Question
Problem Six (15 marks) You work for a small investment management firm. You have been provided with the following historical information for three stocks and
Problem Six (15 marks)
You work for a small investment management firm. You have been provided with the following historical information for three stocks and the market index. The information is shown in the table below.
| AAA Inc. | BBB Inc. | CCC Inc. |
| |||
| Stock Price | Dividend | Stock Price | Dividend | Stock Price | Dividend | Market Index |
2012 | $33 |
| $110 |
| $170 |
| 20,840 |
2013 | $41 | $1.40 | $120 | $1.40 | $155 | $3.50 | 23,320 |
2014 | $45 | $1.40 | $98 | $1.55 | $165 | $3.60 | 22,220 |
2015 | $50 | $1.70 | $115 | $1.65 | $180 | $3.65 | 25,325 |
2016 | $42 | $1.85 | $140 | $1.75 | $175 | $3.65 | 21,520 |
2017 | $52 | $1.85 | $150 | $1.90 | $195 | $3.75 | 26,100 |
2018 | $60 | $1.90 | $120 | $2.00 | $201 | $3.80 | 27,500 |
2019 | $75 | $2.00 | $140 | $3.20 | $222 | $4.33 | 31,020 |
Using the data provided you are to calculate the following for each of the stocks and the market index.
- What is the average annual return for the past seven years?
- What is the geometric average annual return (effective annual rate of return) for the past seven years?
- What is the population standard deviation and the sample standard deviation?
- What is the correlation coefficient between Stocks AAA and BBB? Between Stocks AAA and CCC? Between Stocks BBB and CCC?
- What is the sample covariance between Stocks AAA and BBB, between Stocks AAA and CCC and between stocks BBB and CCC?
- What is the coefficient of variation for each of the stocks and the market index? You should use the sample standard deviation.
- What is the beta of each of the stocks? You can use Excels slope function to estimate this.
- Assume that the beta of stock AAA is 0.60, the beta of stock BBB is 1.1 and the beta of stock CCC is 1.9. What is the beta of a portfolio where the weight in stock AAA is 30% the weight in stock BBB is 50% and the weight in stock CCC is 20%?
- Assuming the risk-free rate is 2.56% and the expected return on the market is 6.21% what is the expected return on the portfolio in part (h) above?
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