Why OHLC Highs and Lows Do Not Identify Asset Correlation
Summary
The document considers whether high and low prices can improve correlation estimates from OHLC bars. Its central point is that open and close observations have known timing, while the relative timing of each asset’s high and low is unknown. A joint estimator that uses highs or lows must therefore assume the corresponding extrema occurred simultaneously across assets, an assumption the author regards as weak.
It distinguishes correlation estimation from variance estimation: OHLC data may support more efficient variance estimates than close-to-close returns. It points to the Yang-Zhang approach for intraday variance, citing simulation tests in which it converges to the variance process more efficiently than other estimators. Combining such variance estimates with a covariance estimate could yield a correlation outside the valid range, so covariance would need suitable constraints. The discussion is conceptual and does not specify or validate a complete OHLC correlation estimator; knowing when highs and lows occurred could enable a more defensible extension.
Key ideas
- OHLC bars do not reveal when the high and low occurred relative to each other.
- Using extrema to estimate cross-asset co-movement requires assumptions about their timing.
- The document recommends Yang-Zhang methods for more efficient variance estimation from OHLC data.
- Combining variance estimates with covariance can produce an invalid correlation unless the covariance is constrained.
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Full text
# Pearson correlation coefficient based on OHLC data
# Pearson correlation coefficient based on OHLC data
Pearson correlation coefficient based on OHLC data
I've found only this article "Estimating correlation from high, low, opening and closing prices" by L. C. G. Rogers and Fanyin Zhou (2007) http://www.skokholm.co.uk/wp-content/uploads/2013/02/RZdraft.pdf about the topic of question, so I would like to ask if there is standard approach of using OHLC data which incorporates high and low prices into estimation process ?
## Answer by David Addison (score 5)
https://quant.stackexchange.com/a/33377
Given only OHLC information, with no timing information as when H and L occured in relation to one another, the covariance between any two assets is only defined for O and C since you know when these occurred in relation to one another. If you use H and L in a co-movement estimator, it must be assumed that H and L of any two assets occured simultaneously. This is a very weak assumption. Therefore, it seems inappropriate to estimate correlation using OHLC. However, it is possible to estimate variance more efficiently using OHLC data than the standard $C_{t}$ to $C_{t-1}$ method.
In order to estimate variance using OHLC data, I highly recommend Yhang Zhang's (YZ) estimator for intraday variance. Please see: Understanding Yang-Zhang Volatility Estimator.
In numerous tests on simulated data, the YZ estimator converges to the actual variance process more efficiently than any other estimator.
Given that:
${\displaystyle \rho _{XY}= \frac{\sigma_{X,Y}}{(\sigma _{X}\sigma _{Y})}}$
you could use YZ to estimate $\sigma_X$ and $\sigma_Y$. However, the correlation may no longer be bounded between $-1$ and $1$. Still, since we know that the realized variances are more likely to estimate the true variance, we can constrain the covariance such that an estimator is bounded appropriately.
Moreover, if its possible to determine when H and L happened in relation to one another, you could use the YZ framework to develop a co-movement estimator than should also converge more efficiently than close-to-close estimators.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.