Rebalancing Strategies

In terms of setting and preserving a trust’s investment policy, commentators generally agree that rebalancing is an indispensable tool. ²⁹  Why would a trustee be unwilling to rebalance a portfolio?  There are several arguments against an active portfolio management process utilizing rebalancing transactions:

• Rebalancing costs money:  trading is not free and, in some instances, trading costs can be formidable (trade commissions, market impact, bid/ask spreads, surrender charges, redemption fees, unamortized front end loads, etc.); ³⁰ 
• Rebalancing may trigger tax liabilities for taxable portfolios: this is an especially acute problem for poorly diversified portfolios invested in only a few assets with a low tax basis; ³¹ and,
• Rebalancing can truncate returns as money is taken away from winners and put into losers. ³²  This problem may be especially acute in trending markets. 

Rebalancing is, therefore, a process that balances transaction and tax costs against potential risk and return enhancements.  A major argument for rebalancing is, in a nutshell, that it preserves the integrity of trust investment policy by adherence to the asset allocation guidelines.  A major argument against rebalancing is that it costs money. ³³

Several academic studies focus on the topic of rebalancing rules.  In general, rebalancing rules prescribe both formulae under which the investor initiates rebalancing, and the extent of the rebalancing actions.  A review of the literature indicates that, in general, the formulae initiating rebalancing actions fall into one of five categories:

1. Calendar based rules: rebalance daily, monthly, quarterly, yearly, etc. ³⁴;
2. Drift from initial asset allocation proportions (i.e., if a 10% proportionate drift triggers a rebalance action, for a two asset class portfolio with a 60% stock allocation, the investor would initiate rebalance transactions if the stock grew to 66% of the portfolio’s value or diminished to 54% (±10% of 60%); ³⁵
3. Fixed percentage drift (i.e., if an asset class drifts more than ±10% of total portfolio value, the investor takes rebalancing actions.  For example, given a 60% allocation to stock, if stock value increases to more than 70% weighting or decreases to less than 50% portfolio weighting, the investor would take rebalance action.  In this category, the investor can set differing upper and lower bounds for each asset class); ³⁶
4. Standard Deviation criteria: rebalancing occurs when an asset’s risk premium (return in excess of the risk-free rate) shows a marked increase or decrease over its historical mean; ³⁷
5. Other criteria: including continuous rebalancing using a derivatives portfolio overlay (futures contracts), probability-based rebalancing based on creating of value-added confidence intervals, and so forth. ³⁸ 

Recommendations regarding the extent of rebalancing (as opposed to the frequency dictated by the above-listed formulae), generally follow one of three recommendations:

1. Rebalance to the normal policy targets (i.e., for the fixed-mix portfolio rebalance to the asset allocation targets);
2. Rebalance to the boundary or threshold limit at which the transaction is triggered; or,
3. Rebalance to a point between the asset allocation target and the boundary.

Mathematical Studies: Rebalancing and the Algebra of Diversification

Mathematical treatments of portfolio rebalancing generally fall into two categories:

1. Examination of the “algebra of diversification;” and,
2. Examination of the cost/utility benefit tradeoffs of rebalance elections.

Often, when studying portfolio investment returns over time, it is important to distinguish between the return from the risk premium ³⁹ of investment positions, and the return generated by rebalance strategies.  Although somewhat counterintuitive, it is well known that portfolios for which the average investment has a risk premium close to zero, can generate substantial compound returns, over time, provided that the portfolio’s investments exhibit certain statistical characteristics.  These include high standard deviations for the individual investment positions as well as low correlations between the positions.  For example, a recent study of commodity futures concludes that incremental portfolio returns are primarily generated by rebalancing strategies as opposed to investment risk premiums. ⁴⁰  Mathematically, the authors define a “diversification return” as the difference between a portfolio’s geometric (compounded over time) return and the weighted sum of the geometric return of each investment position held within the portfolio.  This difference, in turn is decomposed into two parts: (1) a variance reduction benefit; and, (2) a covariance drag.  Algebraically:
Diversification Benefit = (Variance Reduction Benefit - Covariance Drag).
The above formula is important with respect to rebalance strategy because the covariance drag term equals the economic impact of not rebalancing (i.e., following a drifting mix asset management approach).  We consider each term in sequence. 

The variance reduction benefit is one of the most important reasons why trustees elect to diversify portfolios especially when they are asked to provide ongoing cash distributions to beneficiaries.  Consider the following example:  if a trustee invests $10,000 for thirty years at a compound return of 13%, the ending wealth amounts to $494,024.  At an 11% return, ending wealth is $271,126.  A 2% difference in compound return translates into a 45% difference in ending wealth.  In this example, terminal dollar wealth tracks investment return (i.e. the higher the return the more dollars produced at the end).  Return and terminal wealth line up because the 13% and 11% returns are constant (i.e. they show no variance).  Constant returns are found in bank CDs, zero-coupon treasuries held to maturity, and similar financial instruments.  The certainty in return, however, means that it is difficult to find high rates for such investments.  Most investments offering higher returns, especially stocks, do not produce a constant return.  For example, the following graph depicts a ten-year period during which returns from US small company stocks generated a 19.72% average yearly return:



Although the average annual return is almost 20%, the return series produced a compound rate of wealth accumulation of only 1.38% despite the fact that there was one year during which the investment earned a 142.87% return. 

The difference between average return and compound return is the subject of a research paper that poses the question “Is your investment return leaking down the variance drain?” ⁴¹  The author points out that investors spend dollars not rates of return.  Variance in investment returns subtracts from ending dollar wealth according to the following mathematical approximation:

Ending Compound Wealth = Initial Wealth x [Average Return - ½ Variance].

Variance, in turn, is the square of standard deviation.  Standard deviation measures how far actual period-to-period investment returns differ from the average return during the entire period.  For example, since 1970, the average US stock has earned approximately 13% per year with a standard deviation of 30%.  This can be contrasted with a portfolio (combinations of individual stocks) that earns 11% with a standard deviation of 14%.  As the following graph indicates, when the variance drain factor is included in calculations of ending wealth, the investor achieves better results under the 11% earnings regime.  Initial value equals $10,000 invested over a 30 year planning horizon:

³² An investor may have neither a well-defined financial goal (a generation-skipping trust’s goal may simply be expressed in terms of growing wealth for a future generation), nor a well-defined planning horizon (e.g. a “dynasty” trust), nor a benchmark allocation calibrated to specific economic objectives and risk tolerances.  Drifting away from the benchmark is, therefore, not a particular concern.   Such an investor is said to be indifferent with respect to risk and may not value portfolio rebalancing actions.  An additional utility-based argument against rebalancing is discussed later in the paper. 

³³Uniform Prudent Investor Act §2 Comment: “Under the present recognition rules of the federal income tax, taxable investors, including trust beneficiaries, are in general best served by an investment strategy that minimizes the taxation incident to portfolio turnover.”  See also, Uniform Prudent Investor Act §7 Comment: “Wasting beneficiaries’ money is imprudent.  In devising and implementing strategies for the investment and management of trust assets, trustees are obliged to minimize costs.”