Market volatility and the "Rebalancing Frown"

Posted by on August 25, 2011 @ 11:34 am in Investing

Given all the market volatility, a lot of folks are wondering about whether now might be the right time to rebalance their portfolio.

Vanguard researchers present an in-depth discussion of rebalancing in this paper. This analysis emphasizes that historically, rebalancing once or twice a year—and only doing so when a portfolio had wandered from its asset-allocation target by at least 5%—produced absolute return/risk results quite close to those resulting from more frequent, complicated, and time-consuming rebalancing efforts. The “take away” is that when it comes to rebalancing, doing it once or twice a year can be useful—and for many investors, there’s little point in making it more complicated than that.

But assuming your financial schedule is such that you’re due for your “once or twice a year” rebalancing right about now, how likely is it that your portfolio is out of whack by 5% or more and actually needs an adjustment?

My colleague Joel Dickson put together a neat little chart* that may give a quick answer. For any given initial portfolio allocation to stocks (on the horizontal axis) in a stock/bond portfolio, the chart shows how far the equity portion would have to slide before the portfolio’s allocation changed by 5% or more. The chart assumes that the non-equity portion of the portfolio has increased by 6%, which is close to the change on the Barclays Capital Aggregate Index year-to-date through Friday, August 19, 2011.

Equity decline to trigger rebalance at 5% interval

The Rebalancing Frown

It’s kind of a neat picture for a couple reasons. First, it clearly shows that unless and until the equity portion has dropped by more than about 13 %, you won’t be at that 5% trigger level with any initial equity allocation. (Through August 19, 2011, year-to-date, the MSCI US Broad Market Index hasn’t been down more than 10.5% at the close.)

Secondly, the chart shows very clearly the obvious relationship between the level of equity exposure in a portfolio and the need to rebalance: as stocks make up more or less of a portfolio, larger and larger market swings are needed to move the allocation by 5%.

If your strategy is really conservative or really aggressive, much larger market declines are needed to “trigger” rebalance.

Given the shape of the line, Joel likes to refer to this chart as the “Rebalancing Frown”—which is certainly how most of us feel about the markets lately. I told him we just need wait for the market to recover, and we can “turn your frown upside down,” as you’d get a similar picture that looks like a smile in the case of positive market changes. (You don’t hang out in the Vanguard research departments for the humor.)

Bottom line, while many of us are frowning a lot about market volatility, my conclusion is that “Don’t just do something, stand there!” still makes a lot of sense for an awful lot of investors—yours truly included.

Note: All investments are subject to risk. Investments in bond funds are subject to interest rate, credit, and inflation risk.

* For the mathematically inclined among you, here’s a detailed look at the calculations behind the chart above.

General case: (all fractions/percentages expressed as decimals, e.g., 5% = .05)

Initial equity allocation: alpha

Rebalance trigger/threshold (always a positive number): tau

Return on non-equity portion: r sub n

The formula that applies when the market is declining is different from when the market is rising:

Formula 1

For 50%, 5%, 6%, you get (.5–.05)*(.5)*(1.06)/((1+.05–.5)*.5)–1 = –.1327

The return on equity required to trigger rebalance (selling equity) in the case of a market increase is:

Formula 2
For 50%, 5%, 6% you get (.5+.05)*(.5)*(1.06)/((1–.05–.5)*.5)–1 = .2956

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