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Chapter8: Understanding Financial Markets + Institutions

Problems

BASIC PROBLEMS

8-1

  

Determinants of Interest Rates for Individual Securities  A particular security's default risk premium is 2 percent. For all securities, the inflation risk premium is 1.75 percent and the real interest rate is 3.5 percent. The security's liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. The security has no special covenants. Calculate the security's equilibrium rate of return. (LG4)

8-2

  

Determinants of Interest Rates for Individual Securities  You are considering an investment in 30-year bonds issued by Moore Corporation. The bonds have no special covenants. The Wall Street Journal reports that one-year T-bills are currently earning 3.25 percent. Your broker has determined the following information about economic activity and Moore Corporation bonds:

  

Real interest rate = 2.25%

  

Default risk premium = 1.15%

  

Liquidity risk premium = 0.50%

  

Maturity risk premium = 1.75%

a.

 

What is the inflation premium? (LG4)

b.

 

What is the fair interest rate on Moore Corporation 30-year bonds? (LG4)

p. 201

8-3

  

Determinants of Interest Rates for Individual Securities  Dakota Corporation 15-year bonds have an equilibrium rate of return is 8 percent. For all securities, the inflation risk premium is 1.75 percent and the real interest rate is 3.5 percent. The security's liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. The security has no special covenants. Calculate the bond's default risk premium. (LG4)

8-4

  

Determinants of Interest Rates for Individual Securities  A two-year Treasury security currently earns 4.14 percent. Over the next two years, the real interest rate is expected to be 2.25 percent per year and the inflation premium is expected to be 1.75 percent per year. Calculate the maturity risk premium on the two-year Treasury security. (LG4)

8-5

  

Unbiased Expectations Theory  Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

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Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. Plot the resulting yield curve. (LG5)

8-6

  

Unbiased Expectations Theory  One-year Treasury bills currently earn 3.45 percent. You expect that one year from now, one-year Treasury bill rates will increase to 3.65 percent. If the unbiased expectations theory is correct, what should the current rate be on two-year Treasury securities? (LG5)

8-7

  

Liquidity Premium Hypothesis  One-year Treasury bills currently earn 3.45 percent. You expect that one year from now, one-year Treasury bill rates will increase to 3.65 percent. The liquidity premium on two-year securities is 0.05 percent. If the liquidity theory is correct, what should the current rate be on two-year Treasury securities? (LG5)

8-8

  

Liquidity Premium Hypothesis  Based on economists' forecasts and analyses, one-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows:

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Using the liquidity premium hypothesis, plot the current yield curve. Make sure you label the axes on the graph and identify the four annual rates on the curve both on the axes and on the yield curve itself. (LG5)

INTERMEDIATE PROBLEMS

8-9

  

Determinants of Interest Rates for Individual Securities  The Wall Street Journal reports that the rate on three-year Treasury securities is 6.00 percent, and the six-year Treasury rate is 6.20 percent. From discussions with your broker, you have determined that expected inflation premium is 2.25 percent next year, 2.50 percent in Year 2, and 2.60 percent in Year 3 and beyond. Further, you expect that real interest rates will be 3.4 percent annually for the foreseeable future.

a.

 

Calculate the maturity risk premium on the three-year Treasury security. (LG4)

b.

 

Calculate the maturity risk premium on the six-year Treasury security. (LG4)

8-10

  

Determinants of Interest Rates for Individual Securities  Nikki G's Corporation's 10-year bonds are currently yielding a return of 8.15 percent. The expected inflation premium is 2.5 percent annually and the real interest rate is expected to be 3.10 percent annually over the next 10 years. The liquidity risk premium on Nikki G's bonds is 0.25 percent. The maturity risk premium is 0.10 percent on two-year securities and increases by 0.05 percent for each additional year to maturity. Calculate the default risk premium on Nikki G's 10-year bonds. (LG4)

p. 202

8-11

  

Unbiased Expectations Theory  Suppose we observe the following rates:

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If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year interest rate expected one year from now, E(2r1)? (LG4)

8-12

  

Unbiased Expectations Theory  The Wall Street Journal reports that the rate on four-year Treasury securities is 5.60 percent and the rate on five-year Treasury securities is 6.15 percent. According to the unbiased expectations hypotheses, what does the market expect the one-year Treasury rate to be four years from today, E(5r1)? (LG5)

8-13

  

Liquidity Premium Hypothesis  The Wall Street Journal reports that the rate on three-year Treasury securities is 5.25 percent and the rate on four-year Treasury securities is 5.50 percent. The one-year interest rate expected in three years is E(4r1), is 6.10 percent. According to the liquidity premium hypotheses, what is the liquidity premium on the four-year Treasury security, L4? (LG5)

8-14

  

Liquidity Premium Hypothesis  Suppose we observe the following rates:

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If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2, L2? (LG5)

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8-15

  

Forecasting Interest Rates  You note the following yield curve in The Wall Street Journal. According to the unbiased expectations hypothesis, what is the one-year forward rate for the period beginning one year from today, 2f1? (LG6)

8-16

  

Forecasting Interest Rates  On May 23, 20XX, the existing or current (spot) one-year, two-year, three-year, and four-year zero-coupon Treasury security rates were as follows:

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Using the unbiased expectations theory, calculate the one-year forward rates on zero-coupon Treasury bonds for years 2, 3, and 4 as of May 23, 20XX. (LG6)

ADVANCED PROBLEMS

8-17

  

Determinants of Interest Rates for Individual Securities  The Wall Street Journal reports that the current rate on 10-year Treasury bonds is 7.25 percent, on 20-year Treasury bonds is 7.85 percent, and on a 20-year corporate bond is 8.75 percent. Assume that the maturity risk premium is zero. If the default risk premium and liquidity risk premium on a 10-year corporate bond are the same as that on the 20-year corporate bond, calculate the current rate on a 10-year corporate bond. (LG4)

8-18

  

Determinants of Interest Rates for Individual Securities  The Wall Street Journal reports that the current rate on five-year Treasury bonds is 6.85 percent and on 10-year Treasury bonds is 7.35 percent. Assume that the maturity risk premium is zero. Calculate the expected rate on a five-year Treasury bond purchased four years from today, E(5r5). (LG4)

8-19

  

Unbiased Expectations Theory  Suppose we observe the three-year Treasury security rate (1R3) to be 8 percent, the expected one-year rate next year—E(2r1)—to be 4 percent, and the expected one-year rate the following year—E(3r1)—to be 6 percent. If the unbiased expectations theory of the term structure of interest rates holds, what is the one-year Treasury security rate, 1R1? (LG5)

p. 203

8-20

  

Unbiased Expectations Theory  The Wall Street Journal reports that the rate on three-year Treasury securities is 5.60 percent and the rate on five-year Treasury securities is 6.15 percent. According to the unbiased expectations hypothesis, what does the market expect the two-year Treasury rate to be two years from today, E(3r2)? (LG5)

8-21

  

Forecasting Interest Rates  Assume the current interest rate on a one-year Treasury bond (1R1) is 4.50 percent, the current rate on a two-year Treasury bond (1R2) is 5.25 percent, and the current rate on a three-year Treasury bond (1R3) is 6.50 percent. If the unbiased expectations theory of the term structure of interest rates is correct, what is the one-year interest rate expected on Treasury bills during year 3, 3f1? (LG6)

8-22

  

Forecasting Interest Rates  A recent edition of The Wall Street Journal reported interest rates of 2.25 percent, 2.60 percent, 2.98 percent, and 3.25 percent for three-year, four-year, five-year, and six-year Treasury security yields, respectively. According to the unbiased expectation theory of the term structure of interest rates, what are the expected one-year rates for years 4, 5, and 6? (LG6)

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