Table 1 LIBOR Forward Rates, Volatilities, and Implied Spot Rates
Period	Rates	Period	Volatilities	Implied spot rates
0 x 3	5.00%	0 x 3	20.00%	5.00%
3 x 6	5.50%	3 x 6	20.00%	5.25%
6 x 9	5.50%	6 x 9	20.00%	5.33%
9 x 12	5.50%	9 x 12	20.00%	5.37%
12 x 15	6.00%	12 x 15	20.00%	5.50%
15 x 18	6.00%	15 x 18	20.00%	5.58%
18 x 21	6.00%	18 x 21	20.00%	5.64%
21 x 24	6.25%	21 x 24	20.00%	5.72%
24 x 27	6.00%	24 x 27	20.00%	5.75%
27 x 30	6.00%	27 x 30	20.00%	5.77%

Using the data in Table 1, what is the one year implied forward rate under the pure expectations theory?

A)   6.39%.

B)   6.07%.

C)   5.72%.

D)   0.33%.

2.Which of the following statements regarding the preferred habitat theory is least accurate?

A)   Falling short term interest rates are indicated by a downward sloping yield curve.

B)   The preferred habitat theory can be used to explain almost any shape of the yield curve.

C)   The risk premium is a positive or negative risk premium related to supply and demand for funds at various maturities.

D)   Borrowers require cost savings (lower yields) and lenders require a yield premium (higher yields) to move out of their preferred habitats.

3.Which of the following most accurately explains 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.

4.Which of the following most accurately explains an upward sloping yield curve according to the (unbiased) pure expectations theory of the term structure of interest rates?

A)   The market expects a risk premium for more distant maturities.

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

Using the data in Table 1, what is the one year implied forward rate under the pure expectations theory?

A)   6.39%.

B)   6.07%.

C)   5.72%.

D)   0.33%.

The correct answer was B)

The implied forward rate is calculated as follows:

Implied Forward Rate_1,2 = (1 + y₂)²/(1 + y₁) – 1

So we have

Implied Forward Rate_1,2 = (1 + 5.72%)²/(1 + 5.37%) – 1 = 6.07% since the 2 year spot rate is 5.72% and the one year spot rate is 5.37%.

2.Which of the following statements regarding the preferred habitat theory is least accurate?

A)   Falling short term interest rates are indicated by a downward sloping yield curve.

B)   The preferred habitat theory can be used to explain almost any shape of the yield curve.

C)   The risk premium is a positive or negative risk premium related to supply and demand for funds at various maturities.

D)   Borrowers require cost savings (lower yields) and lenders require a yield premium (higher yields) to move out of their preferred habitats.

The correct answer was A)

The liquidity theory states that forward rates reflect investors' expectations of future spot rates plus a liquidity premium positively related to maturity to compensate them for exposure to interest rate risk. This could result in a positive or negative sloping yield curve depending upon the rate at which interest rates are expected to either: increase, stay the same, or decrease.

3.Which of the following most accurately explains 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 of the security, the greater is thought to be the risk of fluctuation in value of principal to the investor.

4.Which of the following most accurately explains an upward sloping yield curve according to the (unbiased) pure expectations theory of the term structure of interest rates?

A)   The market expects a risk premium for more distant maturities.

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

The correct answer was D)

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