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University of Wollongong *
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Course
222
Subject
Finance
Date
Jan 9, 2024
Type
Pages
3
Uploaded by ProfessorLapwing6374
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1
of
3
FIN222 Week 5 Workshop Solutions on Risk and Return
1.
If FALSE, correct the sentence.
a.
Beta is a measure of systematic risk.
TRUE
b.
The market will compensate investors for bearing
both
systematic risk
only and
unsystematic risk
.
FALSE
This is because unsystematic risk can be diversified away.
c.
The beta of a stock is primarily determined by how its returns co-vary with the market
returns.
TRUE
d.
An investor investing in a two-asset portfolio can achieve diversification benefit
as long
as two assets are less than perfectly positively correlated (i.e. as long as Corr < 1) only
when two assets are negatively correlated
.
FALSE
e.
Assuming a two-asset portfolio, a maximum reduction in portfolio risk occurs when the
correlation coefficient between the two assets is equal to
minus onezero
.
FALSE
2.
Which one of the following is
TRUE
? If it is FALSE, correct the sentence.
a.
The intercept of the SML is a
risk free ratereturn on the market
.
FALSE
b.
In equilibrium, all assets are priced according to their
systematic riskstandard deviation
.
FALSE
c.
A security having a higher
betastandard deviation
will always have a higher required rate
of return than a security having a lower
standard deviationbeta
.
FALSE
Although a security has a lower standard deviation, if the beta of this security is greater,
then the security having a lower standard deviation would require a higher return.
d.
A stock is called overpriced when it is located
belowabove
the SML.
FALSE
e.
A stock is said to be underpriced when its expected return is greater than the
required return.
TRUE
Page
2
of
3
3.
What is the portfolio's standard deviation if you invest 45% of your money into stock 1 which has a
standard deviation of returns of 15% and the rest into stock 2 which has a standard deviation of returns
of 10%? Assume that the correlation coefficient between the returns of the two stocks is +0.80.
𝑉𝑎𝑟൫𝑅
൯ ൌ 𝑊
ଵ
ଶ
𝑆𝐷ሺ𝑅
ଵ
ሻ
ଶ
𝑊
ଶ
ଶ
𝑆𝐷ሺ𝑅
ଶ
ሻ
ଶ
2
𝑊
ଵ
𝑊
ଶ
𝐶𝑜𝑟𝑟ሺ𝑅
ଵ
,
𝑅
ଶ
ሻ𝑆𝐷ሺ𝑅
ଵ
ሻ𝑆𝐷ሺ𝑅
ଶ
ሻ
W
1
=0.45,
SD
1
=0.15, W
2
= 1-W
1
=0.55, SD
2
=0.1, Corr = +0.8
𝑉𝑎𝑟൫𝑅
൯ ൌ ሺ
0.45
ሻ
ଶ
ሺ
0.15
ሻ
ଶ
ሺ
0.55
ሻ
ଶ
ሺ
0.1
ሻ
ଶ
2
ሺ
0.45
ሻሺ
0.55
ሻሺ
0.8
ሻሺ
0.15
ሻሺ
0.1
ሻ
ൌ
0.013521
𝑆𝐷൫𝑅
൯ ൌ √
0.013521
ൌ
0.1163
4.
The covariance of the market's returns with the stock's returns is .006. The standard deviation
of the market's returns is 8% and the standard deviation of the stock's returns is 15%. What is
the correlation coefficient between the stock and market's returns?
𝐶𝑜𝑟𝑟
ଵ
,
ଶ
ൌ
𝐶𝑜𝑣
ଵ
,
ଶ
𝑆𝐷
ଵ
∗ 𝑆𝐷
ଶ
𝐶𝑜𝑟𝑟
ଵ
,
ଶ
ൌ
0.006
0.08
∗
0.15
ൌ
0.5
5.
The risk- free rate is 6% and the expected market return is 15%. An investor sees a stock with a
beta of 1.20 selling for $25. The investor thinks that the stock will sell for $29 at year end. The
stock is ______ so the investor should _______ :
a.
overpriced, buy it
b.
overpriced, sell it
c.
underpriced, buy it
d.
underpriced, sell it
E(R
i
)=rf + Beta (E(R
Mkt
-r
f
)) =0.06+ 1.2 (0.15 – 0.06) = 0.168 (required return)
Expected return =
29
െ
25
25
ൌ
0.16
ሺ𝑙𝑒𝑠𝑠
𝑡ℎ𝑎𝑛
𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑
𝑟𝑒𝑡𝑢𝑟𝑛ሻ
Page
3
of
3
6.
The market risk premium is 6% and the risk-free rate is 2.65%.
Mcdonald has a beta of 0.5. Assuming the realised return of 8%, is the security fairly priced?
Yahoo has a beta of 1.46. Assuming the realised return of 5%, is this security fairly priced?
Answer the questions by completing the below and drawing the SML.
Hints: Fill the gap as you develop ideas for the question.
The Security Market Line (SML) shows the relationship between
required return
and
beta
.
From the question, we know
o
r
f
=
2.65%
and Market risk premium=
6%
.
Given above, let’s establish CAPM equation E(Ri)=_
r
f
+ B[E(R
MKt
)–r
f
]=2.65 + 6B
To determine whether a security is correctly priced, we need to compare
required
rate of return to
realised
rate of return.
Beta
Realised
return
Required return
(Compute!)
Overpriced?
Underpriced?
Buy or Sell?
Mcdonald
0.5
8%
2.65+ 0.5*6=5.65%
Underpriced
Buy
Yahoo
1.46
5%
2.65+ 1.46*6=11.41%
Overpriced
Sell
E(Ri)
11.41%
Mc
5.65%
(
r
f
)
2.65%
0.5
1.46
Beta
8%
5
%
yaho
o
I am
E(R
MKt
)–r
f
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Related Questions
EXERCISE 1Indicate whether each of the following statements is true or false. Support your answerswith the relevant explanations.1) The higher the systematic risk of a company’s stock, the higher the value of itsbeta. The higher the beta, the higher the return required by the investors.(Explain your reasoning.)
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QUESTION 7
According to the capital asset pricing model (CAPM), fairly priced securities should have
A. A non-zero alpha.
в.A fair return based on the level of systematic risk.
C. A fair return based on the level of unsystematic risk.
D.A beta of 1.
QUESTION 8
Diversification can increase fair return.
True
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The part of a stock's risk that can be eliminated is know as _______________risk
The portion of the stock's risk that cannot be eliminated is called ___________ risk
Answer 2 Question 5
Market risk is also referred to as ________________ risk
Answer 3 Question 5
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Question 2Using the data generated in the previous question (Question 1);a) Plot the Security Market Line (SML) b) Superimpose the CAPM’s required return on the SML c) Indicate which investments will plot on, above and below the SML? d) If an investment’s expected return (mean return) does not plot on the SML, what doesit show? Identify undervalued/overvalued investments from the graph
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true or fslse
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common economic events
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unsystematic risk
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Question 17 options:
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Question content area bottom
Part 1
(Select the best choice below.)
A.
Investors don't care about diversifiable risk and so don't hold any.
B.
Investors care about diversifiable risk, but hedge their positions so they don't demand a risk premium.
C.
Although investors must hold diversifiable risk, they don't care about it, so there is no risk premium.
D.
Investors can remove diversifiable risk from their portfolio by diversifying. They therefore do not demand a risk premium for it.
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