- (50 points) Complete “Homework #4: 50%” on MyFinanceLab under “Assignments.” Students can try each question up to three times. Excel may be used to solve some of the problems (e.g., you may use Excel to find standard deviation of stock returns.)
- (30 points) Jane Warren is considering building a portfolio containing two assets, L and M. Asset L will represent 40% of the dollar value of the portfolio, and asset M will account for the other 60%. The expected returns over the next 6 years, 2012-2017, for each of these assets, are shown in the following table. (Please use the Excel template posted on Canvas under “AssignmentsàHW4àHW4 Excel Example and Template.” An example can be found in the same Excel document.)
Expected Return | ||
Year | Asset L | Asset M |
2012 | 14% | 20% |
2013 | 14 | 18 |
2014 | 16 | 16 |
2015 | 17 | 14 |
2016 | 17 | 12 |
2017 | 19 | 10 |
- Calculate the expected portfolio return, k_{p}, for each of the 6 years.
Solution
This is calculated using the following formula;
Where W is the weighted value of the item and R is its return in percentage.
In order to calculate the expected return () for every year, weighted value and its return of the Asset are replaced in the equation
- Calculate the expected value of portfolio return, , over the 6-year period.
Solution
can be calculated using the following formula,
In order to calculate, we insert the values given in the table.
- Calculate the standard deviation of expected portfolio returns, ,over the 6-year period.
Solution
can be calculated using the following formula;
Where x is the value of the asset in the year, is the mean value and N is the number of variables (years in this case)
- How would you characterize the correlation of returns of the two assets L and M?
Assets L and M negatively correlate, as it can be seen from the fact when asset L has the highest return of 19% asset M has the lowest return of 10%. In the same way, when asset M has the highest return rate of 20%, asset L yields the lowest return rate of 14%.
- Discuss any benefits of diversification achieved through creation of the portfolio.
The following are benefits of diversification;
Solution
- Risk Reduction. This is because an investor can diversify assets among classes making it less exposed to stock market risk.
- Capital Preservation. This allows an investor to protect the capital he or she has instead of focusing on the rate of return for the investment
- It allows one to hedge portfolio. This is because diversification allows one to have portfolio grow both in a case when the market boom and the return crumble in one sector.
- (20 points) Use the basic equation for the capital asset pricing model (CAPM) to work each of the following problems.
Solution
CAPM basic equation is given as
Where;
- A stock has a beta of 1.2, the expected return on the market is 14 percent, and the risk-free rate is 5.2 percent. What must the expected return on this stock be?
Solution
Using the CAPM equation.
But we have , and
- A stock has an expected return of 13 percent, the risk-free rate is 4.5 percent, and the market risk premium is 7 percent. What must the beta of this stock be?
Solution
- A stock has an expected return of 12 percent, its beta is .70, and the risk-free rate is 5.5 percent. What must the expected return on the market be?
Solution
- A stock has an expected return of 15 percent, its beta is 1.45, and the expected return on the market is 12 percent. What must be risk-free rate be?
Solution