No. of Recommendations: 3

There are pro's and con's associated with scaling daily GSD's to annualized measures. From my experience, I'm not sure that you want to time disaggregate more than to monthly data.


First, let me say thanks for the link to the article; it was an interesting read. I've enjoyed your various posts that remind us there is a lot of research out there, either when you have articulated the background yourself or pointed us to a relevant research paper.

Second, I agree with you that monthly-measured volatility is probably fine for our purposes. RatioFool also made this comment. Several folks had been asking for some validation (or identification of problems) of our volatility measures, especially for the annual screens, so I think the daily-based GSDs served that purpose well: the monthly-based GSDs matched well with the daily-based GSDs, but the annual-based GSDS did not.

The rest of this post may not be of interest to many readers who think this is all too academic (so please feel free to skip!). But I bring the issues up because they may affect how we choose to calculate volatility for LorenCobb's exponential growth model, or future variations. I have suggested using daily data if available rather than the weekly data used so far. Also, I've been building and looking at portfolio allocation tools that use the correlation among stocks (or screens) to build an efficient frontier to choose "best" mixes from. The question may arise: is it appropriate to use stock daily returns, or should some lower frequency be used?

<Detailed comments follow!>

After reading the paper, I think it doesn't really change how we should use daily or monthly data for our primary purposes here. The point of the paper, I believe, was to say that the "square root of time" volatility scalar approach is not appropriate for a particular situation that doesn't really match ours. I'll try to make the point in three ways, and let me know if (where?) you disagree with my logic.

1. The focus of the article seems to be toward those managing risk of current investments on an ongoing basis by measuring and assessing historical volatility to build updated estimates of near-term future volatility. Their contention, which seems well-founded, is that measuring 1-day volatility and then multiplying by SQRT(n) to estimate n-day volatility is incorrect and misleading.

Our focus is more to understand, in a relatively straightforward way, the volatility that occurred during the past 14 (or more) years. We are not generally worried about the small change in volatility estimates we make as each new month of data gets added to the backtester, and we aren't creating new updates of future volatility estimates as that data comes in. We simply want to know which screen or set of screens was more or less volatile, relative to each other, over our backtest history. (We're hoping this is an indication of relative future volatility, just as we hope relative historical CAGRs will be repeated.)

So, I think the purposes are slightly different. The first might be characterized as "dynamic and absolute", whereas our purpose is more "static (historical) and relative".

2. The paper says that the time-scaling approach " ... produces volatilities that are correct on average ... ", but tend to magnify the volatility fluctuations of the longer time periods over time.

For our purposes, we are really just using that average volatility for the fixed backtest period. So, it seems that the simple approach will still be appropriate.

3. Empirically, item 2. seems to bear out in two ways:

a. The comparison of our monthly-based GSDs and the daily-based GSDs using the screens selected by Peter seem to support the SQRT(n) scalar approach for our purposes.

b. I built a spreadsheet to match the 10,000-day GARCH(1,1) process that the authors of the paper used as a base for demonstrating their point. As they did, I ignored the "start-up period" of 1,000 days, and assumed the remaining 9,000 days of returns were presented to me to measure volatility from.

I calculated the volatility for the entire period on a daily basis, obtaining a measure very close to the theoretical value I started with. Pressing F9 (calculate) several times generated new series of random numbers and results, but the measured volatility jumped around the desired result.

I then calculated the 5-day and 21-day volatility in two ways:

(1). 1-day volatility times the square root of 5 or 21, respectively.

(2). Obtaining sequential n-day returns (n=5 or 21), starting at the first of the 9,000 days, then calculating the volatility of those returns.

The results for (1) and (2) were remarkably similar, varying with each iteration of course.

My conclusion from this simple simulation is that it would be OK to use daily-based or monthly-based volatility measures when we are addressing 14 (or more) years and are simply looking backward (static). Over shorter periods (e.g., 6 months) it may be useful to use the daily-based approach to ensure we don't run into the same problem we see with the 14-year annual-based approach.

<End of detailed comments!>

Thanks again for pointing us to some useful and educational stuff!


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