Determining Portfolio Volatility

Consider an investment manager analyzing the returns of three different portfolios over a year. The returns for Portfolio A are: 5%, 7%, 8%, 10%, and 12%. The returns for Portfolio B are: -2%, 4%, 6%, 10%, and 14%. Lastly, Portfolio C shows returns of 0%, 3%, 5%, 9%, and 15%. The manager is trying to determine which portfolio has the highest volatility, as measured by the standard deviation of returns.

Using the formulas for the sample standard deviation of a set of values, which is given by $$ s = rac{ ext{sqrt} igg( rac{1}{n-1} imes ext{sum}(x_i - ar{x})^2 igg)} $$, where $n$ is the number of observations and $ar{x}$ is the mean of the observations, calculate the standard deviation for each portfolio and identify the portfolio with the highest standard deviation.