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Information:

Fill in the following table reflecting which premiums are added to r* for the different types of debt.

| |Inflation Premium |Maturity Risk Premium |Default Risk Premium |Liquidity Premium |

|Short Term Treasury |X | | | |

|Long Term Treasury |X |X | | |

|Short Term Corporate |X | |X |X |

|Long Term Corporate |X |X |X |X |

Equations:

r = r* + IP + MRP + DRP + LP

Problems:

1. The real risk-free rate of interest is 3 percent. Inflation is expected to be 2 percent this year and 4 percent during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 3-year Treasury securities?

r = r* + IP + MRP

r = 3 + ((2+4+4)/3) + 0

r = 6.33%

2. The real risk-free rate is 2.5%. Inflation is expected to average 2.8% a year for the next 4 years, after which time inflation is expected to average 3.75% a year. Assume that there is no maturity risk premium. An 8-year corporate bond has a yield of 8.3%. Assume that the liquidity premium on the corporate bond is 0.75%. What is the default risk premium on the corporate bond?

r = r* + IP + MRP + DRP + LP

8.3 = 2.5 + (((2.8 *4)+(3.75*4))/8) + 0 + .75 + DRP

DRP = 1.775%

3. The real risk free rate is 3%, and inflation is expected to be 3.5% for the next 2 years. A 2 year treasury security yields 6.8%. What is the maturity risk premium for the 2 year security?

r = r* + IP + MRP

6.8 = 3 + 3.5 + MRP

MRP = .3

4. The real risk free rate is 4%. Inflation is expected to be 3% this year, 4% next year, and then 2% for the following 2 years. Assume that the maturity risk premium is 0. What is the yield on 2 year Treasury securities? What about 4 year treasury securities?

r2 = r* + IP + MRP

r2 = 4 + ((3+4)/2) + 0

r2 = 7.5%

r4 = r* + IP + MRP

r4 = 4 + ((3+4+2+2)/4) + 0

r4 = 6.75%

5. You read in The Wall Street Journal that 30-day T-bills are currently yielding 5.5%. Your brother-in-law, a broker at Safe and Sound Securities, has given you the following estimates of current interest rate premiums:

Inflation premium= 3.25%

Liquidity premium= 0.6%

Maturity risk premium= 1.8%

Default risk premium= 2.15%

On the basis of these data, what is the real risk-free rate of return?

r = r* + IP

5.5 = r* + 3.25

r* = 2.25%

6. Using the information and risk free rate found in #5, what would the yield of a 30-day corporate bond be?

r = r* + IP + DRP + LP

r = 2.25 + 3.25 + 2.15 + .6

r = 8.25%

7. 4-year corporate securities are currently yielding 5.8%. You know the following are the current interest rate premiums. Calculate the inflation premium.

Liquidity premium= 1.2%

Maturity Risk premium= 0.75%

Default Risk premium= 1.35%

Risk Free Rate = 1.8%

r = r* + IP + MRP + DRP + LP

5.8 = 1.8 + .75 + 1.35 + 1.2 + IP

IP = .7%

8. Interest rates on 4-year Treasury securities are currently 7%, while interest rates on 6-year Treasury securities are currently 7.5%. If the pure expectations hypothesis is correct, what does the market believe that 2-year securities will be yielding 4 years from now?

(1 + .075)6 = (1 + .07)4 * (1 + x)2

1.5433 = 1.3108 * (1 + x)2

Divide both sides by 1.3108

1.1774 = (1 + x)2

Take the square root of both sides to get ride of the 2

1.0851 = 1 + x

x = .0851 or 8.51%

9. Interest rates on 3-year treasury securities are currently 8%, while 6-year treasury securities are 8.5%. If pure expectations hypothesis is correct, what does the market believe that 3-year securities will be yielding 3 years from now?

(1 + .085)6 = (1 + .08)3 * (1 + x)3

1.6315 = 1.2597 * (1 + x)3

Divide both sides by 1.2597

1.2951 = 1 + x)3

Take both sides to the 1/3 power to get ride of the 3

1.09 = 1 + x

x = .09 or 9%

10. One-year Treasury securities yield 4.78%. The market anticipates that 1 year from now, 1-year Treasury securities will yield 5.29%. If the pure expectation theory is correct, what should be the yield today for 2-year Treasury securities?

(1 + x)2 = (1 + .0478) * (1 + .0529)

(1 + x)2 = 1.1032

Take the square root of both sides to get ride of the 2

1 + x = 1.0503

x = .0503 or 5.03%

11. 3-year treasury securities beginning two years from now are expected to yield 5.75%, whereas a 2-year Treasury security is currently yielding 5%. A 2-year security is expected to yield 6.2% beginning 3 years from now. What is the yield for a 3-year treasury security beginning today?

(1 + x)3 * (1 + .062)2 = (1 + .05)2 * (1 + .0575)3

(1 + x)3 * 1.1278 = 1.1025 * 1.1826

(1 + x)3 * 1.1278 = 1.3038

Divide both sides by 1.1278

(1 + x)3 = 1.1561

Take both sides to the 1/3 power to get ride of the 3

1 + x = 1.0495

x = .0495 or 4.95%

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