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PORTFOLIO ANALYSIS AND INVESTMENT

QUESTION
Suppose that investor A holds a portfolio (portfolio A) consisting of five shares. The portfolio return is equal to 10% while its risk (st.dev) equals 12%. The market portfolio (consisting of all n shares) at this point of reference rewards investors with 15% and its risk is equal to 10%.
a) Is this portfolio (portfolio A) an efficient one? Explain.
(weight 10%)
b) Suppose that the risk free interest rate is 2%. What is the diversification benefit of another investor (investor B) who holds a perfectly diversified portfolio (portfolio B) that embeds the same level of risk with that of portfolio A (i.e. σΑ=σΒ=12%)? Explain.
(weight 25%)
c) How this portfolio (portfolio B) can be constructed? Explain.
(weight 25%)

d) How does the existence of the risk free interest rate affect the optimum portfolio construction? Explain.
(weight 40%)

QUESTION
Suppose that you are investigating two mutual exclusive investments (investment A and B) which correspond to two listed firms A and B, respectively. The NCFs of these investments are the following:
t0 t1 t2 t3
A (10,000) 11,500 200 100
B (10,000) 0 0 14,000

The risk free interest rate is 2% and the market portfolio return is 7%.

a) If the beta coefficient (systematic risk) for firm A and B is equal to 0.5 (i.e. bA=bB=0.5) which investment would you proceed with according to the Net Present Value (NPV) and the Internal Rate of Return (IRR) investment appraisal techniques? Is there any difference in the decisions made, based on the NPV and the IRR criteria? Explain.
(60%)
b) If the beta coefficient (systematic risk) for firm A and B is equal to 1.65 (i.e. bA=bB=0.5) which investment would you proceed with according to the Net Present Value (NPV) and the Internal Rate of Return (IRR) investment appraisal techniques? Is there any difference in the decisions made, based on the NPV and the IRR criteria? Explain.
(40%)
QUESTION
Suppose that you consider the consumption preferences of an investor with initial endowment equal to 30,000$. The preferences of this investor are characterized by the following indifference curve: the slope of which is equal to:
dc1/dc0 = – c1/c0.
Moreover, the available investment opportunity set is expressed through the following equation: c1 = g(c0) = 300 (30,000 – c0)1/2
The risk free interest rate is equal to 10%.
a) Which is the optimal financing decision? (40%)
b) What are the implications of your findings for modern portfolio theory and, specifically, how your findings are related to the separation fund theorem in portfolio theory? (60%)
Explain your answer analytically.

QUESTION
Suppose that there exist two securities (A and B) with an annual expected return equal to rA = 3% and rB 6% and a standard deviation of the returns equal to σΑ = 5% and σΒ = 7%, respectively. Moreover, the correlation coefficient between the returns of these securities is ρ = -0.8.

a. What is the risk-return profile (i.e. expected return and standard deviation) of an equal-weighted portfolio consisting of these two securities? (20%)

b. What is the risk-return profile of a portfolio consisting of these two securities with the minimum variance? (20%)

c. What is the risk-return profile of a value-weighted portfolio consisting of these two securities if you hold 10 shares of the A and 10 shares of the B security? The first security is traded at 50$ while the second at 75$. (30%)

d. How does the number of the securities of a portfolio affect its risk-return trade-off? Please explain your answer analytically. (30%)
Explain your answers analytically.

QUESTION
Suppose that you investigate the case of two mutual exclusive investments, investment A and investment B, the Net Cash Flows of which are given below:
t0 t1 t2 t3
A (10,000) 4,000 4,000 10,000
B (50,000) 15,000 15,000 40,000

The risk free interest rate is equal to 2% while the market portfolio yields 7% on an annual basis.

a. Suppose that these investments refer to a firm the systematic risk factor of which (i.e. beta coefficient) is equal to 0.5. Which investment would you choose according to the Net Present Value (NPV) and the Internal Rate of Return (IRR) investment appraisal techniques? Is there any difference in the decisions made, based on the NPV and the IRR criteria? Why?
(30%)

b. Suppose that after a careful consideration of the firm under investigation you revise your expectation about the systematic risk factor from 0.5 to 2.4. (i.e. beta coefficient is equal to 2.4). Which investment would you choose according to the NPV and the IRR investment appraisal techniques? Is there any difference in the decisions made, based on the NPV and the IRR criteria? Why?
(30%)

c. Please explain in detail the role of the beta coefficient in your investment decisions of the previous sub-questions. (40%)
Explain your answers analytically.

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