# Variance calculation

How could I calculate variance when I have a snapshot of a portfolio that shows the following for each stock:

Purchase Price, Close Price, Change in value, Change in percentage, Shares owned, Starting market values in dollars, Ending Market Values in dollars, and Beta for each security. I do not have a full time series for each stock.

You could use beta ($\beta$) to get a very crude approximation of the standard deviation ($\sigma$) of the stock.
$$\beta_s = \rho_{s,m} \frac{\sigma_s}{\sigma_m}$$
Where the subscript $s$ stands for a stock and the subscript $m$ for the market. $\sigma_s$ is known. You could assume an industry wide correlation ($\rho$) value for stocks in a specific industry (e.g. energy). I do not know how much these correlations vary across different equities.