Question

One-year government bonds yield 6.9 percent and 3-year government bonds yield 3.8 percent.

Assume that the expectations theory holds.  What does the market believe the rate on 2-year

government bonds will be one year from today?

2.05%

2.45%

2.35%

2.15%

2.25%

The real risk-free rate of interest is 3 percent.  Inflation is expected to be 2 percent this

coming year, jump to 3 percent next year, and increase to 4 percent the year after (Year 3).  

According to the expectations theory, what should be the interest rate on 2-year, risk-free

securities today?

5.80%

5.90%

5.70%

5.50%

5.60%

Currently, 3-year Treasury securities yield 9%, 7-year Treasury securities yield

9.3%, and 10-year Treasury securities yield 9.5%. If the expectations theory is

correct, what does the market expect will be the yield on 3-year Treasury

securities seven years from today?

9,32%

9.97%

10.17%

9.77%

9.57%

Keys Corporation's 5-year bonds yield 6.9%, and 5-year T-bonds yield 5.4%.

The real risk-free rate is r* = 2.2%, the inflation premium for 5 years bonds is

IP = 2.8%, the default risk premium for Keys' bonds is DRP = 0.43% versus

zero for T-bonds, and the maturity risk premium for all bonds is found with

the formula MRP = (t – 1)*0.1%, where t = number of years to maturity. What

is the liquidity premium (LP) on Keys' bonds?

0.81%

0.89%

0.94%

1.07%

1.00%

Suppose the interest rate on a 1-year T-bond is 3.3% and that on a 3-year

T-bill is 5.2%. Assuming the pure expectations theory is correct, what is the

market's forecast for 2-year rates 1 year from now?

6.35%

6.45%

6.25%

6.15%

6.60%

Answer 1

Part 1:

Given, Spot rate for 3 years S3= 3.8% and Spot rate for 1 year= 6.9%

Two year rate, one year from now= {[(1+3.8%)^3/(1+6.9%)]^1/2}-1

= [(1.118387/ 1.069)^(1/2)]-1 = [1.046199^(1/2)]-1= 2.2839% Rounded to 2.25%

The answer is last option

Part 2:

Spot rate for year1 = Real rate of 3% plus Inflation 2%= 5%

Forward rate for year 2, after one year= Real rate 3% plus inflation 3%= 6%

Therefore, spot rate for 2 years now = {[(1+5%)*(1+6%)]^(1/2)}-1

=[1.113^(1/2)]-1 = 1.054988-1 = 5.4988% Rounded to 5.5%

The answer is 4th option.

Part 3:

Spot rate for 7 years (S7)=9.3%

Spot rate for 10 years (S10)=9.5%

Three year forward rate after 7 years= {[(1+S10)^10 / (1+S7)^7]^(1/3)}-1

={[(1+9.5%)^10 / (1+9.3%)^7]^(1/3)}-1 = [(2.47822761/1.86355036)^(1/3)]-1

=1.099681-1 = 9.9681% Rounded to 9.97%

The answer is 2nd option.

Part 4:

Given,

Yield on Key Corporation 5 year bond (NIR)= 6.9%

Risk free real rate for 5 years (RF)= 5%

Default Risk Premium (DRP)= 0.43%

Maturity Risk Premium (MRP)= (5-1)*0.1= 4*0.1= 0.40%

Therefore, liquidity premium= NIR- RF-DRP-MRP = 6.9%-5%-0.43%-0.4%= 1.07%

The answer is 4th option.

Part 5:

Given S1= 3.3%, S3= 5.2%

2 year rate 1 year from now={[(1+S3)^3 / (1+S1)]^(1/2)}-1

=={[(1+5.2%)^3 / (1+3.3%)]^(1/2)}-1 = [(1.16425261/1.033)]^(1/2)}-1= 6.1631% Rounded to 6.15%

Answer is 4th option.