The following table shows historical end-of-week adjusted close prices (including dividends) for a stock and the S&P 500.

	A	B	C
1	Week	Stock	S&P 500
2	0	39.53	2,758
3	1	40.17	2,700
4	2	43.1	2,742
5	3	42.47	2,783
6	4	39.77	2,836
7	5	42.07	2,762
8	6	43.84	2,829
9	7	39.77	2,768
10	8	40.1	2,866
11	9	40.98	3,019
12	10	42.15	2,982

2. What is the geometric average weekly return for the S&P 500?

3. What is the annualized return for the S&P 500 (EAR)?

4. Calculate the weekly returns. What is standard deviation of weekly returns for the S&P 500?

5. What is the beta of the stock?

6. Assume the risk-free rate (Treasury bill yield) is 2%. What is the annualized Sharpe ratio of the stock?

Hint: Use the annualized return and standard deviation. The variance of returns over N weeks is N times the weekly variance. The standard deviation of returns over N weeks is N^0.5 times the weekly standard deviation.

7. For the next few parts, create a portfolio of 20% stock and 80% S&P 500. If you rebalanced such a portfolio every week to keep the weights at 0.2/0.8, what is the holding period return over the 10 weeks for the portfolio?

8. What is the standard deviation of weekly returns for such a portfolio if you rebalanced every week?

9. What is the beta of such a portfolio if you rebalanced every week?

10. What is the annual Sharpe ratio of a portfolio with 20% invested in the stock and 80% in the S&P 500?

Assume that the expected returns are equal to the realized returns (EARs), and that the annualized variances and covariance stay the same as in the past.

Hint: The covariance of returns over N weeks is N times the weekly covariance.

Hint: Since we're looking at only one period (of one year), the distinction between rebalancing and not rebalancing is irrelevant here.

11. What is the annual Sharpe ratio of the optimal risky portfolio?