Assignment 2 : questions about fundamental finance
Econ 305 Prof. M. H. Engineer
Assignment 2
Due: Monday October 22 by 11am in ECON 305 assignment box; or for 2 bonus marks by
Wed 17 5pm in the 305 assignment box, or 1 bonus mark beginning of class on Friday Oct 19.
The assignment is out of 24 marks and counts towards 2.4% of your final grade. Three of
the following 5 problems will be randomly selected and marked.
If you work with others, please indicate their names in the top right-hand corner of your
assignment. In any event, write up the work on your own. Copying/paraphrasing will be
considered cheating. Correct answers without derivations will receive zero marks.
1. Part (d) of Section 3 of Midterm 1 (Version 1) derives the LPT forecast of 2.39% for the
expected spot rate one-year in the future (Oct 3 2019) using the Oct 3 2018 yield curve.
(a) What is the corresponding highest and lowest real interest rate expected for the year starting Oct 3 2019 given that the US Fed is expected to keep inflation between 2-3%?
(Note: so far this year the US inflation rate has been about 2.9%.)
The announcement on Oct 5, 2018 of unexpected high employment levels in the US lead
to a change in yields: 1-Year 2.61%, 2-Year was 2.89% and the 30-year was 3.41%. The
following article argues that the market reacted to this news because it interpreted the “Jobs
report becomes an inflation report.” https://www.reuters.com/article/us-usa-stocks/wall-
street-slides-as-bond-yields-climb-on-jobs-data-idUSKCN1MF1HW
(b) What does the article imply is the (qualitative) change in expected inflation, and how would that explain the above increase in yields?
(c) Is stock prices decreasing consistent with the Gordon Growth Model? Consider a two-year treasury with face value of 1 million dollars. Suppose you bought it
on Oct 3 and sold it on Oct 5. (Treat both bonds as if they had a full two years to maturity.)
(d) Roughly, how much money have you made? What is your two day rate of return?
2. Use the yields for Oct 2018 from Section 3 of Midterm 1, and consider a two-year coupon bond that pays annual coupons and has a coupon rate of 5%. Denote the actual price of the
two-year bond in Oct 2018 by P0 and the present value of the bond at the same time as PV0.
(a) Find PV0. Hint: Use the methodology on slide 40 of the Ch. 6 notes. Note, since you are not given the face value you’ll have to solve for the present value, PV, in terms of
F. (If you can’t solve for a variable F, use F =1000. One mark will be deducted.)
If the bond is priced correctly according to fundamental analysis, then P0=PV0.
(b) Find the yield i on this coupon bond when P0=PV0. Hint: to find i you’ll have to either iterate to the solution (i.e. guess i and verify that P0=PV0) or use a financial calculator.
Your answer for i maybe close but should be different than i2,t.
3. The posted article “What the stock market is telling us about future returns” applies the Gordon Growth Model to derive the required rate of return on the S&P/TSX Composite
Index.
(a) Briefly, describe the S&P/TSX Composite Index, and state your source(s). The article says the “current” price to earnings ratio is about 14. This is vague. It is not
clear whether the ratio refers to the “forward” ratio P0/E1 or the “lagged ratio” P0/E0, where
E0 is the earnings over the last year and E1 is the earning anticipated over the current year.
Econ 305 Prof. M. H. Engineer
(b) Assuming the article is referring to the “forward” ratio P0/E1, derive the required rate of return when the growth rate of dividends is 4%. Show your work and give a
percentage answer to 2 decimal places (e.g. 5.15%).
(c) Assuming the article is referring to the “lagged” ratio P0/E0, derive the required rate of return when the growth rate of dividends is 4%.
The article ends with the enigmatic statement: “Financial markets are efficient mainly
because a large number of investors believe they can beat the average, so we should
encourage this belief.”
(d) If everybody were a passive investor would markets be informationally efficient? Briefly, explain. (See Rationale Behind the Hypothesis on p157 in chapter 7.)
4. Download yield data for Sept 14, 2018 (latest data available for “zero-coupon” bond yields) from http://www.bankofcanada.ca/rates/interest-rates/bond-yield-curves/
(a) Roughly sketch the yield curve, indicate the specific yields in % for 1, 2, 3, 5, 10, 20, 30 years. (Note that the US yields for Oct 3 are well above these rates.)
(b) What is the peak yield in the data and what maturity is it? (c) What is the expected short rate 15 years from now according to the Expectations
Theory? Hint: you should use yields ZC1500 and ZC1600 in your analysis. (Note: This
interval is just before the peak of the yield curve and so should give the highest forecast
for any year in the next 29 years.)
The (real) yield on Real Return Bonds – Long-term is about 0.63% on Sept 14, 2018
(http://www.bankofcanada.ca/rates/interest-rates/canadian-bonds/)
(d) What is the upper bound on the expected inflation rate in Canada long-term under the Expectations Theory? Assume that when the real yield on all long bonds is about 0.63%
(i.e. the real yield curve is flat) and that your calculation in part (c) gives the highest
expected short interest rate.
5. Chapter 7 Problem 24. (a) Derive the answer to price of the stock in 5 years (i.e. Find: P5.) The question does not specify expected dividends or the required rate of return for beyond
five years. Assume that following the fifth year (i.e. in the 6th year) that dividends grow at
a constant rate forever and that the required rate of return remains at 10%.
(b) Find the growth rate of dividends that is consistent with your answer in part (a) to P5. (Hint: use the Gordon growth model.)
Now suppose that you are not given the price of the stock at P0 but are told that P5 =101.
(c) What is the price of the stock today? Finally, suppose that dividends stay at $1 forever.
(d) What is the price of the stock today?