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#2. In the data below, there are 4 stocks with returns over 10 days.

Day	Stock 1	Stock 2	Stock 3	Stock 4
1	12.00%	4.40%	-2.20%	2.40%
2	-1.70%	-1.30%	4.80%	-1.10%
3	10.70%	11.00%	5.70%	-1.60%
4	-2.60%	11.10%	9.50%	3.30%
5	-4.50%	3.70%	4.60%	-2.60%
6	16.60%	-1.40%	6.30%	-3.80%
7	-5.50%	-4.70%	-4.80%	4.90%
8	-3.00%	14.30%	-6.10%	6.90%
9	12.20%	-7.70%	5.10%	-2.00%
10	1.20%	2.40%	-2.30%	6.60%

(a) (Risk measure) Assume that you have $100. You invest $10 in stock 1, $20 in stock 2, $30 in stock 3, and $40 in stock 4. Find the portfolio expected return and standard deviation.

(b) (Risk profiling and asset allocation) After conducting a risk-profiling survey, your client is likely to be moderately conservative in terms of risk tolerance. According to your portfolio theory analysis, you plan to recommend a stock portfolio with a return of 2.5%~3.0% and a standard deviation of 3.5%~4.5%. Construct a stock portfolio that meets the conditions.

Note: Assuming that you can use only the proposed stocks (stock 1 to 4) above. There could be more than one answer, but it is okay to propose only one.

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