Limits of OHLC Volatility Estimators for Portfolio Return Series

# How do I estimate the volatiliy of my portfolio with an estimator that requires High, Low, Open, etc


# How do I estimate the volatiliy of my portfolio with an estimator that requires High, Low, Open, etc












I have obtained the daily returns of my portfolio $R^{port}_t$ using a certain strategy.

Now I want to estimate the realized volatility $\sigma^{port}_t$ using the past 60 days. An obvious way to do this is by taking the standard deviation on the daily returns.

However, I want to use an alternative estimator (see Yang Zhang) which requires as input the Open High and Low prices. How can this estimator be applied to estimate the volatiliy of my portfolio?

## Answer by David Addison (score 1)

https://quant.stackexchange.com/a/34186

There are a few different ways to approach this problem.

One possibility is to transform your daily price/return data into weekly open, high, low, close data. You may then calculate the Yhang-Zhang or other suitable OHLC variance estimator (e.g., Garman-Klass, etc) as per the canonical approaches.

This approach is enumerated in this the attached spreadsheet. In the spreadsheet, given only daily close data and dates, a weekly OHLC series was constructed. The YZ estimator was then taken over the entire data range.

Another possibility is to perform a moving time-series analysis, which may be more appropriate if one believes that the variance is non-stationary. I've had success incorporating YZ into autoregressive moving average (ARMA) models, such as generalized auto-regressive conditional heteroskedasticity (GARCH) models. In order to do so, one starts by calculating the YZ error over each interval.

Note: The weekly YZ estimator is not likely to result in a more efficient estimate than the daily close-to-close estimator. It will, however, provide an alternate measure of dispersion.

## Answer by Matthew Gunn (score 1)

https://quant.stackexchange.com/a/34187

- You lack the intraday data to calculate an intraday high or low of your portfolio.

- The Yang-Zhang volatility estimator requires the intraday high and low.

The logical conclusion would be that you cannot use the Yang-Zhang estimator to estimate your portfolio's volatility.

#### Discussion

The idea behind Yang-Zhang and other advanced volatility estimators is that intraday movements provide additional information. By utilizing this information, they generate more precise volatility estimates from the same number of days of data.

But in your situation, you essentially have no information on the intraday movements of your portfolio, and so there's no intraday information to add.