1. W has discovered a good stock S. Since he believes in a focused investment strategy, W invests all his money in the stock. Jack Treynor believes diversification is as important as picking the right stock, so he includes the market index fund in his portfolio in addition to holding the stock S. The correlation coefficient between return on stock S and return on the market index fund is 0.5.

	Expected Return	Standard Deviation	b
Stock S	20%	30%	1.2
Market index fund	12%	20%	1.0
T-Bill	2%	0	0

Required:

1. Suppose CAPM holds, verify whether stock S is undervalued.
2. Jack forms an equally weighted portfolio (C) with stock S and market index fund M. What are expected return and standard deviation for portfolio C?
3. Can Jack beat Warrens investment strategy?

2. Suppose you can invest in the S&P500 index fund (S) and a US T-bill fund (r_F). The expected returns and standard deviation are as follows.

	E(r)	Standard deviation
S	13%	20%
rF	3%	0

Required:

1. Calculate the Sharpe ratio for investing in the S&P500 index fund..
2. If you allow 50% of your investment in the S&P500 index fund, what will be the expected return for your portfolio?
3. To achieve a standard deviation of 25%, how will you allocate between two assets?