Assignment 4 Economics 3215
Due Date: November 2017
1. Interest rates on a wide range of assets have been quite low in Canada, the United States and a variety of other countries over the past several years.Let’s look at some possible explanations.
(a) The Supply-Demand model can provide some idea of what might be going on.
(i) Provide a Supply-Demand diagram showing an equilibrium interest rate of 6% (about the level of the
yield on a medium-term bond pre-financial crisis). (see below)
(ii) The current equilibrium interest rate on an asset of this type is now about 3%. Provide a diagram
showing how afall in interest rates from 6% to 3% could have occurred as a result of a demand
curve shift. Provide a second diagram showing how the fall in interest rates could have occurred due to a supply curve shift.
(b) Now let’s think about what kinds of factors might have produced the possible demand or supply curve shifts in (a)(ii). Severalideas have been suggested (some by quite prominent economists).
(i) One suggestion is that trends in the inflation rate could be responsible. Explain how this might work
using the Supply-Demand model.
This is the Fisher effect (see class notes). The Fisher effect says that changes in the expected inflation rate will be reflected 1-for-1 in the nominal interest rate other things equal. In terms of the diagram, a 3% fall in the expected inflation rate will shift the Demand curve down by 3% and also shift the Supply curve down by 3% this will lower the equilibrium interest rates from 6% to 3%:
(ii) A second suggestion is that the low interest rates could reflect actions of the central bank. How might this relate to your suggested shifts in (a)(ii)?
All I was looking for here was some mention of how monetary policy might enter the model. There are a couple of ways you can make this link: think about an open-market operation that buys T-Bills or some other asset. This shifts the Demand curve for assets right. Or think about the deposit expansion process. The central banks creates more reserves, chartered banks then lend out these extra reserves (that extra lending is extra demand for assets, drivinginterest rates down).
(iii) Have a look at this March 2015 post by Ben Bernanke (former Chair of the US Federal Reserve):
What does he think of the inflation and monetary policy explanations for low interest rates? Explain why.
He seems to think that other factors have affected real interest rates and that these other factors help explain current low rates. He notes that inflation affects nominal interest rates (the Fisher effect) and monetary policy mainly affects short-term interest rates. Yet we see that real rates are low for longer-term assets too.
(iv) Bernanke has pushed the idea of a ‘global savings glut’ as an explanation for low interest rates. Have a look at the post below:
Based on the post, what is the source of the ‘savings glut’. How does it relate to your diagrams in (a)(ii)?
This is a Demand shift story (extra lending). The extra assets demand is caused by high savings internationally (East Asia, oil producers and, more recently, Germany)
(v) Larry Summers (big name economist, ex-President of Harvard University, former US Treasury Secretary) has been pushing the idea of ‘secular stagnation’ as an explanation of low interest rates. Have a look at the excerpt from his 2016 article ‘The Age of Secular Stagnation’(it is at the end of the assignment sheet). According to Summers, what factors lie behind low interest rates? Are they supply-side, demand-side factors or both? Explain.
Summers gives an interesting mix of factors some of which will affect the amount of saving (so shifting Demand for assets right, e.g. inequality, demographics and retirement uncertainties) and others work through Supply (limited borrowing due to changes in the economic structure and nature of new industries – in particular that they are less capital intensive).
2. (i) Say that a financial asset promises to pay $1000 per year for eight years. If the yield on other similar assets is 5% what would you expect the price of this asset to be? Explain and show your calculations.
Price =1000 + 1000+ 1000 + 1000+ 1000 + 1000 + 1000 + 1000
(1+i) (1+i)2 (1+i)3 (1+i)4 (1+i)5 (1+i)6 (1+i)7 (1+i)8
=$6463.21 when i=.05 (5%)
(ii) If the yield on similar assets is 6% use i=.06 in the formula above to get Price=$6209.79
(iii) Say that instead of your answer in (i) the asset in (i) was currently being sold at a price of $5000. Show how you would find its yield, i.e. set up the equation you need to solve. Provide an estimate of the yield of this asset. Given that similar assets pay 10% use a supply-demand story to explain what will happen to this asset. (Note: you can generate the yield estimate numerically. You can do this in Excel using the "Solver" add-on -- see the Solver instructions on the course website).
Solve the following equation for i (you will get i=.118 (11.8%):
$5000 =1000 + 1000 +1000 + 1000+ 1000 + 1000 + 1000 + 1000
(1+i) (1+i)2 (1+i)3 (1+i)4 (1+i)5 (1+i)6 (1+i)7 (1+i)8
3. The Bank of Canada website ( provides some historical data. Go to the top of the page and highlight “Statistics”. The resulting pull down menu gives you a few options click on “Interest Rates”. On the interest rate page click on “Bond Yields” and scroll down the page. Report the most recent yield for the 2-year, 3-year, 5-year, 7-year and 10-year Government of Canada bonds. Go back to the interest rate page and click on “Treasury Bill Yields” then scroll down the page and find the yield for a 1-year Treasury Bill (use the yield reported for the date closest to that used for your bond yields).
(i) Use the data collected above to plot the yield curve for Government securities of 10-years to maturity or less (use the 1-year T-Bill as your 1 year bond).
Here is the yield curve for Nov. 28 (yields on the vertical axis and the term (number of years to maturity) on the horizontal axis.
Data (format: .013 means a 1.3% yield):
Term / Yield Nov 281 / 0.013
2 / 0.0142
3 / 0.0146
5 / 0.0159
7 / 0.0169
10 / 0.0184
(ii) Assume that the expectations theory of the yield curve is correct. Based on the data (and the theory) what does the “market” expect will be the yield on a 1-year Treasury Bill which will be issued one year in the future? How about for a one-year Treasury Bill to be issued in two-year’s time? What is the expected yield on a 2 year-bond that will be issued three-years from now? How about a five-year bond issued five years in the future? Show your calculations.
The option of investing in two one-year bonds sequentially and one 2-year bond will pay the same return: (1+R1)(1+E11)=(1+R2)2
R1=.013(1.3%), R2=.0142substituting these values into the equation and solving gives E11=.0154 (E11 is the yield expected on a 1-yr bond issued one-year in the future). Note that you can also use the approximation version (longer rates equal the average of shorter rates): (R1+E11)/2 = R2 to find E11.
To find the expected yield on a one-year bond issued in two years (E12) you can use: (1+R2)2(1+E12)=(1+R3)3 Solve this for E12=.0154 and use R2=.0142, R3=.0146
You could also use your answer for E11 and note that three one-year bonds held sequentially should have the same payoff as a three-year bond:(1+R1)(1+E11)(1+E12)=(1+R3)3 (you know R1, R3 and E11 so solve for E12). The approximation version would use: (R1+E11+E12)/3 = R3(you know R1 , R2 and E11 so solve for E12).
A two-year bond issued in three years time:
You can use: (1+R3)3(1+E23)2=(1+R5)5 (left hand side is payoff from investing $1 in a 3-year bond followed by a two-year bond whose yield is expected to be E23. The right hand side is the payoff to investing in a 5-year bond. R3=.0146, R5=.0159. Solving for E23 gives .01785.
The approximation version would use: (3/5)R3+(2/5)E23=R5 notice that the three-year bond and the two-year bond yields are weighted by the share of the five years that the money is in each bond (rather than equal weights). Then solve the expression for E23.
5-year bond issued five year in the future: use the observed yields on a current 5-year and 10-year bond and the equation (1+R5)5(1+E55)=(1+R10)10 then find E55=.0209.
4. Canada vs US yields and uncovered interest parity.
November 28 data:
The yield on a 1-year Treasury bill: Canada .013 (1.3%) US .0161 (1.61%)
The yield on a 3-year Bond: Canada .0146 (1.46%) US .0185 (1.85%)
Notice that the American yields are higher than the Canadian yields. If lenders are to regard these as equally good investments lenders must anticipate that the Canadian dollar will appreciate vs. the US dollar (The appreciation will boost the return to a US lender buying a Canadian bond to the level of the return on the US bond. From the point of view of a Canadian lender the appreciation in the Canadian dollar reduces the Canadian dollar return from buying the American bond to that paid on the Canadian bond).
More formally
If you look at the yield on a 1-year T-Bill:
iC=.013 (1.3%) and iUS=.0161 (1.61%)
these two options need to give the same return if we are in equilibrium so:
(1+iC) =(1+ iUS)(X1/X0) where X0 = is the exchange rate in Cdn $ per US $ at the time of the investment and X1 is its anticipated value one year later.
This gives” X1/X0= (1.013/1.0161)=.9969 so the exchange rate in one-year’s time (X1) will be about .9969 of what it is now, i.e. it will take fewer Canadian dollars to buy a US dollar in one-year’s time. X0=$1.2807 Cdn per US on Nov. 28 so X1=.9969x1.2807 = $1.2768 Cdn per US.
Comparing the 3-year bonds:
(1+iC)3=(1+ iUS)3(X3/X0)
((1.0146)3 =(1.0185)3(X3/X0)
X3/X0=.9886
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