downward sweeping.

D)   hump-backed.

The correct answer was B)

The liquidity theory holds that investors demand a premium to compensate them for interest rate exposure and the premium increases with maturity. Add this premium to a flat curve and the result is an upward sloping yield curve.

14.Assuming the pure expectations theory is correct, an upward sloping yield curve implies:

A)   interest rates are expected to increase in the future.

B)   longer-term bonds are riskier than short-term bonds.

C)   interest rates are expected to decline in the future.

D)   shorter-term bonds are less risky than longer-term bonds.

The correct answer was A)

The yield curve slopes upward because short-term rates are lower than long-term rates. Since market rates are determined by supply and demand, it follows that investors (demand side) expect rates to be higher in the future than in the near-term.

15.According to the pure expectations theory, how are forward rates interpreted? Forward rates are:

A)   equal to futures rates.

B)   expected future spot rates if the risk premium is equal to zero.

C)   expected future spot rates.

D)   the expected future difference between short and long-term rates.

The correct answer was C)

The pure expectations theory, also referred to as the unbiased expectations theory, purports that forward rates are solely a function of expected future spot rates. This implies that long-term interest rates represent the geometric mean of future expected short-term rates, nothing more.

16.According to the liquidity theory, how are forward rates interpreted? Forward rates are:

A)   expected future spot rates if the risk premium is equal to zero.

B)   equal to futures rates.

C)   expected future spot rates.

D)   the expected future difference between short and long-term rates.

The correct answer was A)

The liquidity theory of the term structure proposes that forward rates reflect investors’ expectations of future rates plus a liquidity premium to compensate them for exposure to interest rate risk, and this liquidity premium is positively related to maturity. The implication of the liquidity theory is that forward rates are a biased estimate of the market’s expectation of future rates, since they include a liquidity premium.

17.Which of the following correctly explains the "locked-in-rate" interpretation of forward rates? The forward rate allows an investor to lock in:

A)   a coupon rate for the current period.

B)   an interest rate for the current period.

C)   a coupon rate for some future period.

D)   an interest rate for some future period.

The correct answer was D)

The pure expectations theory can be explained using a “locked-in-rate” line of reasoning, whereby forward rates are interpreted as the rate that can be “locked in” for some future period.

18.The liquidity premium theory of the term structure of interest rates projects that the normal shape of the yield curve will be:

A)   downward sloping.

B)   flat.

C)   variable.

D)   upward sloping.

The correct answer was D)

The liquidity theory holds that investors demand a premium to compensate them to interest rate exposure and the premium increases with maturity. By itself, the liquidity theory implies an upward sloping yield curve.

19.Which of the following is TRUE according to the pure expectations theory? Forward rates:

A)   always overestimate future spot rates.

B)   exclusively represent expected future spot rates.

C)   are biased estimates of market expectations.

D)   are always non-negative.

The correct answer was B)

The pure expectations theory, also referred to as the unbiased expectations theory, purports that forward rates are solely a function of expected future spot rates. Under the pure expectations theory, a yield curve that is upward (downward) sloping, means that short-term rates are expected to rise (fall). A flat yield curve implies that the market expects short-term rates to remain constant.

20.What are the implications for the shape of the yield curve according to the liquidity theory? The yield curve:

A)   is always flat.

B)   must be upward sloping.

C)   may have any shape.

D)   must be downward sloping.

The correct answer was C)

The liquidity theory holds that investors demand a premium to compensate them to interest rate exposure and the premium increases with maturity. Even after adding the premium to a steep downward sloping yield curve the result will still be downward sloping.

21.A portfolio manager who believed in the liquidity premium theory would expect:

A)   long-term securities to offer higher returns than short-term securities.

B)   rational investors to pay a price premium for short-term securities.

C)   all of the choices are correct.

D)   long-term rates to be higher than investors’ expectations of future rates, because of the liquidity premium.

The correct answer was C)

The liquidity theory of the term structure proposes that forward rates reflect investors’ expectations of future rates plus a liquidity premium to compensate them for exposure to interest rate risk, and this liquidity premium is positively related to maturity. The implication of the liquidity theory is that forward rates, since they include a liquidity premium, are a biased estimate of the market’s expectation of future spot rates.

22.Which of the following correctly explains the "break-even-rate" interpretation of forward rates? The forward rate is the rate that will make an investor indifferent between investing:

A)   now or at a forward time.

B)   investing at the spot or forward interest rate.

C)   for the full investment horizon, or for part of it, and then rolling over the proceeds for the balance of the investment horizon at the forward rate.

D)   for the full investment horizon or for part of it.

The correct answer was C)

The pure expectations theory can be explained using a “break-even rate” line of reasoning. The break even rate is the forward rate that leaves investors indifferent between investing for the full term of their investment horizon or investing in part of the horizon and rolling the investment over at the “break-even” forward rate for the remainder of the term.