If the correlation coefficient, p,is equal to +1.0, perfectly positively correla

Question

If the correlation coefficient, p,is equal to +1.0, perfectly positively correlated, has diversification worked? Yes or No Is this a risky portfolio? Yes or No It the correlation coefficient, p, is equal to -1.0, perfectly correlated, has diversification worked? Yes or No Is this a risky portfolio? Yes or No Suppose you are the manager of a $10,000,000 investment fund. The fund consists of 4 stocks with the following investments and beta coefficients: If the market's required rate of return (r_M) is 13% and the risk-free rate(r_RF) is 6%, what is the funds required rate of return, r? You must first find the beta for the portfolio. Then use it to calculate the required rate of return using the SML equation. Show work here.

Explanation / Answer

Calculating the weights of each individual stock:

For stock-A: $400,000 / $4,000,000 = 0.1 or 10%
For stock-B: $600,000/ $4,000,000 = 0.15 or 15%
For stock-c: $1,000,000 / $4,000,000 = 0.25 or 25%
For stock-D: $2,000,000 / $4,000,000 = 0.5 or 50%

Calculating the portfolio beta :

Portfolio beta = W1 * Beta of stock-A + W2 * Beta of stock-B + W3 * Beta of stock-C + W4 * Beta of stock-D

                     = 0.1 * 1.50 + 0.15 * (0.50) + 0.25 * 1.25 + 0.5 * 0.75

                     = 0.15 - 0.075 + 0.3125 + 0.375

                     = 0.7625

Now, calculating the required rate of return:

E(Rp) = Rf + [Rm - Rf] * portfolio beta

         = 0.06 + [0.14-0.06] * 0.7625

         = 0.06 + 0.061

         = 0.121 or 12.1%

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