(1)According to expectations theory if the 2 year interest rate is 4% and the 1

Question

(1)According to expectations theory if the 2 year interest rate is 4% and the 1 year rate is now 3%, the 1 year rate next year is expected to be

a)3%

b)8%

c)5%

d)4%

(2)Refer to the following table:

Maturity (years)

1

2

3

4

5

Zero-coupon YTM

3.88 %

5.35 %

5.35 %

5.13 %

4.32 %

Suppose you wanted to lock in an interest rate for an investment that begins in one year and matures in five years. What rate would you obtain if there were no arbitrage opportunities? (Use at least four decimal places in all intermediate calculations.)

The rate for an investment that begins in one year and matures in five years would be____%.

(Round to two decimal places.)

(3)Use the table for the question(s) below.

Consider the following zero?coupon yields on default free securities:

Maturity (years)

1

2

3

4

5

Zero?Coupon

5.80%

5.50%

5.20%

5.00%

4.80%

The price today of a 3 year default free security with a face value of $1000 and an annual coupon rate of 6% is closest to:

a)$1013

b) $1000

c) $1005

d)$1021

(4)Suppose the yield on a one-year, zero-coupon bond is 5%. The forward rate for year 2 is 4 %, and the forward rate for year 3 is 3%.

What is the yield to maturity of a zero-coupon bond that matures in three years?

The yield to maturity is____%.

(Round to three decimal places.)

(5)Refer to the following table:

Maturity (years)

1

2

3

4

5

Zero-coupon YTM

4.04 %

5.34 %

5.34 %

5.16 %

4.46 %

What is the forward rate for year 2 (the forward rate quoted today for an investment that begins in one year and matures in two years)? (Use at least four decimal places in all intermediate calculations.)

The forward rate for year 2 is___%.

(Round to two decimal places.)

Maturity (years)

1

2

3

4

5

Zero-coupon YTM

3.88 %

5.35 %

5.35 %

5.13 %

4.32 %

Explanation / Answer

1. (1+r2)2 = (1+r1) * (1+r1,2) . Using this equation, we get : (1+r1,2) = (1+r2)2 / (1+r1)

Plugging in the values and solving, we get : r1,2 = (1+4%)2/(1+3%) -1 = 5% (option C)

2. 5 year YTM = 4.32% and 1 Year YTM = 3.88%. Using the above equation, the no arbitrage ytm should be : (1+r1,5)4 = (1+4.32%)5/(1+3.88%) ; solving we get r1,5 = 4.43%

3. We will use the zero coupon ytm to discount the respective cash flows of coupon paying bond, as below:

Price = 60/(1+5.80%) + 60/ (1+5.50%)2 + (1000+60)/(1+5.20%)3 = 1021.07 or rounded to 1021 (option D)

4. 3 year bond yield = [(1+5%) * (1+4%) * (1+3%](1/3) - 1 = 3.997%

5. (1+r2)2 = (1+r1) * (1+r1,2); re-arranging we get : (1+r1,2) = (1+r2)2 / (1+r1) ; plugging in the values we get: r1,2 = (1+5.34%)2/(1+4.04%) - 1 = 6.6562%

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