rebalancing (part 3)

As contemplated, I've rounded out our examination of rebalancing with some random number generation...

The Test

Have Excel generate artificial returns over 500 weeks for each of 10 artificial stocks. This was accomplished by using the random number generator utility that allows one to select the statistical distribution (I selected a Normal distribution in keeping with Modern Portfolio Theory) and the associated parameters (mean, variance). I specified the random numbers be drawn from a Normal distribution with a mean annual return of 20% and an annualized standard deviation of 20%.

Observations

Under these conditions, I found that Rebalancing provided for a higher return than Buy&Hold only 4 out of 10 times (not very conclusive). However, the Rebalanced portfolio was always much less volatile than the Buy&Hold portfolio, which provided for a higher Sharpe Ratio every time. The Sharpe Ratio is basically just Return divided by Standard Deviation, which helps provide a feel for the 'significance' of the total Return over the investment period relative to how much that Return bounced around during the investment period (technical note: for simplicity I assumed the risk free rate = 0% when calculating the Sharpe Ratio).

[Caution: these are 'long-term' results (i.e. 500 weeks = approx. 10 years). In fact when I ran the test 10 times using an extreme annualized variance of 100%, rather than the more realistic 20%, I found the Rebalanced portfolio was actually MORE volatile than the Buy&Hold portfolio in 7 of the 10 trials. I think the reason is because under conditions of such extreme volatility, it takes longer than 10 years to begin to observe the 'long-term' result where a Rebalancing strategy can benefit from Reversion to the Mean.]

In terms of Alpha, the Rebalanced portfolio only outperformed 6 out of 10 times (again, not very conclusive) - I'm not sure why (a mystery for another day). However, in keeping with the theme of lower volatility, the Rebalanced portfolio had a Beta less than 1.0x every time (as calculated against the Buy&Hold portfolio).

Model Portfolio vs. Benchmarks

Just a quick update, the model portfolio has held up well against our benchmarks (VT, ACWI, FWWFX) and also the S&P 500 during the recent market correction. See charts above. For an explanation of how these results are calculated by Folioinvesting.com, see here.

Also, fyi, I placed trade orders today to rebalance the stocks within each of the Model Portfolio's sectors to restore the targeted equal weighting of each stock. The actual weights had drifted over time since the Model Portfolio was established 9/4/09. Amazingly, using Folio's platform, I was able to place the 665 trade orders within just a few minutes by simply entering orders to rebalance to equal weight for each of our sector portfolios. The orders should be executed Tuesday morning because the markets are closed Monday for Presidents Day.

Roth Conversions

We interrupt our series on rebalancing with a note that if you have an IRA account, this is the year to seriously consider converting it to a Roth IRA account. In a future post, I intend to demonstrate why this is advisable for folks under all but the most obscure of scenarios. In the meantime, here are three worthwhile links outlining much of the rationale and process.

Roth Conversion Mistakes to Avoid

7 Steps to a Roth IRA Conversion

10 Things You Need to Know About Roth IRA Conversions

Rebalancing (Part 2)

The second chart above summarizes the results of the rebalancing test conducted last week (the first chart conveys the Alpha and Sharpe Ratio, which although interesting to me and potentially others, are not really salient to this post). Essentially, the take-away is: "When there's no trend, rebalancing is your friend" (I'm a poet and didn't know it). In other words, when the stock market is range-bound (i.e. oscillating back and forth with no consistent direction) as illustrated in 'Phase I' of the chart, then the practice of selling your winners and buying your losers will outperform a buy&hold strategy. The reason is because 9 times out of 10, the stocks that perform the best when the market rises will perform the worst when the market falls. In fact, it's this tendency that is captured by the statistical metric, Beta.

However, when there is a strong trend as illustrated in 'Phase II' of the chart, then rebalancing will underperform the buy&hold strategy. That's because as the overall market continues to rise, the same stocks with higher betas continue to outperform. If you're consistently selling these stocks and reinvesting in the underperformers... you get the picture.

In 'Phase III' of the chart, you can see the sharp reversal in the overall market. Since the rebalanced portfolio contains less of the high beta stocks when this reversal occurs, its total value declines less than the buy&hold portfolio. So in the end, rebalancing ended up roughly equal to the buy&hold strategy with less volatility along the way. However, at the peak of the market, the rebalanced portfolio was approximately 15% lower than the buy&hold portfolio. You would have needed the emotional fortitude and conviction to stick with your rebalancing strategy for roughly 5 years while it underperformed the overall market from 2004 through 2009. Otherwise if at some point you abandoned the rebalancing strategy and let your high beta stocks become a larger component of your portfolio, then you would have experienced more of the subsequent market downturn and your portfolio would not have caught up to the buy&hold portfolio.

This all highlights one of the central tenants of investing: strategy matters, but unless you can accurately time the market, consistency matters more. So what's the conclusion? For me, I don't think it's worth rebalancing in my regular brokerage account that is subject to taxes on the gains because the tax costs would overwhelm the small benefit of rebalancing. However, for my IRA accounts that are not subject to taxes, when I'm eventually able to move them over to Folio Investing (zero trading commissions except for an annual fee of $290), I will rebalance on occasion in order to mitigate the portfolio volatility and perhaps eke out an incremental return advantage in the really long-run. But rather than rebalancing every week, I may choose to rebalance only when I expect the market to experience a reversal (thoughts on market-timing strategy to come in later posts).

Footnote 1: this insight as it relates to rebalancing being akin to market-timing isn't often mentioned in the typical investing books you might find at your local Barnes & Noble. It is however expounded upon in an excellent book called "The Intelligent Portfolio", which is based on insights from Bill Sharpe, who won a Nobel prize for his work on option pricing theory. If nothing else, you should spend the $20 on the book just for the included free 1-year subscription to Financial Engines, which is an excellent tool that conveys your probability of achieving an adequate retirement nest egg based on your financial plan, with the analysis based on Monte Carlo simulation (state of the art for financial planning).

Footnote 2: You may have noticed this portfolio of 10 stocks pretty much doubled in value over a time period when the overall market essentially went nowhere. That is primarily a quirk of choosing the 10 stocks now, rather than back in 2000, which reflects Survivorship Bias. For instance, if I were choosing 10 stocks back in 2000, I may have selected Lehman Bros. (which went bankrupt) rather than JP Morgan.

Rebalancing (Part 1)

Rebalancing is one of those things that always seemed to make intuitive sense to me although I've only recently developed a more in-depth appreciation for the consequences upon one's portfolio. Basically, rebalancing just means selling a portion of stocks that have done well and using the proceeds to buy more of the stocks that have lagged behind, in order to make the weighting of each stock in the portfolio more in line with your targets. If your portfolio is constructed to simply hold the same stocks as an index, then there is no rebalancing required because both the index weights and the weightings in your portfolio will drift together over time as certain stocks outperform others. However, if your target weights are fixed (e.g. equal weighting for each stock), then you will need to periodically rebalance lest your actual weightings diverge so much from the target weights that you become uncomfortable with the portfolio composition.

So what are those consequences of rebalancing? To answer that, it's helpful to create a model of what would have happened over the past 10 years if you had a 10-stock portfolio and rebalanced it every week back to equal weightings vs. if you had not rebalanced and simply let the weightings drift (i.e. Buy&Hold strategy). The three charts at right and bottom provide the results of this test. The stocks used in the model were taken from the list below of the largest companies in each economic sector.

Next week I'll discuss the results of this model and see if there are any insights to be had about rebalancing. We may also take a look at another model of the same thing, except rather than using the price histories of 10 real stocks, we'll construct a synthetic portfolio using the random number generator function in Excel, which will allow us to easily sensitize the results for varying levels of the artificial stocks' volatility, correlation, and returns. This way, we'll be able to see if rebalancing 'should' be beneficial in theory or if the model using real stock data is just a fluke based on the idiosyncrasies of those particular stocks.

Rebalancing (Prelude)

As a prelude to my thoughts on rebalancing, using the data at Google Finance, I made a list of all the economic sub-sectors and found the largest company in the world (based on market capitalization) for each sub-sector that trades on one of the U.S. stock exchanges. The result is the table shown at right. The companies highlighted in yellow are the largest in each sector.

A few observations:

1. Since I associate Retail with goods or 'stuff', it's interesting to remember it's a Service. Retailers don't make the stuff, they provide the service of getting the stuff from the factories to you.

2. Companies with headquarters located in the US comprise 69% of the total market cap for this list. However, US companies comprise only about 36% of the total market cap of all publicly traded companies in the world. Therefore, one can infer that US companies make up a disproportionate share of the world's largest companies.

3. The average Beta of these companies is 1.31 (calculated relative to the S&P 500). One might have assumed a list of the largest companies in the world would have more 'stability' than average, which would have been incorrect. The average Beta for the US companies on the list is 1.28, while the average Beta for non-US companies on the list is 1.37.

Program Note

Well it only took a month before I fell short of my new years resolution to do one blog entry per week. My habit is to write an entry on Saturday morning (my favorite time of the week) after sleeping late and then having my coffee and oatmeal. Last Saturday, an old college friend and I both took our two dogs and drove through the snowstorm to his brother's house to play with his two dogs. The six dogs had lot's of fun until someone dropped a beer can and my youngest pup (blood hound) ended up biting one of our host's dogs over it (awkward). My bad for letting my pup have a small sip of my beer on occasion. [Note: I recently learned beer isn't good for dogs so I don't share anymore, but alas he has already acquired the taste.]

Then I had a little too much fun with some neighbors/friends that night and Sunday ended up being a write-off as a result (my wife and 4-month old son were out of town visiting her parents and some friends for the weekend). However, I'm back in the saddle today and will just have to tweak the new years resolution to commit to keeping the blog one year plus one week in order to make up for the 'snow day' last week.