September 24, 2013
Introducing The Rebalancing Opportunity Index
Rebalancing in one form or another is usually at the heart of success (or failure) in portfolio management. The challenge is distinguishing between those times when the rebalancing opportunity appears comparatively ripe vs. periods when this field is fallow. In a bid to enhance clarity on this critical issue, consider the latest addition to The Capital Spectator’s quantitative toolkit: the Rebalancing Opportunity Index (ROI).
The premise is that tracking the dispersion of performance data among the assets in a portfolio yields valuable perspective for estimating the ebb and flow of rebalancing opportunity overall. As a simple example, imagine a portfolio with just two assets—we’ll call them A and B. In times when the trailing returns are similar for these assets, the implied rebalancing opportunity is relatively weak. By contrast, if the trailing performance spread for the pair is wide, rebalancing’s prospects for the portfolio are considerably more appealing. Therein lies the inspiration for analyzing portfolios with ROI.
Tracking this to and fro of rebalancing’s potential is relatively easy for a two-asset-class portfolio. But as the number of holdings increases, analyzing the related rebalancing opportunity becomes more complicated. Yes, the first order of business is monitoring changes in a portfolio’s asset allocation. But as a supplement for quantifying a portfolio’s overall profile for purposes of assessing rebalancing potential, you can also analyze the holdings with a metric known as the median absolute deviation (MAD). This is the basis for the ROI data that will show up periodically on these pages, and in every weekly issue of The ETF Asset Class Performance Review, starting with the next issue that will be published this weekend.
Here’s a brief summary of how ROI is calculated and what it’s telling us about rebalancing opportunity. As noted, the engine under ROI’s hood is MAD, a statistically robust measure of dispersion. When directed at the individual returns of asset classes in a portfolio, MAD tells us—in one number—how the range of performance histories compare. It’s similar to standard deviation (volatility), but MAD is less vulnerable to extreme values that can skew the overall results and so it’s a superior measure for profiling and summarizing the various return histories within a given portfolio.
The first step in the calculation for the Rebalancing Opportunity Index is generating the MAD data for the portfolio's holdings, based on each day’s trailing return histories (we’ll use one-year rolling performance as the standard historical window). Next, we compute the average of those daily MAD calculations for the past year. Now we can calculate the ratio of the current MAD number to its trailing 1-year average. The result is multiplied by 100. Finally, we take that number and subtract 100. In other words:
ROI= (MAD daily / 1-year average of MAD daily data * 100) – 100
Plugging in actual numbers, based on the ETF-based version of the Global Market Index (GMI.F) and its rolling 1-year return, gives us the following chart. (For a list of component ETFs in GMI.F, see this post.) Notice how the ROI (black line) spiked higher back in May, just before GMI.F’s trailing return fell sharply. As you’ll recall, quite a lot of market turbulence in several asset classes started in May. The fact that ROI climbed sharply was a sign that it was a good time to rebalance GMI.F.
For a longer-term view, here’s how ROI and GMI.F’s rolling one-year return compare over the past decade, this time using monthly data:
Once again, we see that ROI tends to rise at major turning points for the portfolio, i.e., times when the trailing return is headed substantially lower or higher.
The details on ROI are sensitive to three variables. First, you’ll get different results for different portfolios, depending on the holdings. Second, it’s important to recognize that ROI will vary with the frequency of the performance histories—daily vs. monthly, for instance. Third, different look-back periods for the trailing returns will offer different results.
To keep things simple and intuitive, the standard ROI measure on these pages will be based on daily calculations of GMI.F with 1-year return data. Based on the numbers through yesterday, ROI was -2.27. How should we interpret this number? When ROI is rising sharply, that’s a sign that rebalancing opportunity for GMI.F is also increasing, and vice versa. ROI values at or above 100 look particularly strong for deciding that rebalancing the portfolio is timely. By that standard, the current -2.27 ROI suggests that rebalancing opportunity is low.
You’ll see ROI analysis show up on The Capital Spectator from time to time, but if you’re looking for regular weekly updates please consider subscribing to The ETF Asset Class Performance Review.
Posted by jp at September 24, 2013 7:37 PM
To calculate ROI, start with the current MAD, based on the returns for all the individual assets in the portfolio. Do this for each day over the past year. Now calculate the average of those daily MAD numbers for the past year. Compute the ratio of the current daily MAD to the trailing average MAD. Take the result and multiply by 100. Finally, take that result and subtract by 100.
For instance, based on data through Sep 23, the current MAD for all 14 ETFs in GMI.F is: 0.05822023. The average MAD for the trailing 250 days through Sep 23: 0.0595752. The ratio of the two numbers: 0.97725614 (0.05822023/0.0595752). Multiple the result by 100: 97.72561401, and then subtract 100. The end result is ROI: -2.274
Posted by: JP at September 25, 2013 5:58 PM
Thanks for sharing this concept! I do have a question though: if the daily MAD is calculated based on the past year of daily returns, and then this daily MAD is compared with the 1-yr average of daily MAD, one needs two years of data to calculate the first ROI - or am I missing something?
Also: you mention that the ROI differs based on the portfolio - how is this possible if the MAD is based on a single asset? Or do you divide the MAD of a single assed by the 1yr median MAD of all assets in the portfolio?
Thanks in advance!
Posted by: Alec at September 25, 2013 11:36 AM