315.1

1. The characteristics of 2 stocks are listed in this table:

1. Stock A and Stock B have a 0.3 correlation (r , or rho). What is the expected return and standard deviation of a portfolio which is 50% Stock A and 50% Stock B? (3 pts)

   The expected return of a portfolio is just a weighted average of the expected returns of the assets in the portfolio. The weights are the proportion of your money invested in each asset. So, in this case:

   E[R]=0.50(.18)+0.50(.10)=0.14

   The standard deviation of a portfolio is more complicated. We start by solving for the portfolio variance. The crucial ingredient here is the correlation coefficient (rho) which is 0.3. The w's are the weights (.5 and .5), and the sigma's are the standard deviations (.2 and .3), so plugging everything in, we have:

   

2. If you have a well-diversified portfolio of 20 stocks and you are considering adding EITHER Stock A or Stock B to that portfolio, which one is a riskier addition and WHY. (1 pt)

Stock A is riskier. It has a higher beta (1.5 vs. 1.1). In a well-diversified portfolio, I’m only concerned about systematic risk since I have diversified away unsystematic risk. Thus, standard deviation is not the measure of risk I look at since it measures total risk. I look at a measure of systematic risk: beta. The beta here tells me that for every 1% move in the market, I can expect Stock A to move 1.5%.

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