Suppose that there are two assets 1 and 2. Asset 1 has an expected return of 0.1

Question

Suppose that there are two assets 1 and 2. Asset 1 has an expected return of 0.12 and a STDEV of 0.2. Asset 1 has an expected return of 0.15 and a STDEV of 0.18. The covariance between the return of Asset 1 and 2 is 0.01.

a) Compute the expected return and STDEV of the portfolio consisted of Asset 1 and 2. Assume the weights are W1 = 0.5 and W2 = 0.5.

b) Compute the expected return and STDEV of the portfolio consisted of Asset 1 and 2. Assume the weights are W1 = 0.25 and W2 = 0.75.

Please show detailed steps. Thanks!

Explanation / Answer

a) The portfolio expected return is calculated as: Portfolio expected return = W1 * E(R1) + W2 * E(R2) = 0.5 * 0.12 + 0.5 * 0.15 = 0.06 + 0.075 = 0.135 or 13.5% The portfolio variance is calculated as Portfolio variance = (W1)^2 * (SD1)^2 + (W2)^2 * (SD2)^2 + 2 * W1*W2*SD1 * SD2* Covariance = (0.5)^2 *(0.2)^2 + (0.5)^2 * (0.18)^2 + 2 * 0.5*0.5*0.2*0.18 * 0.01 = 0.25 *0.04 + 0.25 * 0.0324 + 0.00018 = 0.01 + 0.0081 + 0.00018 = 0.01828 But we know that square root of portfolio variance is standard deviation. SD of portfolio = SQrt.(0.01828) = 0.1352 or 13.52% b) The portfolio expected return is calculated as: Portfolio expected return = W1 * E(R1) + W2 * E(R2) = 0.25 * 0.12 + 0.75 * 0.15 = 0.03 + 0.1125 = 0.1425 or 14.25% The portfolio variance is calculated as = (W1)^2 * (SD1)^2 + (W2)^2 * (SD2)^2 + 2 * W1*W2*SD1 * SD2* Covariance = (0.25)^2 *(0.2)^2 + (0.75)^2 * (0.18)^2 + 2 * 0.25* 0.75 *0.2 * 0.18 * 0.01 = 0.0625 *0.04 + 0.5625 * 0.0324 + 0.000135 = 0.0025 + 0.018225 + 0.000135 = 0.02086 But we know that square root of portfolio variance is standard deviation. SD of portfolio = SQrt.(0.02086) = 0.1444 or 14.44% Therefore, the standard deviation of portfolio is 14.44%

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