Rebalancing and Market Conditions: An Example

Even a portfolio that has all its individual investment positions passively managed (e.g., a portfolio of index funds), cannot be neglected or ignored.  Irrespective of whether the investment manager takes active views regarding specific securities within the investment opportunity set, the trustee has the obligation to monitor the aggregate portfolio to assure that it continues to meet the “…trust’s return requirements, risk tolerance, general purposes, specific terms, and other pertinent circumstances.” ¹⁵

There is a large body of academic literature on the topic of portfolio management.  Much of the literature focuses on techniques for improving the risk/return tradeoffs faced by non-taxable investors with wealth accumulation objectives. ¹⁶  Some recent research discusses taxable investors as well as investors operating portfolios subject to periodic distributions.  Research papers sometimes contrast buy-and-hold (drift) portfolio management approaches with tactical and fixed mix asset allocation oriented approaches.  A survey of the extent literature reveals that research generally falls into two categories:

1. An empirical approach to the subject; or,
2. A mathematical approach to the subject. 

Some papers employing an empirical (historical) approach are subject to the flaw in statistical analysis known as ‘data mining.’  Although the term ‘data mining’ covers a wide range of abuses in sound research methodology, ¹⁷ in this case it refers primarily to basing a conclusion on a sample of data that may not be representative of the true, but largely unknown, population of both past and future results.  Statements such as “based on historical back testing, you should rebalance the portfolio to its asset allocation targets on a semi-annual basis in order to generate the greatest amount of ending wealth,” although possibly correct in a narrowly defined sense, are merely ad hoc rules that either (1) do not apply to the investor (because of interim cash flows or the need for dynamic liability matching); (2) are sensitive to the beginning and ending dates of the historical period under evaluation; or (3) merely reflect past occurrences without exhibiting predictive force under future economic conditions. ¹⁸  By contrast, many useful insights flow from studies using more mathematical approaches.  However, the benefits of such approaches are often limited in practice by the demands imposed by intensive tax calculations, transaction costs, portfolio software limitations, limitations in investment advisor skill sets, custodian capabilities, and other real world constraints. ¹⁹ 

Rebalancing is a type of active portfolio management strategy employed, depending on the study under consideration, either to enhance returns, control risk or both.  A simple example illustrates both the concept and mechanics of rebalancing.  Assume a portfolio that, at time zero, places $1,000 into each of three investments.  This is comparable to stating that the portfolio has a one-third allocation to each asset and that the trust’s investment policy requires a fixed mix asset management approach.  Over the forthcoming period, investment A earns a return of 10% ($1,100); investment B earns a return of –3% ($970) and investment C earns a return of 5% ($1,050).  At time period one, the aggregate portfolio has a value of $3,120.  In order to maintain the one-third allocation, the investor sells $60 of investment A and $10 of investment C.  The $70 in sales proceeds is reallocated to investment B.  Each rebalanced investment position has a value of $1,040, which is exactly one-third of the portfolio’s total period one value. 

This simple example provides several interesting insights.  The rebalance decision under the fixed mix asset management approach forces the trustee to sell high and buy low.  This is one of the hallmarks of a contrarian market strategy. ²⁰  Investors pursuing a fixed mix rebalancing strategy are natural counterparties to investors pursuing an insured portfolio management strategy.  The fixed mix investor, in the process of portfolio rebalancing, sells insurance.  Under an insured portfolio management strategy, the investor rebalances out of risky assets when they decline in value and moves into risk-free Treasuries.  Fixed mix rebalancing, by contrast, demands that the trustee buy into weakness and sell into strength because money is moved out of the relative winners and into the relative losers.  Thus, when seen in terms of buying or selling insurance, it seems as if rebalancing under a fixed mix approach should add value to returns (insurance has a premium cost and if you sell insurance you expect to receive a fair price for it).  Paradoxically, however, the purchase of insurance mitigates risk while the sale of insurance increases risk (technically, the risk is not increased but is transferred from the buyer to the seller for consideration received).  It is important to note the historical failure of the insured portfolio approach under conditions of extreme market volatility, although an extensive discussion of the reasons for its failure lie beyond the scope of this essay. ²¹  In the main, reference to rebalance strategies will assume a fixed mix portfolio management approach unless otherwise noted. 

Just as certain types of market conditions favor one asset allocation approach over another, ²² so also, market conditions will favor one type of rebalance strategy over another.  A recent study by Vanguard, for example, details the relation between market conditions and rebalancing results. ²³  The study assumes that the investor selects a fixed mix approach to portfolio management so that the investment policy’s original asset allocation is maintained.  The investor faces two risks: (1) relative tracking risk—the risk that the rebalance strategy will fail to keep the actual portfolio’s allocation from significantly deviating from the target allocation; and, (2) absolute performance risk—the risk that the rebalanced portfolio’s returns will significantly underperform those of a non-rebalanced portfolio. 

The Vanguard study creates simulations of extreme and admittedly unrealistic market conditions in order to isolate the economic consequences of rebalancing decisions.  In trending markets, for example, rebalancing to a target asset allocation means that assets that continue to perform strongly are sold in favor of assets that have relatively weaker performance.  Although more frequent rebalancing helps the investor to control the first type of risk, it does so at the cost of increasing the second.  That is to say, in a trending market, rebalancing mitigates tracking risk but generates the worst absolute return.  By contrast, in mean-reverting markets rebalancing both reduces tracking risk and enhances the portfolio’s returns.  The risk/reward tradeoff in a mean reverting market is a function of rebalancing frequency and/or threshold bounds.  It is not clear, for example, whether the increased average equity exposure that occurs as either threshold bounds widen or periodic rebalance intervals lengthen will generate returns above or below the average return improvements of rebalancing mean reverting assets.  Finally, in a random-walk market environment, rebalancing also results in portfolios that more tightly track the target asset allocation (i.e., decrease tracking risk) and produce returns that only modestly deviate from those of the target asset allocation benchmark. 

The simulated market conditions, however, did not incorporate factors for taxes and transaction costs.  The author points out that the type of rebalancing costs (fixed costs or costs that are proportional to the amount traded) will influence the optimal rebalance strategy.  If possible, rebalancing should occur with dividends, interest payments and new contributions into the portfolio.  Using new money enables the portfolio manager to accomplish most of the risk-control objectives at minimum cost.  The author concludes, “Just as there is no universally optimal asset allocation, there is no universally optimal rebalancing strategy.  An institution selects a rebalancing strategy based on its tolerance for risk relative to a target allocation.” 

Empirical Studies

Moving from a simple hypothetical three-asset rebalancing example into the study of historical data provides a variety of noteworthy and sometimes contradictory results. ²⁴  To illustrate the empirical approach, we discuss two studies by Craig Israelsen. ²⁵  The first, appearing in 2001, considers the historical returns of portfolios invested equally in US large company stocks, US small company stocks, and International large company stocks.  Israelsen evaluates results over several time periods and compares a drifting-mix passive portfolio management approach to a constant mix (annually rebalanced) active portfolio management approach.  The initial value of each portfolio is $1,000.  The end-of-period results appear in the following table:

These results are noteworthy because they suggest that the return enhancing benefits of portfolio rebalancing are sensitive to the time period under consideration.  However, the data also suggest that annual rebalancing reduces portfolio risk.  Israelsen concludes: “Asset allocation can serve the important function of dampening the downside risk without unduly penalizing return.” 

His second study covers only the single twenty-five year period from 1977 through 2001.  However, the study incorporates investment costs by comparing drifting-mix and fixed-mix results achieved by investors in three mutual funds (Vanguard 500 index fund, Vanguard US Small Cap index fund, and Scudder International Stock fund).  The initial portfolios are each valued at $3,000 instead of $1,000; and all other assumptions are the same.  In this case, rebalancing the portfolio to the fixed mix allocation generates 9% more ending wealth with 17.6% less volatility.  

Unfortunately, however, the conclusions of empirical studies like Israelsen’s have only limited application.  Many trust portfolios are not strictly accumulation vehicles but operate under conditions of cash outflows.  This means that terminal portfolio wealth (as well as, perhaps, interim consumption financed from the portfolio) is path dependent.  Given the fact that a precise repetition of the sequence of past returns is highly improbable, past behavior may not be a good indication of future results.  Additionally, there is the problem of creating an equal playing field for risk.  A portfolio that produces more return for less risk dominates a portfolio that produces less return at greater risk.  However, how does the trustee compare two portfolios when one has both greater return and greater risk?  Under certain conditions, the return-per-unit-of-risk for each portfolio ²⁶ can be evaluated to determine which portfolio has the superior risk-adjusted return.  But there is the expectation that a portfolio allocated between stocks and bonds under a drifting-mix passive management regime will eventually approach a portfolio that is 100% stocks given a sufficiently long planning horizon. ²⁷  Not only is the risk of a drifting mix portfolio much greater, the expected risk increases over time as equities dominate the asset weightings.  Reward to risk ratios may not be the best comparative measure under these circumstances.  This problem is known as “equity drift” and it presents a difficult task to the trustee wishing to make an apples-to-apples comparison of a static portfolio and a dynamic portfolio over time.  There are a variety of ways to achieve “risk-calibration.”  Common adjustment methodologies involve simulation of returns to determine the average degree of equity drift or examination of historical portfolio positions to determine the average proportion of equity allocation.  The starting equity weighting of the fixed-mix portfolio is adjusted to the average equity weighting so that risk exposures, “on average,” are comparable. ²⁸ 

¹⁸A good example of simplistic, rule-of-thumb maxims is found in Trone, Donald B., Allbright, William R., & Taylor, Philip R., The Management of Investment Decisions, McGraw-Hill (New York, 1996) p. 215: “An optimal limit would require readjustments twice a year on average—more than twice a year and the benefits may be eroded by transaction costs….” 

¹⁹Bruckenstein, Joel, “Rebalancing Act,” Financial Planning Journal (May, 2006) http://www.financial-planning.com/pubs provides a critical assessment of commercial rebalancing software applications. 

²⁰ A strict contrarian strategy, however, is a function of valuation estimation as much as it is a function of trading against the crowd.  There is no forecasting in a mechanical portfolio rebalancing system.  The strict contrarian investor hopes that he or she will not be “bagged” by momentum traders because of a misestimation of the intrinsic or justified value of the securities. 

²²Generally, an upwardly trending market favors the ‘drift’ and ‘portfolio insurance’ asset management approaches because winners are not cut back and profits accumulate unabated.  Mean reverting or volatile markets favor a ‘fixed mix’ approach. 

²³ Tokat, Yesim, “Portfolio Rebalancing in Theory and Practice,” Vanguard Investment Counseling & Research (Number 31, 2006). 

²⁴An interesting example is provided in: Horvitz, Jeffrey E., “The Implications of Rebalancing the Investment Portfolio for the Taxable Investor,” The Journal of Wealth Management (Fall, 2002), p. 51: “In 1987 the stock market fell dramatically in a day. An investor who rebalanced quickly reaped substantial benefits.  In 1929 the stock market also fell dramatically, but an investor who rebalanced immediately (and thereafter) probably was soon eating at soup kitchens, as the market plummeted in subsequent years.” 

²⁵ Israelsen, Craig, “Rebalancing Acts,” Financial Planning (June, 2001) pp. 59-62; and “Rebalance of Power,” Financial Planning (April, 2002) pp. 102-106. 

²⁷This is because the expected return from stocks is higher than the expected return from bonds or cash.  However, the fact that the stock investment is riskier (has a greater dispersion in its returns) pushes the planning horizon out to amazingly long periods.  Mark Rubinstein has a most interesting proof of this fact.  He asks: “how long must an investor be prepared to wait before the probability becomes high that an all-stock portfolio will outperform an all-bond portfolio?”  Rubinstein develops the following theorem: Assume that all available assets collectively follow a stationary random walk in continuous time (with finite variance).  Let X and Y be the values after elapsed time t > 0 from following two strategies (with equal initial total investment), each being the result of continuously rebalancing a portfolio to maintain constant proportions in the available assets.  Then:
Probability (X > Y) = N {}
where N is a joint standard lognormal probability distribution, mXt is the expected value of log (X), mYt is the expected value of log (Y),  is the standard deviation of log (x), is the standard deviation of log (Y), and r is the correlation between log (X) and log (Y).