Assignment 2 : questions about fundamental finance

Econ 305 Prof. M. H. Engineer

Answers to Assignment 2 Fall 2018

1. Given: t =2018, ,

1 2019 = =2.39%

e e LPT

t i i 

from Midterm 1*; 1 2019 = [2%,3%]

e e

t  

 

(a) Given: 1 2019 = [2%,3%]

e e

t  

  0.5 mark

Find: ,min ,max ,min ,max

1 1 1 1 1 [ , ] = [ , ] =[2.39-3, 2.39-2]=[-0.61, 0.39]

e e e e e

t t t t t r r r r r       1 mark

As Fisher equation: 1 1 1 1 1 1

e e e e e e

t t t t t t i r r i             0.5 mark

Given: Oct 5, 2018 yields: 1-Year 2.61%, 2-Year was 2.89% and the 30-year was 3.41%

(b) Find: 0 e

  ; the article suggests that inflation is expected to increase. (“The jobs

report has become an inflation report.”) 1 mark

Explain increase in yields from Oct 3 to Oct 5: An increase in expected inflation (

0 e

  ) decreases the demand for bonds and increases the supply of bonds. Thus, the

price of bonds falls and (as yields are inverse to prices) yields rise. 1 mark

(c) Is the decrease in stock prices consistent with the Gordon Growth Model? Yes, since an increase in yields, ceteris paribus, increases the required return on stocks

and required return is inversely related to price. 2 marks

or Uncertain, the job report also indicates the economy is doing “better”. This could

both reduce the risk premium on stocks and increase the growth rate of stocks. Both of

these changes go in the opposite direction and act to increase the price of stocks. Thus,

when all three effects are at work, it is hard to predict the direction. (Advanced. The article indicates the Fed reserve will likely increase their lending rate to slow

down the economy. Thus, the “good” jobs report doesn’t necessarily indicate higher growth for

firms or a lower risk premium. This suggests that Yes is the better answer. Bonus 0.5 marks)

(Note: -- The explanation in the article is that stocks have to be competitive with bond yields;

this implies the required return on equity must increase.) Given: two-year treasury with F = 1 million; bought on Oct 3 and sold on Oct 5.

(d) Find: 2 days 0 2 2 (1. 8364 10 ) (1 0.0289) (1 0.0288)

F F P P F

      

  ⁴ 1 mark

Find:

2

2 days 0 2 days 4

2

0 0

1 0.0288 -1 1 -1. 9437×10

1 0.0289 day

P P P RET

P P

 



        

  1 mark

(Note These rough calculations overlook 2 things. First, if the bond had 2 years to go Oct 3 then

on Oct 5 it would have 1 year 363 days to go, so 2 days (1 363/365)

(1 0.0289)

F P

  

 . Second, using

the simple difference 2 days 0 P P  to measure how much money have made is misleading to the

extent that it mixes money today with money in the future. A future value or a present value

would be a consistent way to measure the “value” of the money made. Making these changes

makes very little difference to the answers.)

2. Given: Oct 2018 yields on Midterm 1, and a two-year coupon bond with coupon rate of 5%.

(a) Find 0 2 2 2,

0.05 0.05 + + 1. 0408

(1 ) (1 ) (1 0.0259) (1 0.0288) t t

C C F F F F PV F

i i

    

    4 marks

Econ 305 Prof. M. H. Engineer

(b) Find: i such that 0 02 2 0.05 1.05

+ + 1. 0408 (1 ) (1 ) (1 ) (1 )

C C F F F P F PV

i i i i

    

    2 marks

implies i =2.87% solves 2

0.05 1.05 + 1. 0408

(1 ) (1 )i i 

  2 marks

3. Given: posted article What the stock market is telling us about future returns (a) Wikipedia has a good two sentence description: “The S&P/TSX Composite Index is

the benchmark Canadian index, representing roughly 70% of the total market

capitalization on the Toronto Stock Exchange (TSX) with about 250 companies included

in it. The Toronto Stock Exchange is made up of over 1,500 companies.” 2 marks

Wikipedia has a short description of the eligibility criteria for a firm to be included in the

index. More detailed information is available from the TSX site: https://web.tmxmoney.com/assets/docs/indices/TSX/Factsheet_TSX.pdf

https://web.tmxmoney.com/assets/docs/indices/TSX/Methodology_TSX.pdf

Given: “Current” price to earnings ratio is 14,

“dividend payout ratio is approximately 50 per cent” D0 / E0 = 1 1/D E = 0.5

(b) Given: g =0.04;

Find:

1

0 1 1

1 1

/ 0.5 =14 7. 57%

0.04

e e

e e

D

P k g D E k

E E k g k

     

  2 marks

(c) Find: 0 1 0 0 0

0

/ (1 ) / (1 0.04)0.5 =14 7.71 %

0.04 e

e e e

P D E g D E k

E k g k g k

      

   2 marks

(d) If everybody were a passive investor would markets be informationally efficient? 2 marks No! – Passive investors do not use firm-relevant information when deciding to invest. If

everybody were passive, then stock prices would be unrelated to firm-relevant

information. Stock prices would not reflect all available information so they would not be

informationally efficient. It would then be possible for an active investor to use available

information to exploit profit opportunities (through “arbitrage trades, see p157 in chapter

7) and make better than average stock market returns. When markets are efficient, there

are no profit opportunities (beyond information efficient risk-adjusted pricing) to exploit. (Note: The statement -- “Financial markets are efficient mainly because a large number of

investors believe they can beat the average, so we should encourage this belief.” -- is ironic.

For efficient markets to work, people have to put in the work of gather and processing

information about valuations. This is expensive and is only worth undertaking if they believe

it will lead to a long-run above average rate of return. But if markets are efficient this work

has zero return and those that expend the cost are irrational. The article is alluding to the

implication that efficient markets need irrational investors to hold!)

4. Find: yield data for Sept 14, 2018 (a) Specific yields are: 1 mark

Year 1YR 2YR 3YR 5YR 10YR 20YR 30YR

Yield 2.0297 2.1233 2.1873 02.2521 2.3428 2.3703 2.3476

Econ 305 Prof. M. H. Engineer

Sketch; Description: The yield curve dips a little from year 1 to 2, but then rises around 15 basis

points to Year 10. Roughly speaking it seems remarkably flat between 10-30 years at around

2.35%. The 30-Year rate is lower than the 20-Year rate, but only 2 basis points lower. 2 marks

(b) The maximum yield is 2.3739%, and it is 16.25 years from now;

i.e. max

, 2018 =

n Sept i i16.25,Sept2018 = 2.3739% 1 mark

(c) Given: n = 16

Find:  ,15 16, 16, 15, = + (16 -1) 2.3738 +15(2.3738 2.3732) =2.3828% e ET

t t t t i i i i 

   2 marks

Given: rn,t = 0.63% on Sept 14, 2018; flat yield on long real bonds; ,

15 =2.3828%

e ET

t i 

is the

highest expected short rate on the nominal yield curve.

(d) Find: 1 1 1

= 2.38 - .63 =1.75% e e e

t n t n t n i r

        approximately 2 marks

where    , 1 , , , 1 , , 1 = + ( -1) 0.63% as 0 e ET

t n n t n t n t n t n t r r n r r r r    

   

5. (a) See MEL Chapter resources set up for derivation of P5 = $100. 2 marks Alternatively, observe that the problem resembles a coupon bond with principal repayment.

5 5

5 5 51 0 15 5 5 51 1

1 1 1

(1 ) (1 ) (1 ) (1 ) (1 ) (1 )

t t t

t tt t e e e e e e e

D P P PD P D

k k k k k k k

 

 

         

        

Given: P5 = $100, ke =.1

(b) Find: g 0.0891 , starting from period 5. Apply Gordon Growth Model (GGM)

6 5 5

(1 ) (1 )1 9 100 100(0.1 ) (1 ) 0.0891

0.1 101 e e

D g D g P g g g

k g k g g

            

   3 marks

(c) Given: P5 = 101. Find: 0 5 5 1 1 101

1 66.504 0.1 (1 0.1) (1 0.1)

P  

       

. 2 marks

Note 66.504-65.883 ≈.62, which is the answer given for increase in P0 in MEL .

(d) Given: Dt = 1 for all t, implies g = 0. Find: P0 = D1/ke = 1/(0.1) = 10. 1 marks

Note: The price in part (d) is much lower because dividend growth increases the value of the

firm dramatically, even if the growth starts in the future.

* The expected interest rate used above in question 1 was copied incorrectly from the answer

sheet and should be 2.37% in which case the range for the expected real rate is [-.63%, -.37%].