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1) You bought a stock one year ago for $50 per share and sold it today for $55 per share
1) You bought a stock one year ago for $50 per share and sold it today for $55 per share. It paid a $1 per share dividend today. a. What was your realized return? b. How much of the return came from dividend yield? c. How much came from capital gain?
2) The table below shows the one-year return distribution for RCS stock.
10% 20% 15% 25% 30% Probability Return -25% -10% 0% 10% 25% Calculate
a. The expected return. b. The standard deviation of the return. (round to the nearest tenth of a percent
3) The last four years of returns for a stock are as follows:
Year 1 2 3 4 Return -4% 28% 12% 4%
a. What is the average annual return? b. What is the variance of the stock's returns? (Round to the nearest .001) c. What is the standard deviation of the stock's returns? (Round to the nearest tenth)
4) You own three stocks: 600 shares of Apple Computer, 10,000 shares of Cisco Systems, and 5000 shares of Colgate-Palmolive. The current share prices and expected returns of Apple, Cisco, and Colgate-Palmolive are, respectively, $500, $20, $100 and 12%, 10%, 8%.
a. What is the portfolio weights of Apple in your portfolio? (Round to the nearest tenth) b. What is the expected return of your portfolio? (Round to the nearest tenth) c. Suppose the price of Apple stock goes up by $25, Cisco rises by $5, and Colgate-Palmolive falls by $13. What are the new portfolio weight of Cisco in your portfolio? CiscoURound to the nearest tenth) d. Assuming the stocks' expected returns remain the same, what is the expected return of the portfolio at the new prices? (Round to the nearest tenth)
Expert Solution
1)
a) Computation of Realized Return:
Realized Return = (Sales Price - Purchase Price + Dividend)/Purchase Price
= ($55 - $50 + $1)/$50
Realized Return = $6/$50 = 12.00%
b) Computation of Dividend Yield:
Dividend Yield = Annual Dividend/Purchase Price
= $1/$50
Dividend Yield = 2.00%
c) Computation of Capital Gain Yield:
Capital Gain Yield = (Sales Price - Purchase Price)/Purchase Price
= ($55 - $50)/$50
Capital Gain Yield = 10.00%
2)
| a) Computation of Expected Return: | |||||||||
| Expected Return | = | Sum of (Probability*Return on Probability) | |||||||
| Expected Return | = | (10%*-25%)+(20%*-10%)+(15%*0%)+(25%*10%)+(30%*25%) | |||||||
| = | 5.500% | ||||||||
| b) Computation of Standard Deviation: | |||||||||
| Standard Deviation | = | Variance of return ^(1/2) | |||||||
| Step-1: | Calculate Variance: | ||||||||
| a | b | c | d=b-c | e=D^2 | f=e*a | ||||
| Probability | Return | Expected Return | |||||||
| 10% | -25% | 5.50% | -30.50% | 9.30% | 0.93% | ||||
| 20% | -10% | 5.50% | -15.50% | 2.40% | 0.48% | ||||
| 15% | 0% | 5.50% | -5.50% | 0.30% | 0.05% | ||||
| 25% | 10% | 5.50% | 4.50% | 0.20% | 0.05% | ||||
| 30% | 25% | 5.50% | 19.50% | 3.80% | 1.14% | ||||
| Variance | 2.65% | ||||||||
| Step-2:Calculate Standard Deviation | |||||||||
| Standard Deviation | = | Variance of return ^(1/2) | |||||||
| = | 2.65%^(1/2) | ||||||||
| = | 16.27% | ||||||||
3)
a) Computation of Average Annual Return:
Average Annual Return =Total Return/Total Number of Periods
= (-4%+28%+12%+4%)/4
Average Annual Return = 10%
b) Computation of Variance of Stock Returns:
Variance of Stock Returns = Total (Return-Average Return)^2/(Time Period-1)
Here,
| Return | (Return-Average Return)^2 |
| -4 | (-4%-10%)^2=0.0196 |
| 28 | (28%-10%)^2=0.0324 |
| 12 | (12%-10%)^2=0.0004 |
| 4 | (4%-10%)^2=0.0036 |
| Total = 0.056 |
Variance of Stock Returns = 0.056/(4-1)
=0.056/3
Variance of Stock Returns = 0.01867
c) Computation of Standard Deviation:
Standard Deviation = Variance^(1/2)
= 0.01867^(1/2)
Standard Deviation = 0.1366 or 13.66%
4)
(a) Computation of Portfolio Weights of Apple in Portfolio:
Investment in Apple = Number of Shares * Share Price
= 600*$500
Investment in Apple = $300,000
Investment in Cisco = 10,000*$20=$200,000
Investment in Colgate = 5000*$100=$500,000
Total Investment = 300,000+200,000+500,000 = $1,000,000
Weight of Apple = Investment in Apple / Total investment
= 300000/$1,000,000
= 0.3 or 30%
Weight of Cisco= Investment in Cisco / Total investment
= 200000/$1,000,000
= 0.2 or 20%
Weight of Colgate = Investment in Colgate / Total investment
= 500000/$1,000,000
= 0.5 or 50%
(b) Computation of Expected Return of Portfolio:
Expected Return of Portfolio = Weight of Apple * Expected Return of Apple + Weight of Cisco*Expected Return of Cisco + Weight of Colgate * Expected Return of Colgate
=(0.3*12%)+(0.2*10%)+(0.5*8%)
Expected Return of Portfolio = 9.60%
(c) Computation of Weights of Portfolio at New Prices:
Investment in apple when price goes up =600*(500+25)=$315,000
Investment in Cisco=10,000*(20+5)=$250,000
Investment in Colgate =5000*(100-13)=$435,000
Total Investment= 315,000+250,000+435,000=$1,000,000
Weight of Apple = 315,000/$1,000,000=31.50%
Weight of Cisco=250,000/$1,000,000=25%
Weight of Colgate = 435000/$1,000,000=43.50%
(d) Computation of Expected Return of portfolio at New Prices:
Expected Return of portfolio at New Prices = (0.3150*12%)+(0.25*10%)+(0.4350*8%) = 11.61%
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