Tutorial Set 7 - Solutions

7/23/2019 Tutorial Set 7 - Solutions

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BFW2631

FINANCIAL MANAGEMENT

TUTORIAL SET 7 - SOLUTIONS

RISK AND RETURN

IMPORTANT: The questions that we encounter within the tutorial set throughout the

semester are an indication of the standard that you will face in the final examination. You are

required to attempt all tutorial questions on your own prior to attending class.

Question OneMr. Henry can invest in Highbull shares and Slowbear shares. His projection of the returns on these

two shares based on the state of the economy are given as follows:

State of

Economy

Probability of

State Occurring

Return on

Highbull Stock (%)

Return on

Slowbear Stock (%)Recession

Normal

Boom

0.25

0.60

0.15

-2

9.2

15.4

5

6.2

7.4

a) Calculate the expected return on each share.

b) Calculate the standard deviation of returns on each share.

c) Calculate the covariance and correlation between the returns on the two shares.

d) Create an equally weighted portfolio and calculate the expected return and standard

deviation for this portfolio.

Solution

a. E(RHB) = (0.25)(-2) + (0.60)(9.2) + (0.15)( 15.4)

= 7.33%

The expected return on Highbulls share is 7.33%.

E(RSB) = (0.25)(5) + (0.60)(6.2) + (0.15)(7.4)

= 6.08%

The expected return on Slowbears share is 6.08%.

b.

VarianceA(

HB) = (0.25)(-27.33)2+ (0.60)(9.27.33)

2+ (0.15)(15.47.33)2

= 33.63

Standard DeviationA(HB) = (33.631/2 = 5.80%

The standard deviation of the returns on Highbulls share is 5.80%.

VarianceB(

SB) = (0.25)(56.08)2+ (0.60)(6.26.08)2+ (0.15)(7.46.08)2

= 0.56

Standard DeviationB(SB) = (0.56)1/2= 0.75%

The standard deviation of the returns on Slowbears share is 0.75%.


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c. Covariance(RHB, RSB)

HB,SB = (0.25)(-27.33)(56.08) + (0.60)(9.27.33)(6.26.08)+(0.15)(15.47.33) (7.46.08)

= 4.25

The covariance between the returns on Highbull shares and Slowbear sharesreturns is 4.25

Correlation r HB,SB = Covariance(RHB,RSB) / (HB* SB)= 4.25/ (5.8 x0.75))

= 0.9770

The correlation between the returns on Highbulls share and Slowbears share

is 0.9770.

d. Expected Return on a portfolio with 50% Highbull and 50% Slowbear,

so E(RP)= (0.5)( 7.33) + (0.5)(6.08) = 6.71%

Standard Deviation of a Portfolio with 50% Highbull and 50% Slowbear

2

P = (HB2wHB

2)+ (SB2wSB

2)+2HBSBwHBwSB rHB,SB

= (0.5025.82)+(0.5020.752) + 20.500.505.80.750.9770

= 10.6756

P = 6756.10 = 3.27%

Question Two

The following table provides a sample of the last six monthly percentage price changes for two

market indexes. You are encouraged to make use of the statistical functionality available with your

calculator when answering this question.

Month Nikkei Russell_2000

1 8 12

2 15 9

3 -12 -7

4 11 13

5 9 4

6 -6 -14

Calculate the following:

a) The expected monthly rate of return and standard deviation for each series

b) The covariance between the rates of return for NikkeiRussell_2000

c) The correlation coefficient for Nikkei-Russell_2000


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Solution

IMPORTANT NOTE TO STUDENTS: You MUST be familiar with the statistical

functionality available within your calculator. These solutions discuss how to calculate

descriptive statistics making use of the Sharp El 735S / SHARP EL-738 Business financial

calculator. If you are using another calculator, it is your responsibility to learn how to use it.

Sharp El 735S / SHARP EL-738 Business Financial Calculator

Step One: place the calculator in Stats mode for linear calculation: [MODE] [1] [1]

Procedure Key Operation Display

Enter calculator into STATS

mode

[MODE] [1] [1] Stat 1

0.00

Step Two: enter the data as follows;

Procedure Key Operation Display

Enter cash flow data 8 (x,y) 12[ENT] DATA SET =

1.00

15 (x,y) 9 [ENT] DATA SET =

2.00

12 [+/-] (x,y) 7 [+/-] [ENT] DATA SET =

3.00

11 (x,y) 13[ENT] DATA SET =

4.00

9 (x,y) 4 [ENT] DATA SET =

5.00

6[+/-] (x,y) 14 [+/-] [ENT] DATA SET =

6.00

Compute expected returnfor Nikkei

[RCL] [4] X = 4.167

Compute expected return

for Russell_2000

[RCL] [7]

Y = 2.833

Compute std. deviation for

Nikkei

[RCL] [5] SX =10.647

Compute std. deviation for

Russell_2000

[RCL] [8] SY =11.017

Compute correlation for

Nikkei-Russell_2000

[RCL] [(]r r =

0.8647

Compute covariance for

Nikkei-Russell_2000

[RCL] [(]r[]

[RCL] [5] [][RCL] [8]

rSxSy=

101.433

a)

4.17%

6

)6(911)12(158

n

R

R

n

1i

i

Nikkei

2.83%or0283.06

)14(413)7(912

n

R

R

n

1i

i

Russel


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b)

let i = Nikkei and j = Russell_2000

c)

10.65%

37.113

37.11316

)17.46()17.49()17.411()17.412()17.415()17.48(

1n

RR

NIKKEI

222222

2n

1i

i

Nikkei

11.02%

37.121

37.12116

)83.214()83.24()83.213()83.27()83.29()83.212(

1n

RR

Russel

222222

2n

1i

i

Russel

1n

RRRRn

1t

jjtiit

ij

101.43

16

83.21417.46......83.2917.41583.21217.48ij

0.8647

02.1165.10

43.101r

RussellNikkei

Russell,Nikkei

Russell,Nikkei


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Question ThreeWhich of the following statements are true about the efficient market hypothesis?

i) It implies perfect forecasting ability

ii) It implies that prices reflect all available information

iii) It implies that prices do not fluctuate

iv) It results from keen competition among investors

Solutioni)

False.Market efficiency implies that prices reflect all available information, but

it does not imply certain knowledge. Many pieces of information that are available

and reflected in prices are uncertain. Efficiency of markets does not eliminate that

uncertainty and therefore does not imply perfect forecasting ability.

ii) True.Market efficiency exists when prices reflect all available information. To be

efficient in the weak form, the market must incorporate all historical data into prices.

Under the semi-strong form of the hypothesis, the market incorporates all publicly

available information in addition to the historical data. In strong form efficient

markets, prices reflect all publicly and privately available information.

iii) False.In efficient markets, prices reflect all available information. Thus, prices will

fluctuate whenever new information becomes available.

iv) True.Competition among investors results in the rapid transmission of new market

information. In efficient markets, prices immediately reflect new information as

investors bid the stock price up or down.

Question FourSuppose the market is semi-strong form efficient. Can you expect to earn excess returns if you

make trades based on:

a) Your brokers information about record earnings for a stock?

b) Rumors about a merger of a firm?

c) Yesterdays announcement of a successful new product test?

Solutiona) No. Earnings information is in the public domain and would be reflected in the current

stock price in a semi strong efficient market.

b)

Possibly. If the rumors were publicly disseminated, the prices would have already adjusted

for the possibility of a merger. If the rumor is information that you received from an

insider, you could earn abnormal returns, although trading on that information is illegal.

c) No. The information is already public, and thus, should already be reflected in the share

price.

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Tutorial Set 7 - Solutions