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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.

Thanks in advance for your help.

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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.

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You can only find the variance for one column at a time e.g. use the close price instead of height in this example.

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if you are interested in conditional variance you need to fit GARCH type model to the difference of the log closing price. Otherwise just compute variance of log(diff(close price)).

If you want the variance of the portfolio you need to assign weights, or with conditional variance fit MGarch models.

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