Unit 4 discusses return and risk, while Unit 5 covers modern portfolio theory. Portfolio theory holds that investing in multiple assets lowers overall risk if profits from one asset can offset losses in others. An optimal portfolio minimizes risk for a given return or maximizes return for a given risk. It is selected from the efficient frontier of portfolios with the highest return per level of risk. The security market line models the relationship between risk and expected return for individual assets based on the capital asset pricing model.

2. Unit- Four and Five
Return and risk- unit Four
Modern portfolio- unit Five

3. Portfolio
Portfolio means making investment in
more than one alternative at the same
time.
It is also called investment
diversification or combination of
investment.
Total investable fund is invested in a
single asset risk become higher.
If investable fund is invested in more
than one asset, risk became lower
because profit from one area can
compensate the loss in another assets.
Portfolio theory
The process of selecting optimal
portfolio is called portfolio theory. A
optimal portfolio is that ratio of
investment, which fulfills the following
objectives.
minimizing risk if return is equal
maximizing return if risk is equal
So portfolio theory is the process of
the selecting low riskier investment.
This model developed by Harry
Markowitz in 1952 AD
This theory is based on the following
assumption.
By nature investor are risk averter
Expected return of any portfolio is
the mean value of probability
distribution of future return.
Deviation of return create the risk.
Higher risk taking investor expects
higher return and lower risk taking
investor expect lower return.

4. Selection of optimal portfolio
1. Create the Risk and Return
indifference curve
Risk
Return
Features of the indifference curve
 Every point which lies on same risk
return indifference curve gives the
same satisfaction level.
 Every upper risk return indifference
curve gives more satisfaction
 In lower level risk return
indifference curve, return does not
increase in accordance to risk
increment but in upper level risk
return indifference curve return
increase as per the risk.
p
q
O
n
r
IC1
X
Y IC3
IC2

5. Selection of optimal portfolio
1. Create the Risk and Return
indifference curve
Y Ic2 Ic1 Ic3
X
Risk
Return
2. Choice the efficient portfolio
Port folio Return Risk
A 10% 7%
B 10% 6%
Portfolio B is efficient base on risk
Port folio Return Risk
A 11% 7%
B 10% 7%
Portfolio 'A' is efficient base on return
3. Opportunity set
Opportunity set is the combination of
efficient and inefficient portfolio. It is
also called attainable set.
ABCD = Efficient portfolio/Frontier
EFG= Inefficient portfolio/set
ABCDEFG= Attainable set
Efficient frontier= The line joining a
portfolio having the hiest return in the
same level of risk is known as efficient
frontier.
Return
Risk
D
C
B
A
E
F
G
Attainable
set

6. 4. Optimal portfolio/Choice
Y Ic2 Ic1 Ic3
Risk
Return
a
b
c
Optimal portfolio is the combination of investment
in assets which helps an investor to minimize risk if
return is same or to maximize return if risk is same
Optimal portfolio is selected involving the risk
return indifference curve from the above efficient
frontier.
The meeting point of risk-return indifference curve
of efficient frontier is assumed as optimal
portfolio.
Above the figure investor select
the portfolio lies in the efficient
frontier of the opportunity set,
which is tangent to the indifferent
curve of the investor, and the
portfolio becomes optimal for him.
The indifferent curve Ic2 tangent
with efficient frontier at point 'b',
here investor optimal portfolio at
point 'b'.
These point makes higher level of
satisfaction to the investor.
Investor would not be selected
points 'a' and 'c' because these
points has lower level of investor's
satisfaction/higher level of risk

7. Portfolio return
Portfolio return refers to the return on the total
investment when an investor invests in more than
one asset.
A portfolio return equals to the weighted average
of the returns of the individual assets held in the
portfolio.
The sum of weight of all assets in a portfolio always
equals to one as an investors spreads his total
investable fund among the assets.
Portfolio risk
Portfolio risk means that risk which is created while
investing in more than one assets all together.
In the other words portfolio risk refers to the
variability of expected returns of the portfolio.
Portfolio risk can be measured in terms of variance
and standard deviation.

8. SML
Krf
Y
Security Market line (SML)
SML is the graphical representation of
Capital Assets Pricing Model (CAPM).
The equation of CAPM is the equation of
SML. CAPM is the pricing model, it
describes relationship between
expected return and systematic risk of
an individual asset.
The SML appears as shown in following
figure.
Total risk = systematic + unsystematic risk
SML only represent the part of systematic
risk out of total risk.
Slope of SML=
𝐾𝑚−𝐾𝑟𝑓
𝞫𝑚
Slope of SML=
𝐾𝑚−𝐾𝑟𝑓
𝟃𝑚
Equation of SML(Rj) = Krf +(Km- Krf) ᵦj
Decision
If Rj > expected return, stock is
overvalued and overvalued stock
should sell.
If Rj < expected return, stock is
undervalued and under valued stock
should purchase.
If Rj = expected return, stock is indifferent
in the market and investors follow the
wait and see strategic. i.e no action.
Km
ᵦj
Risk
premium
Km- Krf
X
Systematic risk
Expected
return

9. Types of risk/sources of risk
a. Business risk => Business risk refers to the uncertain
about the rate of return caused by nature of business
b. Financial risk=> The risk related to firm's capital
structure i.e. debt mgmt, preferred stock and
common share.
c. Liquidity risk=> Liquidity risk associated with the
uncertainly created by the inability to the sell the
investment quickly for cash.
d. Interest rate risk=> Change in the interest rate in
market.
e. Management risk=> The risk created due to different
management policies decision and programs affect
the risk faced by investors.
f. Purchasing power risk=> The risk caused by inflaction.

10. Risk free assets
Some of investment, return of which is exactly
known is called risk free assets.
In other words, the assets with zero standard
deviation in result between actual and expected
return is called risk free assets.
In case of Nepal treasury bill is an example of risk
free assets.
Treasury bill is defined as risk free assets because its
maturity period and holding period are equal.
If risky and risk free assets is given
𝑅𝑝= 𝑅𝑚 𝑋 𝑊𝑚+𝑅𝑟𝑓 𝑋 𝑊𝑟𝑓
𝑹𝒑= 𝑹𝒎 𝑿 𝑾𝒎 + 𝑹𝒓𝒇 (𝟏−𝑾𝒎)
ᆚ𝑝= 𝟃𝑚 𝑋 𝑊𝑚

14. We have given,
Weighted of investment A (𝑊𝐴) =
30,000
1,00,000
= 0.3
Weighted of investment AB(𝑊𝐵) =
70,000
1,00,000
= 0.7
Expected return for investment A(𝑅𝐴) = 10%
Expected return for investment B(𝑅𝐵) = 15%
Calculate the expected return on portfolio(𝑅𝑃)
By the formula
(𝑅𝑃) = 𝑡=1
𝑛
𝑅𝑗𝑋 𝑊
𝑗
= 𝑅𝐴 X 𝑊𝐴+ 𝑅𝐵 𝑋 𝑊𝐵
= 10 X 0.3 + 15 X 0.7
= 13.5%

15. Year End
price
P1
Beg
price
Po
Percentage return
𝑹𝒋 =
𝑷𝟏−𝑷𝟎
𝑷𝟎
𝑹𝒋 − 𝑹𝒋 (𝑹𝒋 − 𝑹𝒋)𝟐
2012 55,000 50,000 55,000−50,000
50,000
= 10%
2013 58,000 55,000 58,000−55,000
55,000
= 5.45%
2014 65,000 58,000 65,000−58,000
58,000
= 12.07%
1015 70,000 65,000 70,000−65,000
65,000
= 7.69%
Calculate the average return over the four year period and standard deviation.
a. Average return(𝑹𝒋) =
𝑅𝑗
𝑁
=
10+5.45+12.07+7.69
4
=
35.22
4
= 8.80
b. Standard deviation(𝟃𝑗)=
(𝑹𝒋 −𝑹𝒋)𝟐
𝑁−1
=
𝑁−1

17. a.
𝑅𝐴 𝑅𝐵 𝑃𝑗 𝑅𝐴 X 𝑃𝑗 𝑅𝐵 X 𝑃𝑗 𝑅𝐴 − 𝑅𝐴 𝑅𝐵 − 𝑅𝐵 (𝑅𝐴−𝑅𝐴 )2𝑋𝑃𝑗 (𝑅𝐵−𝑅𝐵)2X𝑃𝑗
10 50 0.3 3 15 -10 20 30 120
20 30 0.4 8 12 0 0 0 0
30 10 0.3 9 3 10 -20 30 120
𝑅𝐴. 𝑃𝑗 𝑅𝐵. 𝑃𝑗 (𝑅𝐴 − 𝑅𝐴)2
. 𝑃𝑗 (𝑅𝐵 − 𝑅𝐵)2
. 𝑃𝑗
= 20% = 30% = 60 = 240
(𝑅𝐴 − 𝑅𝐴) ( 𝑅𝐵 − 𝑅𝐵 ) 𝑋𝑃𝐽
-60
0
-60
(𝑅𝐴 − 𝑅𝐴) ( 𝑅𝐵 − 𝑅𝐵 ) 𝑋𝑃
𝐽
-120

18. I) Calculate the Expected return (𝑅𝑗) for each stock.
For stock A (𝑅𝐴) = 𝑅𝐴. 𝑃𝑗 = 20%
For stock B (𝑅𝐵) = 𝑅𝐵. 𝑃𝑗 = 30%
Portfolio return (𝑅𝑃) = 𝑅𝐴 X 𝑊𝐴 + 𝑅𝐵 X 𝑊𝐵
= 20 X 0.5 + 30 X 0.5
= 25%
II) Calculation of standard deviation (ᆚ𝑗) for each stock.
For stock A (ᆚ𝐴) = (𝑅𝐴 − 𝑅𝐴)2. 𝑃𝑗 = 60 = 7.75%
For stock B (ᆚ𝐵) = (𝑅𝐵 − 𝑅𝐵)2. 𝑃𝑗 = 240 = 15.49%
Portfolio risk/ standard deviation of portfolio (𝟃𝑃)
(𝟃𝑃) = 𝟃𝐴
2
. 𝑊𝐴
2
+𝟃𝐵
2
. 𝑊𝐵
2
. +2𝐶𝑂𝑉𝐴𝐵. 𝑊𝐴. 𝑊𝐵
= 7.752. 0.52 + 15.492. 0.52 + 2 𝑋 −120 0.5 𝑋0.5
= 15.00065
= 3.87%

19. (𝟃𝑃) = 𝟃𝐴
2
. 𝑊𝐴
2
+𝟃𝐵
2
. 𝑊𝐵
2
. +2𝑟𝐴𝐵. 𝟃𝐴. 𝟃𝐵𝑊𝐴. 𝑊𝐵

21. Calculate the portfolio return over the four year period.
Portfolio between Portfolio between
XY XZ
Year 𝑅𝑥 𝑅𝑦 𝑅𝑧 𝑃𝑅𝑥𝑦 = 0.5𝑋𝑅𝑥 + 0.5𝑋𝑅𝑦 𝑃𝑅𝑥𝑧 = 0.5𝑋𝑅𝑥 + 0.5𝑋𝑅𝑧
2012 16 17 14 0.5x16+0.5x17 = 16.5 0.5x16+0.5x14 = 15
2013 17 16 15 0.5x17+0.5x16 = 16.5 0.5x17+0.5x15 = 16
2014 18 15 16 0.5x18+0.5x15 = 16.5 0.5x18+0.5x16 = 17
2015 19 14 17 0.5x19+0.5x14 = 16.5 0.5x19+0.5x17 = 18
𝑅𝑥 =70% 𝑃𝑅𝑥𝑦 = 66% 𝑃𝑅𝑥𝑧 = 66%
Portfolio average return, if 100 percent is invested in assets 'X'
𝑅𝑥 =
𝑅𝑥
𝑁
=
70
4
= 17.5%
Portfolio average return, if 50 percent is invested in assets 'X' and rest in 'Y'
𝑅𝑥𝑦 =
𝑅𝑥𝑦
𝑁
=
66
4
= 16.5%
Portfolio average return, if 50 percent is invested in assets 'X' and rest in 'Z'
𝑅𝑥𝑧 =
𝑅𝑥𝑧
𝑁
=
66
4
= 16.5%

22. B. Calculate the standard deviation.
If 100 percent invested in investment 'X'
Year 𝑅𝑥 𝑅𝑥 − 𝑅𝑥 (𝑅𝑥 − 𝑅𝑥 )2
2012 16 -1.5 2.25
2013 17 -0.5 0.25
2014 18 0.5 0.25
2015 19 1.5 2.25
(𝑅𝑥−𝑅𝑥 )2 = 5
If 50 percent invested in investment 'X' and rest in investment 'Y'
Year 𝑅𝑥𝑦 𝑅𝑥𝑦 − 𝑅𝑥𝑦 (𝑅𝑥𝑦 − 𝑅𝑥𝑦 )2
2012 16.5 0 0
2013 16.5 0 0
2014 16.5 0 0
2015 16.5 0 0
(𝑅𝑥𝑦−𝑅𝑥𝑦 )2 = 0

23. If 50 percent invested in investment 'X' and rest in investment 'Z'
Year 𝑅𝑥𝑧 𝑅𝑥𝑧 − 𝑅𝑥𝑧 (𝑅𝑥𝑧 − 𝑅𝑥𝑧 )2
2012 15 -1.5 2.25
2013 16 -0.5 0.25
2014 17 0.5 0.25
2015 18 1.5 2.25
(𝑅𝑥𝑧−𝑅𝑥𝑧 )2 = 5
Standarddeviation(𝟃𝑥) =
(𝑅𝑥−𝑅𝑥 )2
𝑁−1
=
5
4−1
= 1.29%
Standarddeviation(𝟃𝑥𝑦) =
(𝑅𝑥𝑦−𝑅𝑥𝑦 )2
𝑁−1
=
0
4−1
= 0%
Standarddeviation(𝟃𝑥𝑧) =
(𝑅𝑥𝑧−𝑅𝑥𝑧 )2
𝑁−1
=
5
4−1
= 1.29%
c. I would prefer portfolio XY comprising of 50 percent investment in assets X
and 50 percent in Y because this portfolo reduces risk to zero .

25. Quarterly holding period for two stocks are given below.
Quarter 𝑅1 𝑅2 𝑅1 − 𝑅1 𝑅2 − 𝑅2 (𝑅1−𝑅1 )2
(𝑅2−𝑅2)2
1 7.2% 0.6% 3.55 -0.613 12.6025 0.3758
2 12.9 6 9.25 4.787 85.5625 22.958
3 7.4 0.6 3.75 -0.613 14.0625 0.3758
4 -2.1 9.7 -5.75 8.487 33.0625 72.029
5 4 -18 0.35 -19.213 0.1225 369.139
6 6.9 6.1 3.25 4.887 10.5625 23.883
7 -8.4 -1.8 -12.05 -3.013 145.2025 9.078
8 1.3 6.5 -2.35 5.287 5.5225 27.952
𝑅1 𝑅2 (𝑅1−𝑅1 )2 (𝑅2−𝑅2 )2
Total 29.2 9.7 306.70 525.7476
a. I) Calculate the expected return for each stockk(𝑅𝑗 )
Average return(𝑅1) =
𝑅1
𝑁
=
29.2
8
=3.65%
Average return(𝑅2) =
𝑅2
𝑁
=
9.7
8
=1.21%

26. a. II) Calculate the standard deviation (𝟃𝒋)
Standarddeviation(𝟃1) =
(𝑅1−𝑅1 )2
𝑁−1
=
306.70
8−1
= 6.62%
Standarddeviation(𝟃2) =
(𝑅2−𝑅2 )2
𝑁−1
=
525.7476
8−1
=8.67%
b. Again, calculate the correlation coefficient between stock 1 & 2 (𝑟12)
Quarter 𝑅1 − 𝑅1 𝑅2 − 𝑅2 (𝑅1 − 𝑅1 ) (𝑅2 − 𝑅2)
1 3.55 -0.613 -2.17615
2 9.25 4.787 44.27975
3 3.75 -0.613 -2.29875
4 -5.75 8.487 -48.80025
5 0.35 -19.213 -6.72455
6 3.25 4.887 15.88275
7 -12.05 -3.013 36.30665
8 -2.35 5.287 -12.42445
(𝑅1 − 𝑅1 ) (𝑅2 − 𝑅2)
= 24.045

27. Covariance between stock 1 & 2 (𝑪𝒐𝒗𝟏𝟐)
(𝑪𝒐𝒗𝟏𝟐)=
(𝑅1−𝑅1 ) (𝑅2−𝑅2)
𝑁−1
=
24.045
8−1
=3.44
Correlation coefficient between stock 1 & 2 (𝒓𝟏𝟐)
(𝒓𝟏𝟐) =
𝐶𝑜𝑣12
𝟃1 𝑋 𝟃2
=
3.44
6.62 𝑋 8.67
= 0.0599
C. We have to given,
Weighted of first stock (𝑊1) = 0.5
Weighted of second stock (𝑊2) = 0.5
Average return(𝑅1) =3.65%
Average return(𝑅2) =1.21%
Portfolio return (𝑅𝑃) = 𝑅1 X 𝑊1 + 𝑅2 X 𝑊2
= 3.65 X 0.5 + 1.21 X 0.5
= 2.43%
Portfolio risk/ standard deviation of portfolio (𝟃𝑃)
(𝟃𝑃) = 𝟃1
2
. 𝑊1
2
+𝟃2
2
. 𝑊2
2
. +2𝐶𝑂𝑉12. 𝑊1. 𝑊2
= 6.622. 0.52 + 8.672. 0.52 + 2 𝑋 3.44 𝑋 0.5 𝑋0.5
= 5.61%
Correlation coefficient two stocks is lower positive so the portfolio offers the benefit
risk reduction. The portfolio risk is lower than individual risk of stock 1 and stock 2.

28. We have given, Risky and risk free assets
Return on risk free assets (𝐾𝑟𝑓) =2%
Return on risky assets (𝑅𝑟) = 2.43 (find in part 'C)
Risk on risky assets (𝟃𝑟) = 5.61(find in part 'C)
Weighted on risk free assets (𝑤𝑟𝑓) = 10% i.e 0.1
Weighted on risky assets (𝑤𝑟) = 90% i.e 0.9
Portfolio return (𝑅𝑁𝑃) = 𝑅𝑟 X 𝑊
𝑟 + 𝐾𝑟𝑓 X 𝑊𝑟𝑓
= 2.43 X 0.9 + 2 X 0.1
= 2.39%
Portfolio risk/ standard deviation of portfolio (𝟃𝑃)
(𝟃𝑁𝑃) = 𝟃𝑟 X 𝑊
𝑟
= 5.61 X 0.9 = 5.05%
= 𝟃1
2
. 𝑊1
2
+𝟃2
2
. 𝑊2
2
. +2𝑟12. 𝟃1. 𝟃2. 𝑊1. 𝑊2.
= 0 𝑋 𝑊1
2
+𝟃2
2
. 𝑊2
2
. +2 𝑋 𝑟12𝑋 0. 𝑋 𝟃2𝑋 𝑊1𝑋 𝑊2.
= 𝟃2
2
. 𝑊2
2
.
= 𝟃2 𝑋 𝑊2

30. Year
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
𝑅𝑚
6
2
-13
-4
-8
16
10
15
8
13
Ɛ𝑅𝑚
45%
𝑅𝐴
11
8
-4
3
0
19
14
18
12
17
Ɛ𝑅𝐴
98%
𝑅𝐵
16
11
-10
3
-3
30
22
29
19
26
Ɛ𝑅𝐵
143%
𝑅𝑚-𝑅𝑚
1.5
-2.5
-17.5
-8.5
-12.5
11.5
5.5
10.5
3.5
8.5
𝑅𝐴-𝑅𝐴
1.2
-1.8
-13.8
-6.8
9.8
9.2
4.2
8.2
2.2
7.2
𝑅𝐵-𝑅𝐵
1.7
-3.3
-24.3
-11.3
-17.3
15.7
7.7
14.7
4.7
11.7
(𝑅𝑚-𝑅𝑚)2
2.25
6.25
306.25
72.25
156.25
132.25
30.25
110.25
12.25
72.25
Ɛ(𝑅𝑚-𝑅𝑚)2
900.50
(𝑅𝐴-𝑅𝐴)2
1.44
3.24
190.44
46.24
96.04
84.64
17.64
67.24
4.84
51.84
Ɛ (𝑅𝐴-𝑅𝐴)2
563.60
(𝑅𝐵-𝑅𝐵)2
2.89
10.89
590.49
127.69
299.29
246.49
59.29
216.09
22.09
136.89
Ɛ(𝑅𝐵-𝑅𝐵)2
1712.10
Average return on market
𝑅𝑚=
𝑅𝑚
𝑁
=
45
10
= 4.5%
Average return on Investment A
𝑅𝐴=
𝑅𝐴
𝑁
=
98
10
= 9.8%
Average return on Investment B
𝑅𝐵=
𝑅𝐵
𝑁
=
143
10
= 14.3%

31. Investment alternatives Variance(𝟃𝑗
2
) standard deviation(𝟃𝑗)
Ɛ(𝑅𝑗−𝑅𝑗)
2
𝑁−1
𝟃𝑗
2
Market
900.50
10−1
= 100.06 100.06 =10%
Investment A
563.60
10−1
= 62.62 62.62 =7.91%
Investment B
1712.10
10−1
= 190.23 190.23 =13.79%

32. Year
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
𝑅𝑚-𝑅𝑚
1.5
-2.5
-17.5
-8.5
-12.5
11.5
5.5
10.5
3.5
8.5
𝑅𝐴-𝑅𝐴
1.2
-1.8
-13.8
-6.8
9.8
9.2
4.2
8.2
2.2
7.2
𝑅𝐵-𝑅𝐵
1.7
-3.3
-24.3
-11.3
-17.3
15.7
7.7
14.7
4.7
11.7
(𝑅𝑚-𝑅𝑚) (𝑅𝐴-𝑅𝐴)
1.8
4.50
241.50
57.80
122.5
102.80
23.10
86.10
7.70
61.20
Ɛ(𝑅𝑚−𝑅𝑚) (𝑅𝐴−𝑅𝐴)
712
(𝑅𝑚-𝑅𝑚) (𝑅𝐵-𝑅𝐵)
2.55
8.25
425.25
96.05
216.25
180.55
42.35
154.35
16.45
99.45
(𝑅𝑚-𝑅𝑚) (𝑅𝐴-𝑅𝐴)
1241.50

33. Covariance between market return
and investment A.( 𝐶𝑜𝑣𝐴𝑚)
𝐶𝑜𝑣𝐴𝑚=
Ɛ(𝑅𝑚−𝑅𝑚) (𝑅𝐴−𝑅𝐴)
𝑁−1
=
712
10−1
= 79.1
Correlation coefficient (𝑟𝐴𝑚)
𝑟𝐴𝑚=
𝐶𝑜𝑣𝐴𝑚
𝟃𝐴𝟃𝑚
=
79.1
7.91 𝑋 10
= 1
Beta coefficient (ᆂ 𝐴
)
ᆂ 𝐴=
𝐶𝑜𝑣𝐴𝑚
𝟃𝑚
2 =
79.1
100.06
= 0.79
Covariance between market return and
investment B.( 𝐶𝑜𝑣𝐵𝑚)
𝐶𝑜𝑣𝐴𝑚=
Ɛ(𝑅𝑚−𝑅𝑚) (𝑅𝐵−𝑅𝐵)
𝑁−1
=
1241.50
10−1
= 137.9
Correlation coefficient (𝑟𝐵𝑚)
𝑟𝐴𝑚=
𝐶𝑜𝑣𝐵𝑚
𝟃𝐵𝟃𝑚
=
137.9
13.79 𝑋 10
= 1
Beta coefficient (ᆂ 𝐵
)
ᆂ 𝐵=
𝐶𝑜𝑣𝐵𝑚
𝟃𝑚
2 =
137.9
100.06
= 1.38
Beta coefficient of investment A is less than 1 so it is less risky than
the market. Conversely, investment B has beta coefficient is greater
than 1 so it is more risky than market.

35. 5.12 calculate the required rate of return (𝑅𝑗) by
using following CAPM.
𝑅𝑗 = 𝐾𝑟𝑓 + (𝐾𝑚 − 𝐾𝑟𝑓)ᵦ𝑗
5.13 calculate the required rate of return (𝑅𝑗) by
using following CAPM.
Return of T-bill= 𝐾𝑟𝑓 = 3%
Beta=ᵦ𝑗= 1.25
Market return =𝐾𝑚 = 13%
Expected rate of return = 14%
𝑅𝑗 = 𝐾𝑟𝑓 + (𝐾𝑚 − 𝐾𝑟𝑓)ᵦ𝑗
Calculate the required rate of return than, compare
with required rate of return for decision making.

37. 𝑅𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑛 (𝐾𝑟𝑓)= 6%
Market return (𝐾𝑚 )= 14%
Beta coefficient of A company(ᵦ𝐴) = 1.55
Beta coefficient of B company(ᵦ𝐵) = 0.75
Price per share of A company = Rs.38
Price per share of B company = Rs.23
Number of share purchased for each company = 100 shares
calculate the required rate of return (𝑅𝑗) by using following CAPM.
𝑅𝑗 = 𝐾𝑟𝑓 + (𝐾𝑚 − 𝐾𝑟𝑓)ᵦ𝑗
a. For company A (𝑅𝐴 )= 𝐾𝑟𝑓 + (𝐾𝑚 − 𝐾𝑟𝑓)ᵦ𝐴
= 6 +(14-6)1.55
= 18.4%
b. For company B (𝑅𝐵 )= 𝐾𝑟𝑓 + (𝐾𝑚 − 𝐾𝑟𝑓)ᵦ𝐵
= 6 +(14-6)0.75
= 12%
c. For Portfolio (𝑅𝑃 )= 𝐾𝑟𝑓 + (𝐾𝑚 − 𝐾𝑟𝑓)ᵦ𝑃
= 6 +(14-6)1.254
= 16.03%
𝑊𝑜𝑟𝑘𝑖𝑛𝑔 𝑁𝑜𝑡𝑒
𝞫𝑃= 𝞫𝐴 X 𝑊𝐴 + 𝞫𝐵 X 𝑊𝐵
= 1.55 X
38
61
+ 0.75X
23
61
= 1.254
OR
𝑅𝑃= 𝑅𝐴 X 𝑊𝐴 + 𝑅𝐵 X 𝑊𝐵
= 18.4 X
38
61
+ 12 X
23
61
= 16.03%

39. 𝑅𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑛 (𝐾𝑟𝑓)= 6%
Market return (𝐾𝑚 )= 11%
Standard deviation on market (𝟃𝑚) = 11%
Correlation coefficient between asset A
and market (𝑟𝐴𝑚) = 0.80
Standard deviation on asset A (𝟃𝐴) = 9%
Calculate the Beta coefficient of asset A
(ᵦ𝐴) =
𝐶𝑜𝑣𝐴𝑚
𝟃𝑚
2
=
𝑟𝐴𝑚𝟃𝐴𝟃𝑚
𝟃𝑚
2
=
0.80 𝑋 9 𝑋 11
112 = 0.65
Asset A is defensive assets because it has
less beta coefficient than market.
calculate the required/Required rate of
return (𝑅𝑗)
𝑅𝐴 = 𝐾𝑟𝑓 + (𝐾𝑚 − 𝐾𝑟𝑓)ᵦ𝐴
= 6 +(11-6)0.65
= 9.25%
𝐷𝑟𝑎𝑤 𝑡ℎ𝑒 𝑆𝑀𝐿 𝑎𝑛𝑑 𝑙𝑜𝑐𝑎𝑡𝑒 𝑎𝑠𝑠𝑒𝑡 𝐴 𝑜𝑛 𝑖𝑡.
Calculate the systematic and unsystematic
risk.
Systematic risk =
𝐶𝑜𝑣𝐴𝑚
𝟃𝑚
=
𝑟𝐴𝑚𝟃𝐴𝟃𝑚
𝟃𝑚
=
0.80 𝑋 9 𝑋 11
11
= 7.2%
Unsystematic risk= 𝟃𝐴(1-𝑟𝐴𝑚)
= 9(1-0.8) = 1.8%
Out of total risk (𝟃𝐴), 80 percent (i.e
7.2
9
)
covered by systematic risk and remaining
20 percent (i.e
1.8
9
) covered by
unsystematic risk.
SML
Y
ᵦj =1 X
𝐾𝑚=11%
𝐾𝑟𝑓=6%
0.65
9.25%
A

41. Stocks
A
B
C
D
Price
100
240
410
190
Beta(𝞫𝑗)
1.4
0.8
1.3
1.8
Weight((𝑊
𝑗)
0.1064
0.2553
0.4362
0.2021
𝞫𝑗 𝑥 𝑊
𝑗
0.14896
0.20424
0.56706
0.36378
𝞫𝑗 𝑥 𝑊
𝑗 = 1.2840
Stocks
A
B
C
D
Price
(P)
100
240
410
190
Beta(𝞫𝑗)
1.4
0.8
1.3
1.8
Weight((𝑊
𝑗)
0.0629
0.3019
0.5157
0.1195
𝞫𝑗 𝑥 𝑊
𝑗
0.08806
0.24152
0.67041
0.2151
Ɛ 𝞫𝑗 𝑋 𝑊
𝑗=1.2151
No. share
(N)
100
200
200
100
Total value
(N XP)
10,000
48,000
82,000
19,000
B. Again calculate the portfolio beta, if an investor purchase each 200 shares of
stock B and C for every 100 shares of A and D.

42. 𝐾𝑟𝑓=
𝐾𝑚=
ᵦ𝐴=
ᵦ𝐵=
ᵦ𝐶=
ᵦ𝐷=
Required:
𝑅𝑗 = 𝐾𝑟𝑓 + (𝐾𝑚 − 𝐾𝑟𝑓)ᵦ𝑗
𝐷𝑟𝑎𝑤 𝑡ℎ𝑒 𝑆𝑀𝐿 𝑎𝑛𝑑 𝑙𝑜𝑐𝑎𝑡𝑒 𝑒𝑎𝑐ℎ
𝑎𝑠𝑠𝑒𝑡𝑠 𝑜𝑛 𝑖𝑡.
SML
Y
ᵦj =1 X

44. 𝞫1 = 1.2
𝞫2 = 0.9
a. Beta portfolio (𝞫𝑃) = ?
If, 𝑊1 & 𝑊2 is 50/50 percent.
b. If, Beta portfolio (𝞫𝑃) = 1.1
𝑊1 & 𝑊2 = ?
𝞫𝑃= 𝞫1 X 𝑊1 + 𝞫2 X 𝑊2
𝞫𝑃= 𝞫1 X 𝑊1 + 𝞫2 (1 − 𝑊1)
𝑊1= ……
Then,
𝑊2 = 1-𝑊1

46. Calculate the portfolio beta for each stock A & B.
Assets Beta(𝞫 𝑗
) W 𝐴 W 𝐵 𝞫𝐴X W 𝐴 𝞫𝐵X W 𝐵
1 1.3 0.1 0.3 0.13 0.39
2 0.7 0.3 0.1 0.21 0.07
3 1.25 0.1 0.2 0.125 0.25
4 1.1 0.1 0.2 0.11 0.22
5 0.9 0.4 0.2 0.36 0.18
0.935 1.11
b. Portfolio beta for stock A is less than one so it is less risky than market.
Conversely, portfolio beta for stock B is greater than one so it is more risky than
market.
c. If Risk free rate of return and market return are 2 percent and 12 percent
respectively. Calculate the required rate of return for both stocks using CAPM.
For stock A(𝑅𝐴 )= 𝐾𝑟𝑓 + (𝐾𝑚 − 𝐾𝑟𝑓)ᵦ𝐴
For stock B(𝑅𝐵 )= 𝐾𝑟𝑓 + (𝐾𝑚 − 𝐾𝑟𝑓)ᵦ𝐵

47. d. At, first Calculate the portfolio expected return for each stock A & B then give
the decision compare with required rate of return.
Assets (R𝑗) W 𝐴 W 𝐵 𝑅𝑗X W 𝐴 𝑅𝑗X W 𝐵
1 16.5 0.1 0.3 1.65 4.95
2 12 0.3 0.1 3.6 1.2
3 15 0.1 0.2 1.5 3
4 13 0.1 0.2 1.3 2.6
5 7 0.4 0.2 2.8 1.4
10.85% 13.15%
Decision
Stocks Expected return Required return Select/Reject
A 10.85 11.35 Reject
B 13.15 13.10 Select

49. Status
Weak growth
Mod growth
Stro growth
𝑅𝐶𝑠
6
12
15
𝑅𝑚
8
10
12
𝑅𝑆𝑑
7
7
7
𝑃𝑗
0.3333
0.3333
0.3333
𝑅𝑚x𝑃𝑗
2.6664
3.333
3.9996
Ɛ 𝑅𝑚x𝑃𝑗
=9.9999
OR
10%
𝑅𝑚x𝑃𝑗
1.9998
3.9996
4.9995
Ɛ 𝑅𝐶𝑠x𝑃𝑗
=10.9989
OR
11%
𝑅𝑆𝑑x𝑃𝑗
2.3331
2.3331
2.3331
Ɛ 𝑅𝐶𝑑x𝑃𝑗
=6.9993
OR
7%
𝑅𝑚-𝑅𝑚
-2
0
2
𝑅𝐶𝑠-𝑅𝐶𝑠
5
1
4
𝑅𝐶𝑑-𝑅𝐶𝑑
0
0
0
(𝑅𝑚-𝑅𝑚)2x 𝑃𝑗
1.3332
0
1.3332
Ɛ(𝑅𝑚-𝑅𝑚)2
x 𝑃𝑗
=2.6664
(𝑅𝑚-𝑅𝑚)(𝑅𝐶𝑠-𝑅𝐶𝑠) 𝑃𝑗
3.333
0
2.6664
Ɛ(𝑅𝑚-𝑅𝑚)(𝑅𝐶𝑠-𝑅𝐶𝑠) 𝑃𝑗
=5.9994
(𝑅𝐶𝑠-𝑅𝐶𝑠)2x 𝑃𝑗
8.3325
0.3333
5.3325
Ɛ(𝑅𝐶𝑠-𝑅𝐶𝑠)2
x 𝑃𝑗
=13.9986
(𝑅𝐶𝑑-𝑅𝐶𝑑)2x 𝑃𝑗
0
0
0
Ɛ(𝑅𝐶𝑑-𝑅𝐶𝑑)2
x 𝑃𝑗
=0

50. A. Calculate the Expected return (𝑅𝑗) for
each stock.
For mutual fund (𝑅𝑚) = 𝑅𝑚. 𝑃𝑗 = 10%
For Common stock (𝑅𝐶𝑠) = 𝑅𝐶𝑠. 𝑃𝑗 = 11%
For Certif. od deposit (𝑅𝐶𝑑) = 𝑅𝐶𝑑. 𝑃𝑗 = 7%
B. Calculation of standard deviation (ᆚ𝑗) for each
stock.
Mutual fund (ᆚ𝑚) = (𝑅𝑚 − 𝑅𝑚)2. 𝑃𝑗
= 2.6664 = 1.6329%
Common stock(ᆚ𝐶𝑠)= (𝑅𝐶𝑠 − 𝑅𝐶𝑠)2. 𝑃𝑗
= 13.9986 = 3.7415%
Certificate of de (ᆚ𝐶𝑑) = (𝑅𝐶𝑑 − 𝑅𝐶𝑑)2. 𝑃𝑗
= 0 = 0%
Certificate of deposit is least/zero risky in terms
of standard deviation and common stock is most
risky in terms of beta because its beta is higher
than mutual fund and certificate of deposit.
C. Calculate the Portfolio risk and return.
Portfolio X has mutual fund (𝑊
𝑚=75%)
and common stock (𝑊𝐶𝑠=25%)
Portfolio Y has common stock (𝑊𝐶𝑠=50%)
and certificate of deposit (𝑊𝐶𝑑=50%)
Cov between mutual fund and common stock
𝐶𝑜𝑣𝑚&𝐶𝑠 = Ɛ(𝑅𝑚-𝑅𝑚)(𝑅𝐶𝑠-𝑅𝐶𝑠) 𝑃𝑗 = 5.9994
Cov between common stock and certificate of
deposit will be Zero because Std deviation of
certificate of deposit is zero.
For X Portfolio
Portfolio return (𝑅𝑃) = 𝑅𝑚 X 𝑊
𝑚 + 𝑅𝐶𝑠 X 𝑊𝐶𝑠
= 10 X 0.75 + 11 X 0.25 =10. 25%
Portfolio risk/ standard deviation of portfolio (𝟃𝑃)
(𝟃𝑃) = 𝟃𝑚
2
. 𝑊
𝑚
2
+𝟃𝐶𝑠
2
. 𝑊𝐶𝑠
2
. +2𝐶𝑂𝑉𝑚&𝐶𝑠. 𝑊
𝑚. 𝑊𝐶𝑠
=
2.6664𝑋0.752 + 13.9986𝑋0.252 + 2 𝑋 5.994𝑋0.75𝑋0.25
=
= 2.1505%
C.V =
𝟃𝒙
𝑅𝑥
=
𝟐.𝟏𝟓𝟎𝟓
10.25
= 0.2098

51. For Y Portfolio
Portfolio return (𝑅𝑃) = 𝑅𝐶𝑠 X 𝑊𝐶𝑠 + 𝑅𝐶𝑑 X 𝑊𝐶𝑑
= 11 X 0.5 + 7 X 0.5 =9%
Portfolio risk/ standard deviation of portfolio (𝟃𝑃)
(𝟃𝑃) =
𝟃𝐶𝑠
2
. 𝑊𝐶𝑠
2
+𝟃𝐶𝑑
2
. 𝑊𝐶𝑑
2
. +2𝐶𝑂𝑉𝐶𝑠&𝐶𝑑. 𝑊𝐶𝑠. 𝑊𝐶𝑑
=
13.9986𝑋0.52 + 0𝑋0.52 + 2 𝑋 0 𝑋0.5 𝑋0.5
=
= 1.871%
C.V =
𝟃𝒚
𝑅𝑦
=
𝟏.𝟖𝟕𝟏
9
= 0.2079
Calculation of portfolio beta (𝞫𝑃)
For portfolio X(𝞫𝑥) = 𝞫𝑚 X 𝑊
𝑚 + 𝞫𝐶𝑠 X 𝑊𝐶𝑠
= 1 x 0.75 +1.2 x 0.25
= 1.05
For portfolio Y(𝞫𝑦) = 𝞫𝐶𝑠 X 𝑊𝐶𝑠+ 𝞫𝐶𝑑 X 𝑊𝐶𝑑
= 1.2 x 0.5 +0 x 0.5
= 0.60
In terms of beta portfolio Y is less risky
D. The standard deviation measure the total risk.
Total risk can be divided in two parts, systematic
risk and unsystematic risk. Beta is calculate to
measure systematic risk. In a well diversified
portfolio we are only bear the systematic risk. So
we calculate the beta.

52. I) Calculate the Expected return (𝑅𝑗) for each stock.
For stock A (𝑅𝐴) = 𝑅𝐴. 𝑃𝑗 = 20%
For stock B (𝑅𝐵) = 𝑅𝐵. 𝑃𝑗 = 30%
Portfolio return (𝑅𝑃) = 𝑅𝐴 X 𝑊𝐴 + 𝑅𝐵 X 𝑊𝐵
= 20 X 0.5 + 30 X 0.5
= 25%
II) Calculation of standard deviation (ᆚ𝑗) for each stock.
For stock A (ᆚ𝐴) = (𝑅𝐴 − 𝑅𝐴)2. 𝑃𝑗 = 60 = 7.75%
For stock B (ᆚ𝐵) = (𝑅𝐵 − 𝑅𝐵)2. 𝑃𝑗 = 240 = 15.49%
Portfolio risk/ standard deviation of portfolio (𝟃𝑃)
(𝟃𝑃) = 𝟃𝐴
2
. 𝑊𝐴
2
+𝟃𝐵
2
. 𝑊𝐵
2
. +2𝐶𝑂𝑉𝐴𝐵. 𝑊𝐴. 𝑊𝐵
= 7.752. 0.52 + 15.492. 0.52 + 2 𝑋 −120 0.5 𝑋0.5
= 15.00065
= 3.87%

54. A. Ranking of stock from most risky to least risky based on beta
Stock Beta Rank
A 0.8 2
B 1.4 1
C -0.3 3
B. If market return increases by 12 percent, the changes in securities return
are as follow.
Stock Beta Increase in Mkt return Change in security's return
(𝞓𝑅𝑚) (𝞓𝑅𝑗) = 𝞫𝑗X 𝞓𝑅𝑚
A 0.8 12% 9.6%
B 1.4 12 16.8
C -0.3 12 -3.6
C. If market return decreases by 5 percent, the changes in securities return
are as follow.
Stock Beta Increase in Mkt return Change in security's return
(𝞓𝑅𝑚) (𝞓𝑅𝑗) = 𝞫𝑗X 𝞓𝑅𝑚
A 0.8 -5% -4%
B 1.4 -5% -7
C -0.3 -5% 1.5

55. d. If we felt the stock market was about to experience a significant decline,
we would be most likely to add to stock 'C' because it has negative beta,
negative beta means when market decline it increases.
e. If we anticipated a major stock market increases, we would be most likely
to add stock 'B' to our portfolio because its beta is the highest and to
produces/increases the market return.