Exam 7: The Term Structure and Interest Rate Dynamics

The following information relates to Questions 16-29 -The Z-spread of bond A is 1.05% and the Z-spread of bond b is 1.53%. All else equal, which statement best describes the relationship between the two bonds?

Is Madison correct in describing key differences in equilibrium and arbitrage-free models as they relate to the number of parameters and model accuracy?

The following information relates to Questions 16-29 -The forward rate for a two-year loan beginning in one year is closest to:

laura Mathews recently hired Robert Smith, an investment adviser at Shire Gate Advisers, to assist her in investing. Mathews states that her investment time horizon is short, approximately two years or less. Smith gathers information on spot rates for on-the-run annual-coupon gov-ernment securities and swap spreads, as presented in Exhibit 1. Shire Gate Advisers recently published a report for its clients stating its belief that, based on the weakness in the financial markets, interest rates will remain stable, the yield curve will not change its level or shape for the next two years, and swap spreads will also remain unchanged. ExHIbIT 1 Government Spot Rates and Swap Spreads Maturity (years) 1 2 3 4 Government spot rate 2.25\% 2.70\% 3.30\% 4.05\% Swap spread 0.25\% 0.30\% 0.45\% 0.70\% Smith decides to examine the following three investment options for Mathews: Investment 1: Buy a government security that would have an annualized return that is nearly risk free. Smith is considering two possible implementations: a two-year investment or a combination of two one-year investments. Investment 2: Buy a four-year, zero-coupon corporate bond and then sell it after two years. Smith illustrates the returns from this strategy using the swap rate as a proxy for corporate yields. Investment 3: Buy a lower-quality, two-year corporate bond with a coupon rate of $4.15 \%$ and a Z-spread of 65 bps. When Smith meets with Mathews to present these choices, Mathews tells him that she is somewhat confused by the various spread measures. She is curious to know whether there is one spread measure that could be used as a good indicator of the risk and liquidity of money market securities during the recent past. -In his presentation of Investment 1, Smith could show that under the no-arbitrage principle, the forward price of a one-year government bond to be issued in one year is closest to:

What are the advantages of using the swap curve as a benchmark of interest rates relative to a government bond yield curve?

laura Mathews recently hired Robert Smith, an investment adviser at Shire Gate Advisers, to assist her in investing. Mathews states that her investment time horizon is short, approximately two years or less. Smith gathers information on spot rates for on-the-run annual-coupon gov-ernment securities and swap spreads, as presented in Exhibit 1. Shire Gate Advisers recently published a report for its clients stating its belief that, based on the weakness in the financial markets, interest rates will remain stable, the yield curve will not change its level or shape for the next two years, and swap spreads will also remain unchanged. ExHIbIT 1 Government Spot Rates and Swap Spreads Maturity (years) 1 2 3 4 Government spot rate 2.25\% 2.70\% 3.30\% 4.05\% Swap spread 0.25\% 0.30\% 0.45\% 0.70\% Smith decides to examine the following three investment options for Mathews: Investment 1: Buy a government security that would have an annualized return that is nearly risk free. Smith is considering two possible implementations: a two-year investment or a combination of two one-year investments. Investment 2: Buy a four-year, zero-coupon corporate bond and then sell it after two years. Smith illustrates the returns from this strategy using the swap rate as a proxy for corporate yields. Investment 3: Buy a lower-quality, two-year corporate bond with a coupon rate of $4.15 \%$ and a Z-spread of 65 bps. When Smith meets with Mathews to present these choices, Mathews tells him that she is somewhat confused by the various spread measures. She is curious to know whether there is one spread measure that could be used as a good indicator of the risk and liquidity of money market securities during the recent past. -The most appropriate response to Mathews question regarding a spread measure is the:

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 exam-ple, 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 Months ago -0.08 0.01 12 Months ago -0.07 0.71 Tyo then suggests that the firm was able to add return by riding the yield curve. The fund plans to continue to use this strategy but only in markets with an attractive yield curve for this strategy.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." -based on Exhibit 1, the results of Analysis 1 should show the yield on the 20-year bond decreasing by:

The following information relates to Questions 16-29 -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:

laura Mathews recently hired Robert Smith, an investment adviser at Shire Gate Advisers, to assist her in investing. Mathews states that her investment time horizon is short, approximately two years or less. Smith gathers information on spot rates for on-the-run annual-coupon gov-ernment securities and swap spreads, as presented in Exhibit 1. Shire Gate Advisers recently published a report for its clients stating its belief that, based on the weakness in the financial markets, interest rates will remain stable, the yield curve will not change its level or shape for the next two years, and swap spreads will also remain unchanged. ExHIbIT 1 Government Spot Rates and Swap Spreads Maturity (years) 1 2 3 4 Government spot rate 2.25\% 2.70\% 3.30\% 4.05\% Swap spread 0.25\% 0.30\% 0.45\% 0.70\% Smith decides to examine the following three investment options for Mathews: Investment 1: Buy a government security that would have an annualized return that is nearly risk free. Smith is considering two possible implementations: a two-year investment or a combination of two one-year investments. Investment 2: Buy a four-year, zero-coupon corporate bond and then sell it after two years. Smith illustrates the returns from this strategy using the swap rate as a proxy for corporate yields. Investment 3: Buy a lower-quality, two-year corporate bond with a coupon rate of $4.15 \%$ and a Z-spread of 65 bps. When Smith meets with Mathews to present these choices, Mathews tells him that she is somewhat confused by the various spread measures. She is curious to know whether there is one spread measure that could be used as a good indicator of the risk and liquidity of money market securities during the recent past. -In presenting Investment 2, Smith should show a total return closest to:

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 exam-ple, 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 Months ago -0.08 0.01 12 Months ago -0.07 0.71 Tyo then suggests that the firm was able to add return by riding the yield curve. The fund plans to continue to use this strategy but only in markets with an attractive yield curve for this strategy.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." -based on Exhibit 1, the results of Analysis 2 should show the yield on the five-year bond:

The following information relates to Questions 16-29 -In a typical interest rate swap contract, the swap rate is best described as the interest rate for the:

The following information relates to Questions 16-29 -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. TheBond will most likely sell:

The following information relates to Questions 30-36 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\% (continued) (Continued) Maturity Par Rate Spot Rate Three years 3.48\% 3.50\% Four years 3.95\% 4.00\% Five years 4.37\% Note: Par and spot rates are based on nnual-coupon sovereign bonds. 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\% Note: Terms are today for a T-year loan. 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? After completing her assignments, Alexander asks about nguyen's current trading activ- ities. nguyen states that she has a two-year investment horizon and will purchase bond Z as part of a strategy to ride the yield curve. Exhibit 1 shows nguyen's yield curve assumptions implied by the spot rates. -based on Exhibit 1, which of the following forward rates can be computed?

The following information relates to Questions 30-36 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\% (continued) (Continued) Maturity Par Rate Spot Rate Three years 3.48\% 3.50\% Four years 3.95\% 4.00\% Five years 4.37\% Note: Par and spot rates are based on nnual-coupon sovereign bonds. 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\% Note: Terms are today for a T-year loan. 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? After completing her assignments, Alexander asks about nguyen's current trading activ- ities. nguyen states that she has a two-year investment horizon and will purchase bond Z as part of a strategy to ride the yield curve. Exhibit 1 shows nguyen's yield curve assumptions implied by the spot rates. -based on Exhibit 1, the five-year spot rate is closest to:

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

Which of Madison's statement(s) regarding equilibrium and arbitrage-free term structure models is incorrect?

A. define the yield to maturity for a coupon bond. b. Is it possible for a coupon bond to earn less than the yield to maturity if held to maturity?

The most appropriate response to Madison's question regarding the spread measure is the:

Is Madison's response regarding the factors that affect short-term and long-term rate vol- atility correct?

The following information relates to Questions 49-57liz Tyo is a fund manager for an actively managed global fixed-income fund that buys bonds issued in Countries A, b, and -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: