demo qs topic 5 part 1

7/27/2019 Demo Qs Topic 5 Part 1

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DEMONSTRATION LECTURE QUESTIONS

TOPIC 5 - RISK AND RETURN

PART 1

Question 1

You are given the following information about the possible returns from an

investment.

Return Probabilities

12% .15

9% .60

6% .25

Required:

(a) Calculate the expected return

(b) Calculate the variance of the return

(c) Calculate the standard deviation of the return.

SOLUTIONS QUESTION 1

a) ( ) ( ) ( ) ( ) ( ) ( ) ( )r r ri t tt

n

= = + + ==

Pr . . . .1

12 015 9 0 6 6 0 25 8 7%

( ) ( )b) Variance = =

r r rt i tt

n2

1

Pr

( ) ( ) ( ) ( ) ( ) ( )= + + =12 8 7 015 9 8 7 06 6 8 7 025 3512 2 2

. . . . . . .

c) Standard deviation = = = 1.8735%


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Question 2

An investor invests 40 per cent of her funds in Company A's shares and the

remainder in Company B's shares. The standard deviation of the returns on A is

20 per cent and on B is 10 per cent. Calculate the variance of return on the

portfolio assuming the correlation between the returns on the two securities is:A) +1.0

B) +0.5

C) 0

D) -0.5

SOLUTION QUESTION 2

. 212,1212

2

2

2

2

1

2

1

22 wwwwp ++=

1.02.06.04.02121

==== ww

a) 0.1, +=BA

( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( )

14.0

0196.01.02.016.04.021.06.02.04.022222

=

=++=

p

p

b) 5.0, +=BA

( ) ( ) ( ) ( ) ( )( )( )( ) ( )

1217.0

0148.01.02.05.06.04.021.06.02.04.022222

=

=++=

p

p

c) 0, =BA

( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( )

1.0

01.01.02.006.04.021.06.02.04.022222

=

=++=

p

p

d) 5.0, =BA

( ) ( ) ( ) ( ) ( ) ( )( ) ( )( )

0721.0

0052.01.02.05.06.04.021.06.02.04.022222

=

=++=

p

p


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Question 3

Consider the following information:

Economy Probability Share A

Returns

Share B

Returns

Share C

ReturnsBoom .40 10% 15% 20%

Bust .60 8% 4% 0%

a) What are the expected returns on the three shares? What are the standard

deviations of the three shares?

b) what is the expected return on an equally weighted portfolio of the three

shares?

SOLUTION QUESTION 3

a) ( ) ( ) 8.8%8%0.610%0.4AShareReturnExpected =+=

Share A

Economy Deviation

(Ri R*)

Squared Deviation

(Ri R*)2

Pi (Ri R*)2

Boom 1.2% 1.44 0.576

Bust -0.8% 0.64 0.384

0.96

0.96=

0.98%=

( ) ( ) 8%0%0.620%0.4CShareReturnExpected =+=

( ) ( ) 8.4%4%0.615%0.4BShareReturnExpected =+=


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Share B

Economy Deviation

(Ri R*)Squared Deviation

(Ri R*)2

Pi (Ri R*)2

Boom 6.6% 43.56 17.424Bust -4.4% 19.36 11.616

29.042=

29.04=

5.4%=

Share C

Economy Deviation

(Ri R*)Squared Deviation

(Ri R*)2

Pi (Ri R*)2

Boom 12% 144 57.6

Bust -8% 64 38.4

962 =

96=

9.8%=

b) Expected Return on equally weighted portfolio:

R*p = (1/3 x 8.8%) + (1/3 x 8.4%) + (1/3 x 8%)

= 8.4%


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Question 4

Assume you have obtained forecasts of the following data on three securities, (as

well as the market portfolio and the risk less asset) in a large and well-traded

securities market. Calculate the expected return and standard deviation of return

on the following portfolios? Which portfolio is preferable?

Portfolio X 40% A 0% B 60% C

Portfolio Y 20% A 30% B 50% C

F

Return SD A B C M

Correlation Matrix

Security A 0.09 0.24 1.0 0.4 0.5 0.6 0.0

Security B 0.10 0.18 0.4 1.0 0.8 0.7 0.0

Security C 0.06 0.15 0.5 0.8 1.0 0.8 0.0

Market

Portfolio(M)

0.15 0.12 0.6 0.7 0.8 1.0 0.0

RisklessAsset (F) 0.10 0.00 0.0 0.0 0.0 0.0 1.0


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SOLUTION QUESTION 4

a)

( ) ( ) ( )( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) %8.7078.006.05.01.03.009.02.0Re

%2.7072.006.06.01.00.009.04.0Re

==++=

==++=

y

X

turnExpected

turnExpected

b)

323,232

313,131

212,121

2

3

2

3

2

2

2

2

2

1

2

1

2

2

2

ww

ww

ww

www

p

+

+

+

++

=

( ) ( ) ( ) ( ) ( ) ( )

( )( )( )( )( )

( )( )( )( )( )

( )( )( )( )( )

%11.161611.0025956.0

15.018.08.06.00.02

15.024.05.06.04.02

18.024.04.00.04.02

15.06.018.00.024.04.0222222

===

+

+

+

++

=X

( ) ( ) ( ) ( ) ( ) ( )

( )( )( )( )( )

( )( )( )( )( )

( )( )( )( )( )

%17.151517.00229986.0

15.018.08.05.03.02

15.024.05.05.02.02

18.024.04.03.02.02

15.05.018.03.024.02.0222222

===

+

+

+

++

=Y

Which of the portfolios is preferable?

Portfolio Y has a higher return and a smaller standard deviation.

demo qs topic 5 part 1

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