This question is worth 10 marks in total. This is a written calculation question, and you should perform the necessary calculations/working on paper to later be scanned and uploaded. Start a new page for this question. For dollar amounts, give your answer to the nearest cent. For interest rates, give our answer as a percentage rounded to 2 decimal places.

If any parts of the question use values from earlier parts, use the EXACT values from earlier parts.

QUESTION START

An investor buys 1 share of ABC Ltd at the price of $30 on December 1, 2021. The firm is not expected to pay any dividends. Consider the following four possible scenarios for the share price on December 1, 2021

• $50 with a probability of 15%

• $34 with a probability of 55%

• $27 with a probability of 20%

• $20 with a probability of 10%

a) Calculate the expected return for holding the share for a year. (2 marks)

b) Calculate the variance of return and standard deviation of return. (3 marks)

c) On December 1, 2021, it turns out that the share is worth $37, and the investor also just received a dividend of $4. Calculate the total holding period return and capital gains return over the one-year period. (2 marks)

d) Discuss a benefit of portfolio diversification. Explain how to achieve this benefit. (2 marks)

e) The standard deviation of a portfolio's return can be reduced to zero by holding all the securities in the market. True or false? Explain. (1 mark)