Question
You estimated the single index (market) model for stocks A and B with the following results: Return on Stock A: RA = 0.06 + 0.5RM
You estimated the single index (market) model for stocks A and B with the following results: Return on Stock A: RA = 0.06 + 0.5RM + eA Return on Stock B: RB = 0.04 + 1.5RM + eB Where RM is return on the single index and eA and eB are error terms which are not correlated with anything and have zero means. In addition, the following statistics are known for the risk-free rate, RM, and the error terms: Mean Standard Deviation Risk-free rate 3% 0% Single index return, RM 10% 15% Error term for Stock A return, eA 0% 20% Error term for Stock B return, eB 0% 10% Based on the information above, calculate the smallest possible portfolio return standard deviation one can get by forming a portfolio of Stock A and B. Hint: Recall the formula for the minimum variance weight on A is: = 2 , 2 + 2 2, where is the return standard deviation of asset i (i=A, B), and , is the covariance between assets A and B
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