In this problem we are going to calculate bond prices and returns
Question 1
In this problem we are going to calculate bond prices and returns
Suppose that the yield on a 3 year note is 1.3%.
a) (10 points) Calculate the price of the 3 year note (face value = $1000) with three annual coupon payments (after year 1, after year 2, after year 3) of $25, i.e., coupon rate is 2.5%.
b) (5 points) Is this note selling at a discount or premium? Explain.
Suppose that after one year and after you receive one coupon payment, you decide to sell your note. Your note is now a two year note with one coupon payment after
1 year and another after year 2. Consider the following two scenarios:
Scenario #1 – interest rates on what is now a two year note (i.e., your note) have fallen to 1.00%
Scenario #2 – interest rates on what is now a two year note (i.e., your note) have risen to 2%
c) (10 points) Calculate the price that you can sell your note for under scenario #1 and the associated rate of return when you sell your note given Scenario #1
d) (10 points) Calculate the price that you can sell your note for under scenario #2 and the associated rate of return when you sell your note given Scenario #2
Question 2
Use the table below to answer the following questions –
|
Data Table for Question 2 |
|
|
DATES |
PRICE INDEX |
|
1974-01-01 |
26.574 |
|
1974-02-01 |
26.883 |
|
1974-03-01 |
27.195 |
|
1974-04-01 |
27.387 |
|
1974-05-01 |
27.657 |
|
1974-06-01 |
27.891 |
|
1974-07-01 |
28.098 |
|
1974-08-01 |
28.391 |
|
1974-09-01 |
28.687 |
|
1974-10-01 |
28.893 |
|
1974-11-01 |
29.110 |
|
1974-12-01 |
29.341 |
|
1975-01-01 |
29.523 |
|
1975-02-01 |
29.684 |
|
1975-03-01 |
29.786 |
|
1975-04-01 |
29.887 |
|
1975-05-01 |
30.007 |
|
1975-06-01 |
30.195 |
|
1975-07-01 |
30.454 |
|
1975-08-01 |
30.586 |
|
1975-09-01 |
30.737 |
|
1975-10-01 |
30.916 |
|
1975-11-01 |
31.114 |
|
1975-12-01 |
31.286 |
a) (5 points) Calculate the rate of inflation from September 1974 (1974-09-01) to September 1975 (1975-09-01).
b) (5 points) Suppose that you earned $15,000 per year back in September of 1975. Assuming that the current price index is 120, how much money would
you have to make now to have the same purchasing power as $15,000 did back in September of 1975?
c) (5 points) In September 1974, the one year interest rate 8.52%. Calculate the ex-post real rate of interest.
d) (5 points) Given your answer in part c), is this an environment attractive to saving or spending? Explain.
Question 3
In this question we are going to address whether the Fed and Alan Greenspan kept interest rates too low for too long following the 2001 recession according to two rules:
The original Taylor Rule and the Mankiw Rule
Use the table below to answer the following questions.
FF – the federal funds rate
PCE INF = PCE inflation
PCE CORE = the core rate of PCE inflation
GDP = real GDP
GDP POT = potential (real) GDP
UR = the unemployment rate
|
Data Table for Question 3 |
||||||
|
DATES |
FF |
PCE INF |
PCE CORE |
GDP |
GDP POT |
UR |
|
2002-04-01 |
1.75 |
1.1 |
1.7 |
12894.7 |
13052.8 |
5.8 |
|
2002-07-01 |
1.74 |
1.5 |
1.9 |
12956.7 |
13161.2 |
5.7 |
|
2002-10-01 |
1.44 |
1.9 |
1.7 |
12962.9 |
13267.4 |
5.9 |
|
2003-01-01 |
1.25 |
2.5 |
1.7 |
13028.6 |
13371.3 |
5.9 |
|
2003-04-01 |
1.25 |
1.8 |
1.5 |
13151.8 |
13470.6 |
6.1 |
|
2003-07-01 |
1.02 |
1.9 |
1.4 |
13374.0 |
13566.8 |
6.1 |
|
2003-10-01 |
1.00 |
1.8 |
1.4 |
13525.7 |
13659.8 |
5.8 |
|
2004-01-01 |
1.00 |
1.9 |
1.7 |
13606.6 |
13748.2 |
5.7 |
|
2004-04-01 |
1.01 |
2.5 |
1.9 |
13710.7 |
13833.5 |
5.6 |
|
2004-07-01 |
1.43 |
2.5 |
2.0 |
13831.0 |
13916.8 |
5.4 |
|
2004-10-01 |
1.95 |
2.9 |
2.1 |
13947.7 |
13999.2 |
5.4 |
|
2005-01-01 |
2.47 |
2.6 |
2.2 |
14100.2 |
14082.6 |
5.3 |
|
2005-04-01 |
2.94 |
2.6 |
2.1 |
14177.2 |
14165.8 |
5.1 |
|
2005-07-01 |
3.46 |
3.1 |
2.1 |
14292.9 |
14249.3 |
5.0 |
|
2005-10-01 |
3.98 |
3.1 |
2.3 |
14372.0 |
14333.2 |
5.0 |
|
2006-01-01 |
4.46 |
3.0 |
2.1 |
14546.4 |
14418.5 |
4.7 |
|
2006-04-01 |
4.91 |
3.1 |
2.3 |
14591.6 |
14504.9 |
4.6 |
|
2006-07-01 |
5.25 |
2.8 |
2.4 |
14604.4 |
14592.0 |
4.6 |
|
2006-10-01 |
5.25 |
1.8 |
2.2 |
14718.4 |
14679.8 |
4.4 |
|
2007-01-01 |
5.26 |
2.3 |
2.4 |
14728.1 |
14768.3 |
4.5 |
|
2007-04-01 |
5.25 |
2.3 |
2.0 |
14841.5 |
14859.1 |
4.5 |
|
2007-07-01 |
5.07 |
2.1 |
2.0 |
14941.5 |
14949.5 |
4.7 |
|
2007-10-01 |
4.50 |
3.3 |
2.2 |
14996.1 |
15038.7 |
4.8 |
|
|
||||||
We are using data from 2004-01-01 to answer parts a), b), and c).
a) (5 points) Using the original Taylor Rule where the equilibrium real rate of interest is estimated to be 2% and the target inflation rate is 2%, what is the federal funds rate
b) implied by the Taylor Rule?
b) (5 points) Using the Mankiw Rule, what is the federal funds rate implied by the Mankiw Rule?
c) (5 points) According to the Taylor Rule, was the Fed being hawkish or dovish during this period? Explain and be specific with numbers.
d) (5 points) Let’s fast forward 3 years to 2007-01-01. Using the original Taylor Rule where the equilibrium real rate of interest is estimated to be 2% and the target inflation
rate is 2%, what is the federal funds rate implied by the Taylor Rule?
e) (5 points) According to the Taylor Rule, was the Fed being hawkish or dovish during this period? Explain and be specific with numbers.
Question 4
You will need to fill in the following exam sheet (see link below) for this question. You may either print out the exam sheet and complete it by hand, or type in/draw your
answers in Word in the document itself.
· Directions for completing the exam sheet by hand: if you hand write the exam sheet, when you are done, you will need to scan and submit the sheet
using the link at the end of this part of the exam.
· Directions for completing the exam sheet in Word: If you complete the exam sheet in Word you will need to save a copy of the file and submit it using
the link at the end of this part of the exam.
You must show all work for full credit.
Download Question 4 Exam Sheet
Leading up to and during the Lehman Brothers collapse, overnight lending markets became quite volatile, as shown by the figure below.
a) (10 points for correct and completely labeled diagram) On your exam sheet, draw a reserve market diagram depicting points A, B, and C. Assume that the Fed
held reserve supply constant and that the volatility in the effective federal funds rate originated from the volatility in reserve demand. Note, this is the period before the
Fed obtained the authority to pay interest on reserves
b) (10 points) In hindsight the Fed could have done a better job in terms of hitting their federal funds target = 2%. Explain in words what they should have done to avoid point B
and what they should have done differently to avoid point C. Note that we are still in the period before the Fed obtained the authority to pay interest on reserves.
c) (10 points) Draw a reserve market diagram depicting your answer for part b) above. Be sure to label points A, B and C. Note that we are still in the period before the
Fed obtained the authority to pay interest on reserves.
d) (20 points total: 10 points for complete and correctly labeled diagram and 10 points for explanation) Now let’s pretend that we were in a new regime (as they are now)
where the Fed sets the interest rate they pay on reserves at 25 basis points below the federal funds target and the discount rate set 25 basis points above the federal
funds target. In the space below, redraw the reserve market diagram accounting for this new regime. Make sure you label points A, B, and C under
this new and current regime. Explain in detail as to why the implied (actual) funds rate is different in this new regime relative to the old regime as in 1.a).
Question 5
You will need to fill in the following exam sheet (see link below) for this question. You may either print out the exam sheet and complete it by hand, or type in/draw your
answers in Word in the document itself.
· Directions for completing the exam sheet by hand: if you hand write the exam sheet, when you are done, you will need to scan and submit the
sheet using the link at the end of this part of the exam.
· Directions for completing the exam sheet in Word: If you complete the exam sheet in Word you will need to save a copy of the file and submit it
using the link at the end of this part of the exam.
You must show all work for full credit.
Download Question 5 Exam Sheet
Consider an economy described by the following:
a) (5 points) Derive an expression for the IS curve and MP curve.
b) (5 points) Derive an expression for the aggregate demand curve.
c) (5 points) We consider two inflation rates to ‘pin’ down our curves. Let point A represent conditions where inflation (Π) = 1% and point B represent conditions
where inflation (Π ) = 2%. Solve for the equilibrium output and the real rate of interest when Π =1. Solve for the equilibrium output and the real rate of interest when Π = 2.
Label these points as points A (where Π =1 ) and points B (where Π = 2) on all three of your diagrams.
Draw three diagrams on your exam sheet with the monetary policy curve and IS curves on top next to each other and the aggregate demand curve
below (15 points for correct and completely labeled diagrams)
e) (5 points) Suppose that falls to 1 trillion. Solve for the equilibrium output and the real rate of interest and label on your diagrams as point C.
