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1) Which forward rate cannot be computed from the one-, two-, three-, and four-year spot rates? The rate for a: A

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1) Which forward rate cannot be computed from the one-, two-, three-, and four-year spot rates? The rate for a:

A. one-year loan beginning in two years.

B. two-year loan beginning in two years.

C. three-year loan beginning in two years.

2. Consider spot rates for three zero-coupon bonds: r(1) = 3%, r(2) = 4%, and r(3) = 5%. Which statement is correct? The forward rate for a one-year loan beginning in one year will be:

A. less than the forward rate for a one-year loan beginning in two years.

B. greater than the forward rate for a two-year loan beginning in one year.

C. greater than the forward rate for a one-year loan beginning in two years.

3. If one-period forward rates are decreasing with maturity, the yield curve is most likely:

A. flat.

B. upward sloping.

C. downward sloping.

The following information relates to Questions 4–7

A one-year zero-coupon bond yields 4.0%. The two- and three-year zero-coupon bonds yield 5.0% and 6.0% respectively.

4. The rate for a one-year loan beginning in one year is closest to:

A. 4.5%.

B. 5.0%.

C. 6.0%.

5. The forward rate for a two-year loan beginning in one year is closest to:

A. 5.0%

B. 6.0%

C. 7.0%

6. The forward rate for a one-year loan beginning in two years is closest to:

A. 6.0%

B. 7.0%

C. 8.0%

7. The five-year spot rate is not given above; however, the forward price for a two-year zero-coupon bond beginning in three years is known to be 0.8479. The price today of a five-year zero-coupon bond is closest to:

A. 0.7119.

B. 0.7835.

C. 0.9524.

8. The one-year spot rate r(1) = 4%, the forward rate for a one-year loan beginning in one year is 6%, and the forward rate for a one-year loan beginning in two years is 8%. Which of the following rates is closest to the three-year spot rate?

A. 4.0%

B. 6.0%

C. 8.0%

9. In a typical interest rate swap contract, the swap rate is best described as the interest rate for the:

A. fixed-rate leg of the swap.

B. floating-rate leg of the swap.

C. difference between the fixed and floating legs of the swap.

10. A two-year fixed-for-floating Libor swap is 1.00% and the two-year US Treasury bond is yielding 0.63%. The swap spread is closest to:

A. 37 bps.

B. 100 bps.

C. 163 bps.

11. A four-year corporate bond with a 7% coupon has a Z-spread of 200 bps. Assume a flat yield curve with an interest rate for all maturities of 5% and annual compounding. The bond will most likely sell:

A. close to par.

B. at a premium to par.

C. at a discount to par.

The following information relates to Questions 12–18

Jane Nguyen is a senior bond trader and Christine Alexander is a junior bond trader for an investment bank. Nguyen is responsible for her own trading activities and also for providing assignments to Alexander that will develop her skills and create profitable trade ideas. Exhibit 1 presents the current par and spot rates.

EXHIBIT 1 Current Par and Spot Rates

Maturity	Par Rate	Spot Rate
One year	2.50%	2.50%
Two years	2.99%	3.00%
Three years	3.48%	3.50%
Four years	3.95%	4.00%
Five years	4.37%

 

Nguyen gives Alexander two assignments that involve researching various questions: Assignment 1: What is the yield to maturity of the option-free, default risk–free bond presented in Exhibit 2? Assume that the bond is held to maturity, and use the rates shown in Exhibit 1.

EXHIBIT 2 Selected Data for $1,000 Par Bond

Bond Name	Maturity (T)	Coupon
Bond Z	Three years	6.00%

 

Assignment 2: Assuming that the projected spot curve two years from today will be below the current forward curve, is Bond Z fairly valued, undervalued, or overvalued?

12. Based on Exhibit 1, the five-year spot rate is closest to:

A. 4.40%.

B. 4.45%.

C. 4.50%.

13. Based on Exhibit 1, the market is most likely expecting:

A. deflation.

B. inflation.

C. no risk premiums.

14. Based on Exhibit 1, the forward rate of a one-year loan beginning in three years is closest to:

A. 4.17%.

B. 4.50%.

C. 5.51%.

15. Based on Exhibit 1, which of the following forward rates can be computed?

A. A one-year loan beginning in five years

B. A three-year loan beginning in three years

C. A four-year loan beginning in one year

16. For Assignment 1, the yield to maturity for Bond Z is closest to the:

A. one-year spot rate.

B. two-year spot rate.

C. three-year spot rate.

17. For Assignment 2, Alexander should conclude that Bond Z is currently:

A. undervalued.

B. fairly valued.

C. overvalued.

The following information relates to Questions 18–20

Rowan Madison is a junior analyst at Cardinal Capital. Sage Winter, a senior portfolio manager and Madison’s supervisor, meets with Madison to discuss interest rates and review two bond positions in the firm’s fixed-income portfolio.

Winter is worried about the effect of yield volatility on the portfolio. She asks Madison to identify the economic factors that affect short-term and long-term rate volatility.

Madison responds:

“Short-term rate volatility is mostly linked to uncertainty regarding monetary policy, whereas long-term rate volatility is mostly linked to uncertainty regarding the real economy and inflation.”

Winter also asks Madison to analyze the interest rate risk portfolio positions in a 5-year and a 20-year bond. Winter requests that the analysis be based on level, slope, and curvature as term structure factors. Madison presents her analysis in Exhibit 1.

EXHIBIT 1 Three-Factor Model of Term Structure

Time to Maturity (years)
Factor	5	20
Level	-0.4352%	-0.5128%
Steepness	-0.0515%	-0.3015%
Curvature	0.3963%	0.5227%

 

Note: Entries indicate how yields would change for a one standard deviation increase in a factor.

Winter asks Madison to perform two analyses:

Analysis 1: Calculate the expected change in yield on the 20-year bond resulting from a two standard deviation increase in the steepness factor.

Analysis 2: Calculate the expected change in yield on the five-year bond resulting from a one standard deviation decrease in the level factor and a one standard deviation decrease in the curvature factor.

18. Is Madison’s response regarding the factors that affect short-term and long-term rate volatility correct?

A. Yes.

B. No, she is incorrect regarding factors linked to long-term rate volatility.

C. No, she is incorrect regarding factors linked to short-term rate volatility.

19. Based on Exhibit 1, the results of Analysis 1 should show the yield on the 20-year bond decreasing by:

A. 0.3015%.

B. 0.6030%.

C. 0.8946%.

20. Based on Exhibit 1, the results of Analysis 2 should show the yield on the five-year bond:

A. decreasing by 0.8315%.

B. decreasing by 0.0389%.

C. increasing by 0.0389%.

The following information relates to Questions 21–28

Liz Tyo is a fund manager for an actively managed global fixed-income fund that buys bonds issued in Countries A, B, and C. She and her assistant are preparing the quarterly markets update. Tyo begins the meeting by distributing the daily rates sheet, which includes the current government spot rates for Countries A, B, and C as shown in Exhibit 1.

EXHIBIT 1 Today’s Government Spot Rates

Maturity	Country A	Country B	Country C
One year	0.40%	-0.22%	14.00%
Two years	0.70	-0.20	12.40
Three years	1.00	-0.12	11.80
Four years	1.30	-0.02	11.00
Five years	1.50	0.13	10.70

 

Tyo asks her assistant how these spot rates were obtained. The assistant replies, “Spot rates are determined through the process of bootstrapping. It entails backward substitution using par yields to solve for zero-coupon rates one by one, in order from latest to earliest maturities.”

Tyo then provides a review of the fund’s performance during the last year and comments,

“The choice of an appropriate benchmark depends on the country’s characteristics. For example, although Countries A and B have both an active government bond market and a swap market, Country C’s private sector is much bigger than its public sector, and its government bond market lacks liquidity.”

Tyo further points out, “The fund’s results were mixed; returns did not benefit from taking on additional risk. We are especially monitoring the riskiness of the corporate bond holdings. For example, our largest holdings consist of three four-year corporate bonds (Bonds 1, 2, and 3) with identical maturities, coupon rates, and other contract terms. These bonds have Z-spreads of 0.55%, 1.52%, and 1.76%, respectively.”

Tyo continues, “We also look at risk in terms of the swap spread. We considered historical three-year swap spreads for Country B, which reflect that market’s credit and liquidity risks, at three different points in time.” Tyo provides the information in Exhibit 2.

EXHIBIT 2 Selected Historical Three-Year Rates for Country B

Period	Government Bond Yield (%)	Fixed-for-Floating Libor Swap (%)
1 Month ago	-0.10	0.16
6 Month ago	-0.08	0.01
12 Month ago	-0.07	0.71

 

She moves on to present her market views on the respective yield curves for a five-year investment horizon.

Country A: “The government yield curve has changed little in terms of its level and shape during the last few years, and I expect this trend to continue. We assume that future spot rates reflect the current forward curve for all maturities.”

Country B: “Because of recent economic trends, I expect a reversal in the slope of the current yield curve. We assume that future spot rates will be higher than current forward rates for all maturities.”

Country C: “To improve liquidity, Country C’s central bank is expected to intervene, leading to a reversal in the slope of the existing yield curve. We assume that future spot rates will be lower than today’s forward rates for all maturities.”

Tyo’s assistant asks, “Assuming investors require liquidity premiums, how can a yield curve slope downward? What does this imply about forward rates?”

Tyo answers, “Even if investors require compensation for holding longer-term bonds, the yield curve can slope downward—for example, if there is an expectation of severe deflation. Regarding forward rates, it can be helpful to understand yield curve dynamics by calculating implied forward rates. To see what I mean, we can use Exhibit 1 to calculate the forward rate for a two-year Country C loan beginning in three years.”

21. Did Tyo’s assistant accurately describe the process of bootstrapping?

A. Yes.

B. No, with respect to par yields.

C. No, with respect to backward substitution.

22. The swap curve is a better benchmark than the government spot curve for:

A. Country A.

B. Country B.

C. Country C.

23. Based on the given Z-spreads for Bonds 1, 2, and 3, which bond has the greatest credit and liquidity risk?

A. Bond 1

B. Bond 2

C. Bond 3

24. Based on Exhibit 2, the implied credit and liquidity risks as indicated by the historical three-year swap spreads for Country B were the lowest:

A. 1 month ago.

B. 6 months ago.

C. 12 months ago.

25. Based on Exhibit 1 and assuming Tyo’s market views on yield curve changes are realized, the forward curve of which country will lie below its spot curve?

A. Country A

B. Country B

C. Country C

26. Based on Exhibit 1 and Tyo’s expectations for the yield curves, Tyo most likely perceives the bonds of which country to be fairly valued?

A. Country A

B. Country B

C. Country C

27. With respect to their discussion of yield curves, Tyo and her assistant are most likely discussing which term structure theory?

A. Pure expectations theory

B. Local expectations theory

C. Liquidity preference theory

28. Tyo’s assistant should calculate a forward rate closest to:

A. 9.07%.

B. 9.58%.

C. 9.97%.