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Question 5 The following are the annual returns for Large Co. and Small Co. as well...
Question 5
The following are the annual returns for Large Co. and Small Co. as well as for the market, for the last 10 years.
Annual returns (%)
Year Large Small Market
1 13.00 15.00 6.00
2 8.00 16.00 5.00
3 1.00 4.00 4.00
4 8.00 2.00 5.00
5 9.00 12.00 8.00
6 6.00 10.00 7.00
7 12.00 8.00 9.00
8 8.00 -2.00 8.00
9 12.00 12.00 10.00
10 5.00 16.00 8.00
Calculate the following:
a. Average annual rate of return for Large, Small and the market
b. Standard deviation of the rate of return for Large, Small and the market
c. Plot Large Co, Small Co and the market on a risk / return graph. Which asset or combination of asset would you invest in? Why?
Question 6
Assume the long term Government bond rate is 4.1%.
a. If the BetaLARGE CO = 1, and the BetaSMALL CO = 0.44, construct the Security Market Line (SML) plotting Large Co, Small Co and the market
b. The expected returns for Large and Small are 5.4% and 9.3%, respectively; plot these returns on the same graph as in (a)
c. Consider each company, would you recommend an investor
to:
- buy shares in either company;
- sell shares in either company; or
- be indifferent between the shares of both companies?
Justify your recommendations
d. How does the measure of risk used in Question 6 differ from the measure of risk used in Question 5?
Solutions
Expert Solution
| Annual Return (%) | Deviation from Average | DEVIATION SQUARED | ||||||||||
| R1 | R2 | R3 | D1=R1-8.2 | D2=R2-9.3 | D3=R3-7.0 | E1=D1^2 | E2=D2^2 | E3=D3^2 | ||||
| Year | Large | Small | Market | Large | Small | Market | Large | Small | Market | |||
| 1 | 13 | 15 | 6 | 4.8 | 5.7 | -1 | 23.04 | 32.49 | 1 | |||
| 2 | 8 | 16 | 5 | -0.2 | 6.7 | -2 | 0.04 | 44.89 | 4 | |||
| 3 | 1 | 4 | 4 | -7.2 | -5.3 | -3 | 51.84 | 28.09 | 9 | |||
| 4 | 8 | 2 | 5 | -0.2 | -7.3 | -2 | 0.04 | 53.29 | 4 | |||
| 5 | 9 | 12 | 8 | 0.8 | 2.7 | 1 | 0.64 | 7.29 | 1 | |||
| 6 | 6 | 10 | 7 | -2.2 | 0.7 | 0 | 4.84 | 0.49 | 0 | |||
| 7 | 12 | 8 | 9 | 3.8 | -1.3 | 2 | 14.44 | 1.69 | 4 | |||
| 8 | 8 | -2 | 8 | -0.2 | -11.3 | 1 | 0.04 | 127.69 | 1 | |||
| 9 | 12 | 12 | 10 | 3.8 | 2.7 | 3 | 14.44 | 7.29 | 9 | |||
| 10 | 5 | 16 | 8 | -3.2 | 6.7 | 1 | 10.24 | 44.89 | 1 | |||
| SUM | 82 | 93 | 70 | SUM | 119.6 | 348.1 | 34 | |||||
| a | Average Annual Return=(Sum of Returns)/Number of Annual Periods | |||||||||||
| Average Annual Return of Large =82/10= | 8.20% | |||||||||||
| Average Annual Return of Small=93/10= | 9.30% | |||||||||||
| Average Annual Return of Market =70/10= | 7.00% | |||||||||||
| b | Variance =SUM of (Deviation of return fromAverage Squared)/(Number of Annual Periods-1) | |||||||||||
| Standard Deviation =Square Root(Variance) | ||||||||||||
| Variance of Return of Large =119.6/(10-1)= | 13.2888889 | %% | ||||||||||
| Variance of Return of Small=348.1/(10-1)= | 38.6777778 | %% | ||||||||||
| Variance of Return of Market =34/(10-1)= | 3.77777778 | %% | ||||||||||
| Standard Deviation of Return of Large | 3.65% | SQRT(13.288889) | ||||||||||
| Standard Deviation of Return of Small= | 6.22% | SQRT(38.6777778) | ||||||||||
| Standard Deviation of Return of Market | 1.94% | SQRT(3.77777778) | ||||||||||
| c | Risk | Return | Return/Risk | |||||||||
| Market | 1.94% | 7.00% | 3.60 | |||||||||
| Large | 3.65% | 8.20% | 2.25 | |||||||||
| Small | 6.22% | 9.30% | 1.50 | |||||||||
| With the data available, investment in market is preferred |
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