CORPORATE FINANCE HW
LIZZZ33
corpfinace-2.docxQuestions
1. Using the information given in Exhibit 1, calculate the historical returns for each company and the market index. With the use of the excel functions calculate the average monthly return and standard deviation of returns for each company and the market index.
|
Returns |
|||
|
Market index |
Excalibur Ltd ($) |
Wizard Ltd |
Knight |
|
214% |
465% |
-400% |
1125% |
|
157% |
593% |
-625% |
-2154% |
|
224% |
-420% |
-333% |
-2482% |
|
-126% |
146% |
460% |
1492% |
|
-165% |
432% |
549% |
1989% |
|
428% |
486% |
-312% |
645% |
|
200% |
-789% |
-430% |
2143% |
|
-106% |
354% |
899% |
2888% |
|
214% |
414% |
515% |
470% |
|
234% |
201% |
-539% |
-3686% |
|
-323% |
-909% |
829% |
-439% |
|
171% |
354% |
-383% |
853% |
|
312% |
486% |
-498% |
907% |
|
186% |
132% |
-524% |
-296% |
|
-259% |
130% |
773% |
-857% |
|
-282% |
256% |
821% |
2771% |
|
266% |
525% |
-427% |
1468% |
|
180% |
451% |
-396% |
1607% |
|
169% |
227% |
-258% |
466% |
|
-167% |
-267% |
529% |
-738% |
|
-162% |
-731% |
503% |
-822% |
|
180% |
690% |
526% |
992% |
|
238% |
553% |
318% |
1153% |
|
173% |
524% |
352% |
528% |
|
|
|
Market Index |
Excalibur Ltd |
Wizard Ltd |
Knight Ltd |
|
Mean (Expected) Return |
0.82 |
1.79 |
0.81 |
4.18 |
|
|
Standard Deviation |
2.14 |
4.59 |
5.41 |
16.18 |
2. Using your answers to Question 1, above, and assuming that investors can only invest in one of the three alternatives in Exhibit 1, use the average return and standard deviation to determine which share would be the most appropriate for a risk-averse investor. Provide numerical justification for your selection.
Based on the data collected, the share that would be most appropriate for a risk-averse investor (a risk averse investor is an investor who prefers lower returns with known risks rather than higher returns with unknown risks), would be Excalibur Ltd. It has an expected return of 1.79 which is what the expected return is to be in the next period as the average. The standard deviation is a measure of risk and tells us how far from the average the return in any particular year is likely to be. For Excalibur Ltd, the standard deviation is 4.59 which is the lowest risk from all 3 shares. Excalibur Ltd is the best option as the higher the standard deviation, the further away the mean is which leads to a higher risk and that share is the least furthest away from the mean compare to the others.
3. Calculate the covariance of returns and correlation coefficients between all shares. Provide an explanation of your results and the implications for diversification.
|
|
|
Market Index |
Excalibur Ltd |
Wizard Ltd |
Knight Ltd |
|
Coefficient of variation |
2.63 |
2.56 |
6.66 |
3.87 |
|
Correlation Coefficien |
|
Excalibur Ltd |
Wizrd Ltd |
Knight |
|
|
|
|
Excalibur Ltd ($) |
1 |
|
|
|
|
|
Wizrd Ltd |
-0.172446046 |
1 |
|
|
|
|
Knight |
0.255232639 |
0.29312374 |
1 |
The correlation measures how returns move in relation to each other. Correlation is a standardized measure ranging from -1 to +1. When a correlation is closer to 1 that indicates a perfectly positive correlation which is bad in terms of risk reduction because if one return increases so does the other. However, a figure close to -1 indicated a perfectly negative correlated which is good in terms of risk reduction because as one companies returns increase, the other companies returns decrease. that Independent risks have no tendency to move together and have zero correlation. But there is a considerable difference between above company's correlations. That is Wizard is more correlated with the Knight than with Excalibur. (Refer below illustration).
4. Determine the expected return and standard deviation of a two-asset portfolios comprised of Excalibur and Wizard; Excalibur and Knight; and Wizard and Knight. Assume equal weightings of each share within each portfolio. Interpret your results and comment and illustrate the impact on risk when combining shares into a portfolio.
|
|
|
|
Correlation With |
|
|
|
Weight |
Volatility |
Excalibur Ltd |
Wizard Ltd |
|
Excalibur Ltd |
0.50 |
4.59 |
1 |
|
|
Wizrd Ltd |
0.50 |
5.41 |
-0.1724 |
|
|
|
|
|
|
|
|
Excalibur Ltd ($) |
0.50 |
4.59 |
1 |
|
|
Knight |
0.50 |
16.18 |
0.2552 |
|
|
|
|
|
|
|
|
Wizard Ltd |
0.50 |
5.41 |
|
1 |
|
Knight Ltd |
0.50 |
16.18 |
|
0.02931 |
The weights, standard deviations and correlation of the two shares are needed to compute the variance and then the standard deviations of the portfolio. (Berk et al. 2014)
The correlation with Excalibur Ltd and Wizard Ltd is shown to be -0.1724, the correlation with Excalibur Ltd and knight is shown to be 0.2552 and the correlation with Wizard Ltd and Knight Ltd is shown to be 0.0293. When combining shares in a portfolio risk can be reduced and are less volatile than the shares individually.
5. Determine the expected return and standard deviation of a three-asset portfolio comprising all three shares. Assume equal weightings of each share within the portfolio. Why is the computation more complex than a portfolio comprising of only two shares? Is this portfolio more efficient than the portfolios constructed in question 5? Provide numerical evidence to support your answer.
6. Determine the systematic risk (Beta) of all three shares. Interpret your answers. The use of excel functions is acceptable to calculate Beta.
|
Beta Coefficient |
Excalibur Ltd |
Wizard Ltd |
Knight Ltd |
|
|
|
|
0.95 |
-0.20 |
-0.79 |
