My brother, not an investment professional, recently asked me whether he ought to rebalance his 401(k) portfolio. The short answer: “Yes!”
One of my first projects after business school had to do with assessing the effects of different hypothetical portfolio weighting and rebalancing schemes in an international equity portfolio, using EAFE countries. Tricky to do with whatever version of Lotus 1-2-3 I was using at the time, never mind that back then MSCI was still lumping Singapore and Malaysia together as if they were a single country.
The EAFE analysis did not lend support for any particular allocation rule; none of the allocation methods clearly dominated the others. However as for rebalancing, each frequency (monthly, quarterly, annual) had its day, ignoring transaction costs. The only one that didn’t was buy-and-hold. The inference we drew: use some rebalancing rule.
Transform losers into a winning rebalanced portfolio?
I recalled this project when reading “The Paradox of Diversification” in the Spring 2010 issue of The Journal of Investing. The author, Michael Stutzer, offers an insightful analysis on why, to reap the payoff from diversifying his portfolio, an investor should rebalance.
Stutzer’s summary on his academic home page reads:
“The current market malaise may keep some investors on the sidelines. The benefits of diversification may not seem as appealing in situations where the constituent investments are likely to lose money. Yet we will see, using relatively simple math, that diversification maintained by rebalancing can easily turn each asset’s negative cumulative returns into positive portfolio cumulative returns. This seemingly paradoxical result is the investing analog of a well-known phenomenon studied by physicists and mathematicians, called Parrondo’s Paradox.”
Stutzer discusses an interesting counter-intuitive example where the median investor could actually earn a positive result while diversifying between two investments that both have negative median returns. One asset, “the market,” randomly returns either 46% or -34% (resulting in a 6% mean return with 40% volatility), while the other asset loses 10bp consistently. The average annual market return is +6% but its median cumulative return after 30 years is a significant loss of approximately 43%. With a 50/50 allocation rebalanced annually, the median portfolio actually grows 34 percentage points after 30 years. That’s right: a rebalanced allocation between two assets with negative median returns generates a positive median return over time.
Seems like alchemy? Such is diversification. A stylized case, perhaps, but it fairly illustrates the benefit of rebalancing.
Not Rebalancing Can Increase Your Risk of Ruin
This alchemy is related to the risk of ruin, in which any investing, trading, or betting strategy that entails some chance of loss, no matter how small, will lead to ruin if you invest too much in it.
Not rebalancing is, in effect, allowing your allocation to change according to market trends. As long as the performance of your portfolio assets is mean reverting, the portfolio will rebalance itself. But if any of the assets start trending, not rebalancing your portfolio increases your risk of ruin. I have vivid memories from the late 1990s of a public fund’s CIO laughing about how much the fund had benefited by not adhering to its written policy of rebalancing to its 65% equity target. Its allocation had grown to 75%, thanks to the bull market of the late 1990s. Of course the fund’s paper profits and funded status more than evaporated in the 2000-2002 bear market. Almost any cost-effective rebalancing discipline would have preserved some of its late 1990s gains.
If you’re not rebalancing, not only are you not diversifying: you’re probably also increasing your risk of ruin.
Stutzer, Michael. “The Paradox of Diversification.” The Journal of Investing 19:1 (Spring 2010), pp. 32-35.
