Post on 19-Feb-2018
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
7/23/2019 Tutorial Set 7 - Solutions
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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.