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LineOfBestFit
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Posts: 60
Joined: August 3rd, 2012, 1:09 am

Scaling Volatility by Hurst Coefficient in Optimization Context

March 10th, 2017, 12:08 pm

Does anyone know where to find guidance on the idea of using something other than the square root of time to scale volatilities (and, by extension, correlation) within the context of say, a mean-variance optimization? Other than ensuring the resulting matrix ends up positive semidefinite so that the estimated parameters tie together for the calculation of a frontier, can anyone relay any potential pitfalls to this approach? I know that there are resources on how to estimate Hurst and scale for individual time series (Mandelbrot, Peters, et al), but I don't know that there's a lot out there when working with multiple series for the purpose of optimization using this concept. 
 
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outrun
Posts: 4573
Joined: April 29th, 2016, 1:40 pm

Re: Scaling Volatility by Hurst Coefficient in Optimization Context

March 10th, 2017, 1:25 pm

Interesting.
There is a direct relation between Hust exponent and autocorrelation (covariance of Fractal Brownian Motion). Series with high Hurtst exponent have high autocorrelation across all time scales and hence are non-Markov.

What I would do is to estimate the autocorrelation and from that estimate the future return distribution conditioned on past returns. A stock that went up a lot and which has a H>0.5 is expected to go up further. So it's not just the variance scaling but also shift in mean that you need to include in your mean-variance optimization.
 
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purbani
Posts: 89
Joined: July 14th, 2002, 3:00 am

Re: Scaling Volatility by Hurst Coefficient in Optimization Context

March 30th, 2017, 11:02 am

You might find the approach of Leon and Reveiz of interest see here and here
 
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LineOfBestFit
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Posts: 60
Joined: August 3rd, 2012, 1:09 am

Re: Scaling Volatility by Hurst Coefficient in Optimization Context

April 11th, 2017, 11:01 am

Thanks for both replies.
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