Assignment 2 : questions about fundamental finance

Econ 305 Prof. M. H. Engineer

Assignment 2

Due: Tuesday Oct 22 in class; or for 3 bonus marks in class or the assignment box by Friday

Oct 18, 4: 30pm. Your assignment must have the posted Cover Page for Assignment 2. Bonus

1 mark for filling it in correctly. Again, copying is cheating. Write up your assignment on your

own after you consult with colleagues.

The assignment is out of 28 marks and counts towards 2.8% of your final grade. I will toss

a coin, and mark either questions 1 and 2 or questions 3-6. The assigned mark will be double

what is posted below.

1. (12 marks) Download yield data for Sep 18, 2019 (latest data available for “zero-coupon” bond yields) from http://www.bankofcanada.ca/rates/interest-rates/bond-yield-curves/

(a) (3 marks) Sketch the yield curve, indicating the specific yields in % for 1, 2, 3, 5, 10, 20, 30 years. (Notation ZC200YR corresponds to yield for a two-year bond.)

Observe that the yield curve is essentially flat over the period 20 to 30 years. In answering

the questions below, assume that the level of the yield curve for the period 20 to 30 years

is given by yield for year 20, i.e. ZC2000YR which is 1.6226%.

(b) (2 marks) What is the expected short rates 20 to 29 years from now implied by the

Expectations Theory? Specifically find 𝑖𝑡+𝑛−1 𝑒 for 21 ≤ n ≤ 30.

(c) (3 marks) Long-term LPT Corp estimates (at t = 18/09/19) that the liquidity premium

on the 20-year bond is 𝑙20,𝑡= 0.5% and is increasing by .01% per year; i.e. 𝑙𝑛,𝑡 = 0.5 + (n - 20)(.01) for n ≥ 20. Using the Liquidity Premium Theory, what is their forecast for

the expected short rates 20 years from now and 29 years from now?

The general Fisher equation can be expressed: iet+n-1 = r e t+n-1 + π

e t+n-1.

The (real) yield on Real Return Bonds Long-Term (for 20-30 years from now) was 0.33%

on Sep 18, 2019 (FYI https://www.bankofcanada.ca/rates/interest-rates/canadian-bonds/)

(d) (2 marks) Assume that the real yield curve that describes long bonds (for 20-30 years

from now) is flat at , 1,n t n t

r r 

 =0.33%. Show that the Expectations Theory (ET),

replacing the nominal yields with the real yields, gives the result that the expected short

real interest rates are 1 ,

e

t n n t r r  

 = 0.33%. What can you infer about the expected

inflation rate in Canada 20 to 29 years from now using ET and the Fisher equation?

Historically, real interest rates have never gone below -4% (see Figure 4.1). Use this value

as a lower bound for the real interest rates in the following question which follows up on

the midterm.

(e) (2 marks) Complete part (c) of the yield curve question on Midterm 1 Section A02: “Using the theories, can you confidently rule out high real interest rates or high inflation in the next two years? (Give numerical qualitative answers for full marks.)”

2. (2 marks) On October 4, 2019, the 3-month US LIBOR was 2.027% (http://www.global- rates.com/interest-rates/libor/american-dollar/american-dollar.aspx), and the 3-month T-

Bill has a yield of 1.69% (Bloomberg).

(a) (1 mark) Calculate the relative TED spread in the same way as done in Yields Illustrated for October 4, 2019

(b) (1 mark) Evaluate the following statement as True, False, or Uncertain, and briefly explain why. (No marks without an explanation.)

Econ 305 Prof. M. H. Engineer

“In Yields Illustrated “The Biggest Price-Fixing Scandal Ever” involves the big

international banks fixing the TED spread.”

3. (3 marks) Negative nominal yields on bonds is a fairly recent phenomena. This is puzzling as investors could do better by simply holding cash.

(a) (1 mark) In your own words, briefly summarize the textbook’s answer (in Ch 4) to this puzzle.

Below use https://www.bloomberg.com/graphics/negative-yield-bonds/

(b) (1 mark) Which three countries have the greatest value of bonds with negative yields on Aug 29, 2019 (or the most recent posted date)?

(c) (1 mark) The article highlights a bond with yield of -0.26%. Assuming this is a zero- coupon bond, calculate the percentage yield to 3 decimal places.

4. (4 marks) Use the (zero-coupon bond) yields for 09/27/19 from Midterm 1 A01, and consider a three-year coupon bond that has a coupon rate of 3%. Denote the actual price of

the bond as P0 and the present value of the bond as PV0.

(a) (2 marks) Find PV0. Use the methodology in the Chapter 6 notes on slide 17 (Using Zero-Coupon Yields to Price Bonds). Note: since you are not given the face value,

solve for PV0 in terms of F.

If the bond is priced correctly, then P0 = PV0 according to fundamental analysis.

(b) (2 marks) Briefly, explain how you would solve for the coupon bond yield i that reconciles P0 = PV0 ; i.e. put in the relevant numbers into this relationship and show

that i can be derived without a value for F. No need to calculate i.

5. (5 marks) This question illustrates a two-stage Gordon Growth Model. Stage One: A junior

growth company has just paid a dividend of $1 (i.e. 𝐷0 = 1), and dividends are expected to grow at 14% per year over the next six years (t = 1,…, 6). The required rate of return on

the stock is 12%, and stock price is expected to be $125 in 6 years (i.e. 𝑃6 = 125). (a) (2.5 marks) Derive the current price 𝑃0 consistent with present value pricing. Stage Two: Starting in the 7th year, dividends are expected to grow at a slower but constant

rate 𝑔′ forever (i.e. for t ≥ 7). As the company will be safer after the initial high growth stage, the required rate of return drops to 10%.

(b) (2.5 marks) Find the constant growth rate of dividends 𝑔′ consistent with 𝑃6 = 125.

6. (2 marks) Assignment 2 last year looked at the G&M article, “What the stock market is telling us about future returns”. According to Bloomberg, the P0/E0 ratio for the Composite

TSX Index on Oct 11, 2019 was 16.7. Using this new ratio, derive the required rate of

return ke on the Index maintaining the other assumptions in the article.