Question

Question 4(14 marks)

1. What is the risk premium of a zero-beta stock?Does this mean you can lower the volatility of a portfolio without changing the expected return by substituting out any zero-beta stock in a portfolio and replacing it with the risk-free asset?                                     (4 marks)

2. Assume all investors want to hold a portfolio that, for a given level of volatility, has the maximum possible expected return. Explain why, when a risk-free asset exists, all investors will choose to hold the same portfolio of risky stocks. (3 marks)

3. Consider the following two independent projects:

Project	Year 0 Cash Flow	Year 1 Cash Flow	Year 2 Cash Flow	Year 3 Cash Flow	Year 4 Cash Flow	Discount Rate
A	90	40	-20	60	-20	16%
B	-80	40	40	30	30	16%

Without doing any calculation, explain why the above two projects canor cannotbe evaluated using the IRR Rule. (3 marks)

4. Suppose ABC and XYZ have volatilities of 25% and 50% respectively and they are perfectly negatively correlated. What portfolio of these two stocks has a zero risk? Show all your calculations. (4 marks)

Answer 1

Answer to Question-1:

Risk premium of zero beta stock : Risk premium in case of a zero beta stock will be zero. It indicates that the stock is uncorrelated with the market. There will be no increase in the risk of the portfolio by adding this stock to the portfolio.

Lower volatility of portfolio without changing expected return: If beta is zero it is uncorrelated with the market but will be positively correlated with itself which also for a part of the market. Market consist of all the stocks and portfolios, therefore this uncorrelated stock will also be a part of market. In order to have zero beta this stock must be negatively correlated with some or the other stock in the market. With this relationship only the risk can be made to zero, therefore taking this stock out will not reduce the risk also.

Answer to Question-2: