1. Sydney Company has made a portfolio of these three securities:
|
Security
|
Cost
|
E(R)
|
σ(R)
|
|
Treasury bond
|
$70,000
|
5%
|
0
|
|
Gold Coast Corporation
|
$60,000
|
15%
|
30%
|
|
Tweed Company
|
$30,000
|
17%
|
35%
|
The correlation coefficient between Gold Coast and Tweed is 0.5. If the returns are normally distributed, find the probability that the return of the portfolio is more than 17%.
2. Suppose you have $20,000 that you want to invest in two companies, Melbourne Oil Company and Brisbane Aluminum. Melbourne has a return of 12% and standard deviation 25%, while Brisbane has return of 16% with a standard deviation of 32%. The correlation coefficient between them is 40%. Your portfolio should have a return of 13%.
(A) Find the amount invested in each of the two companies.
(B) Find the standard deviation of this portfolio's returns.
3. Perth Corporation preferred stock sells for $51.25 a share and pays an annual dividend of $5. The β of this stock is 1.3. The current riskless rate is 3%. The common stock of Perth was downgraded by the analysts from ‘buy' to ‘hold' today. In response to the news, the preferred stock dropped in price by $1.25. Find the new β of Perth preferred.
4. The Adelaide Corp stock has a β of 1.55 and it will pay a dividend of $1.65 next year. The expected rate of return of the market is 12% and the current riskless rate is 5%. The expected rate of growth of Adelaide is 5%. Find the value of its common stock.
5. Newcastle Company has β = .8, whereas the return on the market is expected to be 12%, with a standard deviation of 10%. The riskless rate is 3% at present. The stock of Newcastle is selling at $100 a share, but it does not pay any dividends. Find the probability that it will be selling for more than $115 by next year. Assume that the entire change in the stock price is due to the change in the market, that is, the correlation coefficient between the market and Newcastle Company is 1.
6. Canberra Company has the same growth rate as Cairns Corp. The current stock price of Canberra is $50 a share, and its dividend this year is $3. The riskless rate is 4% and the expected return on the market is 12%. Cairns Corp stock is selling at $30 a share. Its dividend next year will be $2 a share and its β is 1.6. Find the β of Canberra stock.
7. Woolongong Metals Corporation has β = 1.3. It is interested in buying Hobart Fasteners Corporation which has β = 1.2. Woolongong believes that after the acquisition, its β will become 1.25. The expected after-tax earnings from Hobart will be $3.5 million for the first year, but this figure is expected to increase by 3% per year in future. The expected return on the market is 10%, and the riskless rate is 4%. Find the amount that Woolongong should spend on this acquisition.
8. Calculate the β of Darwin Corporation from the following data.
|
Year
|
Price of
Darwin stock
|
Dividend
per share
|
S&P 500
index
|
S&P 500
dividend
|
Riskless
rate
|
|
beginning
|
end
|
beginning
|
end
|
|
2010
|
$55
|
$60
|
$2.00
|
1000
|
1050
|
3.05%
|
2.00%
|
|
2011
|
60
|
70
|
$2.00
|
1050
|
1100
|
3.20%
|
2.50%
|
|
2012
|
70
|
90
|
$3.00
|
1100
|
1300
|
3.50%
|
3.50%
|
|
2013
|
90
|
120
|
$3.00
|
1300
|
1400
|
3.00%
|
4.00%
|