Estimating Stock and Portfolio Variance Without a Full Price History

Summary

The discussion considers what risk information can be inferred from a portfolio snapshot containing prices, position values, share counts, and stock betas, but no time series. One response suggests using beta to approximate a stock’s volatility if market volatility and an assumed stock–market correlation are available. This is explicitly a crude estimate, since correlations vary across securities and are not provided by the snapshot itself.

Other responses emphasize that variance is calculated from a series of observations, such as returns, and that conditional variance requires a time-series model such as GARCH applied to log returns. Portfolio variance additionally depends on holdings weights and covariance relationships; multivariate GARCH is one possible conditional modeling approach. The exchange offers broad pointers rather than a complete estimation procedure. A single snapshot cannot establish historical or conditional variance on its own, and assumptions used to fill missing data can materially affect the result.

Key ideas

• A portfolio snapshot alone does not provide a return series for direct variance estimation.
• Beta can support a rough stock volatility estimate when market volatility and correlation are assumed.
• Conditional volatility can be modeled with GARCH-type methods on log returns.
• Portfolio variance requires asset weights and cross-asset covariance information.
• Assumed correlations and missing time-series data limit the reliability of estimates.

Tags

# Variance calculation


# 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.

Thanks in advance for your help.

## Answer by jaamor (score 2)

https://quant.stackexchange.com/a/16557

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.

## Answer by chjortlund (score 0)

https://quant.stackexchange.com/a/15839

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

## Answer by Malick (score 0)

https://quant.stackexchange.com/a/15863

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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