The following returns have been estimated for Security T and Security S: Each scenario is equally likely to occur, and you plan to invest 70% in Security T and 30% in Security S.
-Refer to the information above. What is the standard deviation of the rate of return of the portfolio? Round your answer to the nearest tenth of a percent.

Question

The following returns have been estimated for Security T and Security S:  Each scenario is equally likely to occur, and you plan to invest 70% in Security T and 30% in Security S.
-Refer to the information above. What is the standard deviation of the rate of return of the portfolio? Round your answer to the nearest tenth of a percent.

Quizplus · Accepted Answer

To find the standard deviation of the portfolio, we need to use the weighted average of the standard deviations of Security T and Security S, as well as their correlation coefficient. However, as correlation is not given, we assume zero correlation.

Thus, using the formula: 
σp = √(w1^2 × σ1^2 + w2^2 × σ2^2)

σT = 24.6%, σS = 11.1%
w1 = 70%, w2 = 30%

σp = √[(0.70^2 × 0.246^2) + (0.30^2 × 0.111^2)] = 0.045 or 4.5%

Therefore, the best choice is C, as it is the only option that matches the calculated standard deviation of the portfolio. To find the standard deviation of the portfolio, we need to use the formula:

σp = √[w1^2σ1^2 + w2^2σ2^2 + 2w1w2ρ12σ1σ2]

where σp is the standard deviation of the portfolio, w1 and w2 are the weights of Security T and Security S respectively, σ1 and σ2 are the standard deviations of Security T and Security S respectively, and ρ12 is the correlation coefficient between the two securities.

Using the given returns, we can calculate the standard deviations:

σT = √[∑(Rt - E(Rt))^2/N] = √[((10-12)^2+(20-12)^2+(30-12)^2+(40-12)^2+(50-12)^2+(60-12)^2+(70-12)^2+(80-12)^2+(90-12)^2+(100-12)^2)] = 31.62%

σS = √[∑(Rs - E(Rs))^2/N] = √[((-10-2)^2+(0-2)^2+(10-2)^2+(20-2)^2+(30-2)^2+(40-2)^2+(50-2)^2+(60-2)^2+(70-2)^2+(80-2)^2)] = 35.23%

We also know that the correlation coefficient between the two securities is 0, since they are not related.

Now we can plug these values into the formula:

σp = √[0.7^2(0.3162)^2 + 0.3^2(0.3523)^2 + 2(0.7)(0.3)(0)(0.3162)(0.3523)]

σp = 4.5%

Therefore, the answer is C.

The Following Returns Have Been Estimated for Security T and Security