Q:1 Consider a market consisting of only two assets A and B. There are 100 shares of asset A in the market sold at a price per share of £1.00. There are 100 shares of asset B in the market with a price of £2.00 per share. Asset A and asset B have an average return of 10% and 6% respectively. The risk-free is 5%. The standard deviation on the market portfolio is σm = 20%. Assume that the market satisfies the CAPM exactly.
1- What is the expected return on the market portfolio?
2- Calculate the β of asset A and asset B?
3- An investment opportunity in this market offers average return of 6% with standard deviation of 19%. Would your portfolio be efficient if you invested all the funds in this opportunity? Explain your answer.
Q2: Suppose you consider investing in a fund that invests 20% of its funds in the risk-free asset at a rate of 6% and the remaining 80% in a portfolio with a β = 0.9 and an expected return of 25%. The market has been returning an average of 26%. Today's price of one share of the fund is £100.
-what is the fair price of one share according to CAPM?
Q3: Suppose that the expected return and standard deviation of the market portfolio are 11% and 20% respectively. The expected return of security 1 is 6%. The expected return of security 2 is 10%and its standard deviation is 18%. An equally-weighted portfolio that invests half its value in security 1 and half in security 2 has a β = 0.5
- What is the specific risk of security 2 according to CAPM?
Q4: In a CAPM market the expected return on the market portfolio is 20% and the risk-free rate is 7%. The market portfolio has a standard deviation of 40%.
- If you wish to have an expected return of 30% what standard deviation should you be willing to tolerate?
- How would you attempt to achieve this value if you have $100,000 to invest?