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In an economy, there are

[ANSWER ALL QUESTIONS, TOTAL 100 MARKS]

QUESTION 1

In an economy, there are three assets available for investment, a risk-free asset F and two risky assets, A and B. The expected returns on the assets are given by μF = 3, μA = 6 and μB = 12 respectively, while the standard deviations of the returns for the risky assets are given by and respectively. The two risky assets are perfectly positively correlated. Assume that, short-selling is not allowed. Consider a portfolio, P, formed by investing equally in the three assets A, B and F.

(a) Determine the expected value and standard deviation of the return on portfolio P.

[4 marks]

(b) For each pair of assets, i.e. AB, AF and BF separately, obtain the equations on the space which denote the portfolios formed form each pair of assets.

[12 marks]

(c) Draw and label the graph of the opportunity set on the space, showing the positions of assets A, B, F, P and the efficient frontier on the graph.

[6 marks]

(d) Construct a portfolio, which has the maximum expected return but the same standard deviation as portfolio P.

[4 marks]

(e) Construct a portfolio, which has the minimum standard deviation but the same expected return as portfolio P.

[4 marks]

[Total 30 marks]

QUESTION 2

  1. Critically discuss and explain the role of heuristics in Behavioural Finance, recent relevant development in the psychology literature and investors’ financial decision making.

[10 marks]

  1. The Efficient Market Hypothesis (EMH) has failed to explain many phenomena in the financial markets even though it dominated the financial literature for more than 30 years. Critically discuss this statement and use examples to explain your argument.

[10 marks]

[Total: 20 marks]

QUESTION 3

You are given the following monthly return data on three companies within a broad stock market, and the returns on the market index:

Month

A

B

C

Index

1

12.05

25.20

31.67

12.28

2

15.27

2.86

15.82

5.99

3

-4.12

5.45

10.58

2.41

4

1.57

4.56

-14.43

4.48

5

3.16

3.72

31.98

4.41

6

-2.79

10.79

-0.72

4.43

7

-8.97

5.38

-19.64

-6.77

8

-1.18

-2.97

-10.00

-2.11

9

1.07

1.52

-11.51

3.46

10

12.75

10.75

5.63

6.16

11

7.48

3.79

-4.67

2.47

12

-0.94

1.32

7.94

-1.15

Calculate the following quantities, assuming returns can be modelled using a single index market model: R(it) = alpha(i) + beta(i)*R(mt) + e(t). Where R(it) denotes the return of stock i at time t, R(mt) denotes the return on the market at time t and e(t) represent the error at time t.

  1. the alpha of each stock [3 marks]

  2. the beta of each stock [3 marks]

  3. the standard deviation of the residuals from each regression [3 marks]

  4. the correlation coefficient between the returns on each security and the return on the market [8 marks]

  5. the average return on the market [1 marks]

  6. the standard deviation of return on the market [2 marks]

[Total: 20 marks]

QUESTION 4

The following industry index model has been suggested to model the rates of return on banks and oil companies. You may assume that the indices are orthogonal.

Ri = ai + biMIM + biBIB + biOIO + ci

The banks A and B, and the oil companies C and D have the following parameters in this model:

Month

A

B

C

D

1

2

3

3

1.2

0.9

0.5

0.4

0.9

1.1

0

0

0

0

0.8

1.3

1

1

8

3

Note – ai has units %, and σci2 has units %%.

  1. You are given that the market has an expected rate of return of 10% and variance of 15%%. The banking index IB has mean −2 % and variance 3%%. The oil index IO has mean 5% and variance 14%%.

  1. Calculate the mean of the rate of return on each of these four assets. [8 marks]

  2. Calculate the variance of the rate of return on each of these four assets. [8 marks]

  3. Calculate the covariance of the rates of return between pairs of assets. [8 marks]

  1. A portfolio has 30% invested in each bank, and 20% invested in each oil company. What is the mean and variance of the rate of return on this portfolio? [6 marks]

[Total: 30 marks]

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