FM - 3

If the nominal interest rate per year is 10 percent and the inflation rate is 4 percent, what is the real rate of interest?

5.8 percent Using Irving Fisher's equation, 1 + rreal = (1 + rnominal)/(1 + rinflation) = 1.1/1.04 = 1.058; rreal = 5.8%.

In the United States, most bonds make coupon payments annually.

False

The longer a bond's duration, the greater its volatility.

True

If a bond's volatility is 10.00 percent and the interest rate goes down by 0.75 percent (points), then the price of the bond

increases by 7.50 percent Percentage change in bond price = -(volatility) × (change in interest rates) = -10 × (-0.75) = +7.5%

One can best describe the term structure of interest rates as the relationship between

spot interest rates and time

Which of the following bonds has the greatest volatility?

10-year, zero-coupon bond

A bond has a face value of $1,000, an annual coupon rate of 7 percent, yield to maturity of 10 percent, and 20 years to maturity. The bond's duration is

10.0 years Step 1: N = 20; PMT = 70; FV = 1,000; I = 10. Compute PV = 744.59. Step 2: Duration = [((1)(70)/1.1) + ((2)(70)/1.1^2) + . . . + ((20)(1070)/1.1^20)]/744.59 = 10 years.

A four-year bond has an 8 percent coupon rate and a face value of $1,000. If the current price of the bond is $878.31, calculate the yield to maturity of the bond (assuming annual interest payments).

12 percent Use trial and error method: (80/1.12) + (80/(1.12^2)) + (80/(1.12^3)) + (1080/(1.12^4)) = $870.51. Therefore, yield to maturity is 12 percent. Or use a financial calculator: PV = -878.31; N = 4; PMT = 80; FV = 1,000. Compute I = 12%.

a. The ten-year bond yields 5.9% and has a coupon of 7.9%. If this yield to maturity remains unchanged, what will be its price one year hence? Assume annual coupon payments and a face value of $100. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the total return to an investor who held the bond over this year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

a. 113.66 b. Total return 5.90 Explanation: a. PV0 = (.079 × $100) × ((1 / .059) - {1 / [.059(1 + .059)10]}) + $100 / 1.05910 PV0 = $114.79 PV1 = (.079 × $100) × ((1 / .059) - {1 / [.059(1 + .059)9]}) + $100 / 1.0599 PV1 = $113.66 b. Return = ($7.90 + 113.66 - 114.79) / $114.79 = .059, or 5.90%

The two-year interest rate is 10.4% and the expected annual inflation rate is 5.2%. a.What is the expected real interest rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Expected real interest rate % b-1. If the expected rate of inflation suddenly rises to 7.2%, what does Fisher's theory say about how the real interest rate will change? Real rate does not change b-3. If the expected rate of inflation suddenly rises to 7.2%, what will be the new nominal rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Nominal rate %

a. 4.94% b-1 b-2 12.50% Explanation: a. r = 1.104 / 1.052 - 1 r = .0494, or 4.94% b-1. The real rate does not change. b-2. The nominal rate increases to: rNominal = 1.0494 × 1.072 - 1 rNominal = .1250, or 12.50%

The volatility of a bond is given by

duration/(1 + yield) and slope of the curve relating the bond price to the interest rate only.

Suppose that you buy a two-year 7.5% bond at its face value. a-1. What will be your total nominal return over the two years if inflation is 2.5% in the first year and 4.5% in the second? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Nominal return % a-2. What will be your real return? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Real return % b. Now suppose that the bond is a TIPS. What will be your total 2-year real and nominal returns? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Real return% Nominal return%

a-1 15.56% a-2 7.89% b Real return 15.56% Nominal return 23.78% Explanation: a-1. Nominal 2-year return: 1.0752 - 1 = .1556, or 15.56% a-2. Real 2-year return: (1.075 / 1.025) × (1.075 / 1.045) - 1 = .0789, or 7.89% b. Nominal 2-year return: 1.0752 - 1 = .1556, or 15.56% Real 2-year return: (1.075 × 1.025) × (1.075 × 1.045) - 1 = .2378, or 23.78%

You buy a 12-year 10 percent annual coupon bond at par value, $1,000. You sell the bond three years later for $1,100. What is your rate of return over this three-year period?

40 percent

Consider a bond with a face value of $1,000, an annual coupon rate of 6 percent, a yield to maturity of 8 percent, and 10 years to maturity. This bond's duration is

7.6 years Step 1: N = 10; PMT = 60; FV = 1,000; I = 8. Compute PV = 865.80. Step 2: Duration = [1(55.56) + 2(51.44) + 3(47.63) + 4(44.10) + 5(40.83) + 6(37.81) + 7(35) + 8(32.42) + 9(30.01) + 10(490.99)]/(865.80) = 7.6 years.

The one-year spot interest rate is r1 = 6.5%, and the two-year rate is r2 = 7.5%. If the expectations theory is correct, what is the expected one-year interest rate in one year's time? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Expected interest rate

8.51% Explanation: 1-year rate in 1 year = 1.0752 / 1.065 - 1 1-year rate in 1 year = .0851, or 8.51%

In February 2015 Treasury 3 7/8s of 2037 offered a semiannually compounded yield to maturity of 2.94%. Recognizing that coupons are paid semiannually, calculate the bond's price. Assume face value is $1,000. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Bond price $1,150.68 Explanation: Semiannual discount rate = .0294 / 2 = .0147, or 1.47% Number of time periods = (2037 - 2015) × 2 = 44 PV = [(.03875 × $1,000) / 2] × ((1 / .0147) - {1 / [.0147 × (1 + .0147)44]}) + $1,000 / (1 + .0147)44 PV = $1,150.68

Once a bond defaults, bondholders can no longer receive any residual payment from the bond.

False

The spread of junk bond yields, over that of U.S. Treasuries, is generally lower than the spread of investment-grade bonds.

False

A 20-year German government bond (bund) has a face value of €600 and a coupon rate of 7% paid annually. Assume that the interest rate (in euros) is equal to 7.00% per year. What is the bond's PV? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Present value €600.00 Explanation: PV = (.07 × €600) × ((1 / .070) - {1 / [.070 × (1 + .070)20]}) + €600 / (1 + .070)20 PV = €600.00

a. The fifteen-year bond yields 6.3% and has a coupon of 8.3%. If this yield to maturity remains unchanged, what will be its price one year hence? Assume annual coupon payments and a face value of $100. (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the total return to an investor who held the bond over this year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Price: 118.25 Total return: 6.30% Explanation: a. PV0 = (.083 × $100) × ((1 / .063) - {1 / [.063(1 + .063)15]}) + $100 / 1.06315 PV0 = $119.05 PV1 = (.083 × $100) × ((1 / .063) - {1 / [.063(1 + .063)14]}) + $100 / 1.06314 PV1 = $118.25 b. Return = ($8.30 + 118.25 - 119.05) / $119.05 = .063, or 6.30%

Which of the following statements about the relationship between interest rates and bond prices is true?

There is an inverse relationship between bond prices and interest rates, and the price of long-term bonds fluctuates more than the price of short-term bonds for a given change in interest rates (assuming that the coupon rate is the same for both).

Consider the impact of inflation risk on the term structure of interest rates. If investors become more wary of inflation, one would expect to observe a steeper, more upwards sloping, term structure of interest rates.

True

Corporate bond yields are generally higher than government bond yields for bonds having the same coupon rate and maturity.

True

If the term structure of interest rates is flat, then the 9-year spot interest rate equals the 10-year spot interest rate.

True

The U.S. Treasury issues inflation-indexed bonds known as TIPs.

True

The duration of a zero-coupon bond is the same as its maturity.

True

The yield to maturity on a bond is really its internal rate of return.

True

Two bonds have the same maturity, risk rating, and face value, but have different coupon rates. The bond with a lower coupon rate will have a longer duration.

True

U.S. Treasury bonds have almost zero default risk but are subject to inflation risk.

True

If a bond's volatility is 5.0 percent and its yield to maturity changes by 0.5 percent (points), then the price of the bond

changes by 2.5 percent