Question

Question 10 The last 4-year returns of the stock of a given company have been the following: Year Return -4 -3 -2 |33,10% -0,10% 16,40% 19,90% . Estimate the standard deviation of a portfolio that allocates 30% of the wealth to be invested to this stock and the rest to the risk-free asset. (Round your answer to two decimal digits). A. 4,10% B. 0,05% C. 1,51% D. 0,00% E, 13,66% F. None of the ábove is correct.

hi can someone please explain step by step how to solve this please

Answer 1

Stock of Company:

Average Return = [(-0.0010) + 0.1640 + 0.3310 + 0.1990] / 4
Average Return = 0.6930 / 4
Average Return = 0.17325

Variance = [(-0.0010 - 0.17325)^2 + (0.1640 - 0.17325)^2 + (0.3310 - 0.17325)^2 + (0.1990 - 0.17325)^2] / 3
Variance = 0.05599675 / 3
Variance = 0.018666

Standard Deviation = (0.018666)^(1/2)
Standard Deviation = 0.1366 or 13.66%

Portfolio:

Variance of Portfolio = 0.30^2 * 0.1366^2 + 0.70^2 * 0.00^2 + 2 * 0.30 * 0.70 * 0.1366 * 0.00
Variance of Portfolio = 0.0016794

Standard Deviation of Portfolio = (0.0016794)^(1/2)
Standard Deviation of Portfolio = 0.0410 or 4.10%