1. Describing Individual Stocks Return & Risk Ex ante approach (projecting the possible futures)

Following table summarizes the possible returns of next period for two stocks under different market conditions.

	Bear	Normal	Bull
Probability	0.2	0.5	0.3
Stock X	-20%	18%	50%
Stock Y	-15%	20%	10%

(1) What are these two stocks expected returns?

(2) What are their return standard deviations?

(3) What are the ex-ante Sharpe Ratio of these two stocks?

(4) Assuming the return follows the normal distribution, what are the lower and upper limits of this stocks return that cover the 95% of possible outcomes?

	Lower Limit	Upper Limit
Stock X
Stock Y

2. Describing Individual Stocks Return & Risk (Statistical Approach)

Following are BAC & Johnson & Johnsons annual returns in the past 10 years.

	1	2	3	4	5	6	7	8	9	10
BAC	5%	11%	13%	5%	-20%	-8%	-1%	20%	10%	9%
J&J	8%	6%	9%	7%	-12%	-2%	-3%	10%	12%	15%

(1) What are these two stocks average yearly return?

(2) What are these two stocks estimated standard deviation?

(3) What are these two stocks returns coefficient of correlation?

(4) What are these two stocks estimated covariance? (note AB=ABAB)

3. Describing Portfolios Return & Risk

A two-asset portfolio is specified as follows:

w_A=0.4; r_A= 5%; _A=8%

w_B=0.6; r_B =8%; _B=10%

a) what is this portfolios total risk if these two assets are uncorrelated (independent)?

b). what is this portfolios total risk if the correlation coefficient between these two assets is 0.7.

(note AB=ABAB)

c).True or False: high correlation among assets mitigates a portfolios ability to lower its total volatility.

d). True or False: a portfolios risk is always less than the weighted average risk of its member assets, as long as these assets are not perfectly positively correlated.

4.Portfolios Diversification Effect (Risk Reduction Effect)

A portfolio has two stocks, their return behaviors are as follows:

	Mean annual return	SD of annul return	Covariance Between A &B
Stock A	7%	6%	30%%
Stock B	10%	10%

Assuming the risk free return is 2%.

(0). What are the Sharpe ratios of Stocks A&B respectively?

(1) What is the Sharpe Ratio of a portfolio characterized as (0.3, 0.7).

(2) What is the Sharpe Ratio of a portfolio characterized as (0.5, 0.5).

(3). which strategy has the highest Sharpe Ratio? Buying individual asset, or one of the two portfolios mentioned above?