Risk and Returns

This assignment consists of two parts.

Part 1

Part one requires qualitative explanations that display your understanding of the concepts of risk and return. You are required to answer the following questions by providing deeper insights about the concepts of risk and return.

Question 1 (10 marks)

Explain how the risk of shares can be calculated by the standard deviation. Your explanation should include the usage of the dispersion statistics, the normal distribution, and the probability, and how those concepts are utilized in real life finance.

Question 2 (20 marks)

Explain how adding new shares to a portfolio can affect the risk and return of that portfolio. You should use the concepts of correlation coefficient and the standard deviation in your explanations.

Question 3 (20 marks)

As you know, the risk of two assets is calculated by getting the square root of the equation:

Equation

Explain what would happen if one of the two assets was a risk-free asset. In other words, what would be the risk of the combination of the two assets? You have to explain that in accordance with the above equation.

Part 2 (50 marks)

Part two requires calculations to answer the questions. Furthermore, it requires qualitative explanations that convey your understanding of the concepts of risk and return of a portfolio. You are required to answer the following questions by providing deeper insights about the concepts of risk and return.

The table below gives information on three risky assets: A, B, and C.

AssetExpected returnStandard Deviation of the ReturnCorrelations
ABC
A102010.50.15
B15350.510.3
C20460.150.31

There is also a risk-free asset F whose expected return is 9.9 percent.

(i) Calculate the expected return and the standard deviation of Portfolio 1, which consists of 30 percent of Asset A and 70 percent of Asset B.

(ii) Calculate the expected return and the standard deviation of Portfolio 2, which consists of 50 percent of Asset A, 32.5 percent of Asset B, and 17.5 percent of Asset C.

(iii) Calculate the expected return and the standard deviation of Portfolio 3, which consists of 5 percent of Asset A, 75 percent of Asset B, and 20 percent of the Free Asset F.

(iv) Calculate the expected return and the standard deviation of Portfolio 4, which is equally weighted of the three risky assets A, B, and C.

(v) Calculate the expected return and the standard deviation of Portfolio 5, which is equally weighted of the four assets (i.e. A, B, C, and F).

(vi) Explain the differences in the risks and the returns between Portfolio 3, 4 and 5. Include the impact of the risk-free asset in your explanation.

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