Tactical Rebalance Strategies

Many recent mathematically-oriented studies extend model building to encompass a greater range of complex issues—tax costs, a wider variety of risk aversion/utility of wealth functions, the introduction of non-liquid assets into the portfolio (e.g., hedge funds, illiquid annuities, and so forth), and non-Gaussian return distributions ⁵⁴  A study published by Lynch and Balduzzi ⁵⁵ finds that realistic transaction costs:

• Cause the rebalancing frequency to decline considerably;
• Do not materially influence the amounts allocated to risky assets (which, presumably, would trigger more frequent rebalancing because of their relatively high variance); but,
• Lowers the amount allocated to risky assets if, in addition to rebalance costs, the risky assets have low liquidity. ⁵⁶

Additionally, the Lynch/Balduzzi study has important implications for rebalancing under tactical asset allocation regimes.  Specifically, when returns are predictable, the no-trade interval widens considerably and the investor is more willing to incur transaction costs when the boundaries are penetrated.  Holding unconditional return parameters (expected return, variance and higher moments of the distribution) constant, the Lynch/Balduzzi model explores an investor’s rebalancing behavior given both the magnitude of single-period predictability and the persistence of predictability over several time periods.  Lack of persistence, the authors find, causes the no-trade region to change from a band or straight-line boundary to a U shaped region.  Furthermore, investors are more comfortable holding risky assets at wider trade ranges when faced with conditional distributions.

Tactical asset rebalance approaches remain controversial.  A tactical approach takes the opportunity to blend periodic or threshold rebalancing elections with the manager’s ‘market timing’ views concerning relative capital market valuations.  Jensen and Mercer advocate rebalancing the portfolio to reflect turning points in the business cycle where such points are proxied by changes in the discount rate set by the Federal Reserve Board’s Open Market Committee. ⁵⁷  Goodsall and Plaxco advocate adjusting asset allocations tactically on either side of the strategic benchmark allocation. ⁵⁸  Such a strategy constrains tacking error while providing the opportunity to add alpha by refraining from rebalancing when forecasting models indicate trending market conditions; or increasing rebalance frequency if models indicate the likelihood of volatile markets. ⁵⁹  Smith and Desormeau provide a comprehensive examination of various rebalance formulae operating over a wide range of asset allocations during the period 1926 through 2003. ⁶⁰  They conclude that, over most allocations, a patient approach to rebalancing, which takes its cues from changes in Federal Reserve monetary policy, is optimal. 

• A key risk of tactical asset rebalance strategies is ‘model risk’—that is the degree to which even a well-specified market-forecasting model may yield spurious results. With regard to model inputs, much, although not all, academic evidence suggests that it is both difficult to find predictor variables; and, when found, such variables may cease to exhibit predictive value in future economies.  With respect to the model itself, although many types of models are compatible with financial data, their forecasts may differ significantly.  In a nutshell, even assuming the existence of valid forecasting model inputs, it remains difficult to form profitable money management strategies at a high level of confidence. ⁶¹  For example, Handa and Tiware co-authored a study examining the economic advantages realized by an informed investor relative to a naïve investor. ⁶²  Investor one is “uninformed” in the sense that he bases decisions on the unadjusted historical distribution of market risk and return.  They term this investor the “i.i.d.” investor, which is shorthand for the statistical phrase “independent and identically distributed.”  Such a distribution is characteristic of a normal (bell curve) distribution of a random variable such as the sum of coin flip results.  Assuming a fair coin, each result is independent of all previous results, and there is no period in which it is more likely to flip either heads or tails.  Investor two, by contrast, is a professional, “informed” investor that uses predictive (conditioning) variables to formulate beliefs regarding the future evolution of stock prices.  They term this investor the “mutual fund” investor.  The mutual fund investor uses combinations of three conditioning variables: (1) lagged stock returns to exploit information regarding serial correlation of time series; (2) lagged dividend yields to take advantage of earnings based information; and (3) book-to-market price ratios to capture information in relative valuations.  The mutual fund investor continuously updates (on a quarterly basis) the parameters of predictive models so that he may capture the dynamics of the unfolding stock price process.  However, the mutual fund investor is only permitted to use data that was actually available at the time in which an investment decision is made. ⁶³ 
• The questions of primary interest to trustees contemplating a tactical rebalancing approach are (1) do the predictor variables allow the informed investor to generate future gains which are both statistically and economically significant when compared to those generated by the i.i.d. investor; (2) are the excess returns stable over time; and, (3) do the gains persist after expenses.  Results are expressed as units of investor utility with each investor exhibiting quadratic utility at various risk aversion values.  The i.i.d. investor optimizes utility by developing a portfolio that uses only the sample mean return and the sample covariance matrix, which are both updated each quarter.  The informed mutual fund investor optimizes utility by forming portfolios based on predicted returns by employing a more complicated set of factors and factor loadings. ⁶⁴  
• The paper presents a matrix of test results.  Tests are based on portfolios formed from either a single risky asset or from multiple risky assets, on investors with various risk aversion parameters (low, moderate and high), on various combinations of the predictor variables, on various methods of adjusting for uncertainty in parameter values, and over various sub periods using market data from January 1954 through December 1998.  In each test, the performance of the i.i.d. investor’s portfolio is compared to that of the mutual fund investor’s portfolio in terms of its Sharpe (Reward to Risk) Ratio and to the Certainty Equivalent measure (mean return - ½ variance x risk aversion coefficient).  In order to mitigate the problem of data snooping and to determine if results are robust, tests are based on simulations of bootstrapped (resampled) data.  The authors test on out-of-sample data by allowing each investor to use a five-year learning period prior to forming portfolios.  Portfolios are then evaluated on a go forward basis.
• The major findings are:
• Under most tests, the predictor variables are unstable over time and have only period specific value;
• Performance gains, if any, realized by the mutual fund investor are not robust and are unlikely to persist into future periods;
• Combinations of two or more predictor variables do not improve the mutual fund investor’s performance;
• Utilizing predictor variables does not result in an increased ability to time markets (“…the market timing ability of the mutual fund strategy is fairly dismal.”). 
• It is noteworthy that the performance of the mutual fund investor significantly lags that of the i.i.d. investor over the most recent sub period (1985 through 1998). 

Historical Returns or Adjusted Returns?

George Santayana’s familiar phrase “Those who cannot remember the past are condemned to repeat it” is often employed by armchair philosophers to draw parallels between current circumstances and past events.  Unfortunately, in financial economics, the past may not be particularly relevant for forecasting the future.  The empirical literature discussing the costs and advantages of rebalancing, usually assumes that the single path of realized historical returns is sufficient to derive trustworthy parameters regarding the distribution of future asset returns.  Designing a portfolio rebalance strategy based on data mining of historical returns, however, may be a suboptimal approach.  This is the case for at least two reasons:

1. Cash flows may create path dependencies.  This means that the order in which returns are earned matters at least as much as the average and variance statistics that summarize the return distribution.  Unless the sequence of past returns repeats exactly—a highly improbable prospect—the relevance of the single pattern of realized past returns is limited.  Good decision making under such conditions is a function of analyzing many possible return paths over a large number of simulated future economies. 
2. Historical returns manifest a degree of dominance by certain asset classes that would not be expected under conditions of equilibrium. ⁶⁵  For example, the most well known equilibrium asset-pricing model—the Capital Asset Pricing Model [CAPM] assumes that all assets should have similar risk-adjusted return.  The market offers little opportunity to generate net present value profits because assets with higher nominal returns must be discounted more heavily for their risk.  This raises an issue concerning the degree of confidence that the investor is willing to put in the informational content of historical data. 

The extent to which an investor is willing to trust historical returns will affect the of asset allocation decision as well as the choice of a suitable rebalance strategy.  A dogmatic reliance on historical return estimates suggests that, in some cases, investors may wish to curtail or refrain completely from rebalancing out of certain historically dominant asset classes. ⁶⁶  Indeed, at the limit, a strict historical point of view may suggest that it is prudent to place all portfolio wealth in the single dominant asset class. 

Taxes

Tax issues further complicate the rebalance decision. ⁶⁷  One area of complexity is the differential tax rates or differing tax treatment of ordinary income (dividends vs. interest), short-term gain or loss, and long-term gain or loss. ⁶⁸  Rebalance actions that harvest losses as opposed to those that recognize gains may be more readily taken. ⁶⁹  Gain recognition destroys the time value of tax deferral which is a form of opportunity cost for the investor.   Given today’s low tax rates, however, the value of the tax deferral may not be great enough to justify portfolio concentration risk through retention of low-basis assets.  One measure of the value of the tax deferral is the amount of tax-payment on the recognized gain discounted by the tax-free investment rate for the applicable planning horizon.  For example, an asset sale that triggers a $1 million long-term gain generates (at a combined 20% state and federal cap gains rate) a tax liability of $200,000.  But the gain is an embedded gain that must, absent a sale, be paid at some future date (other than a sale after the date of the owner’s death).  The value of the tax liability deferral for a five-year period is, therefore, the present value of a future payment of $200,000 discounted by the five-year muni-bond rate.  Assuming a tax-free rate of 3%, the value of the deferred payments equals $172,518.  Thus the tax cost of the transaction equals ($200,000 - $172,518), or $27,482.  When a $27 thousand tax cost on sale of a $1 million position (assuming a zero basis) is weighed against the risk of maintaining an underdiversified or misallocated portfolio, the costs of not rebalancing may well outweigh the acceleration of the tax liability. ⁷⁰

Prudence, Utility Theory, and Portfolio Rebalancing

Under what circumstances might it be prudent to drift?  One possible answer to this question is based in utility theory.  Most investors prefer more wealth to less wealth, but have a decreasing marginal rate of satisfaction.  Earning an additional dollar produces slightly less satisfaction than losing a dollar produces dissatisfaction.  Most investors are sensitive to changes in their dollar wealth (they exhibit “risk aversion”) such that they exhibit increasing utility of wealth curves with positive first derivatives and negative second derivatives (head upwards but at a constantly decreasing rate).  There are a variety of curves that can fit into the generalized mathematical model known as von Neumann-Morgenstern utility functions. ⁷¹ 
Two curves that fit nicely into the von Neumann-Morgenstern family are a logarithmic curve (Utility = log of wealth) and a quadratic curve (Utility = square root of wealth). The investor with the logarithmic utility curve is said to be more sensitive to changes in wealth because the curvature produced by the function is greater.  Chances are that the portfolio that will best satisfy the log of wealth investor will not be the portfolio that will best satisfy the quadratic utility investor.  The reason for this preliminary conclusion lies in the fact that these investors have very different views about risk and reward.  A few investors have utility curves that are straight line (linear with respect to wealth).  These investors are ‘risk-neutral.’  Others exhibit “gamblers’ curves.”.  For gamblers, the thrill of the wager often has greater utility than the level of expected wealth offered by the wager’s payoff. 

Quadratic utility assumes that the investor becomes more risk averse as wealth increases.  This means that the investor exhibits Absolute Risk Aversion [ARA] because a 5% negative return causes a millionaire to lose more dollars than a 5% negative return causes a child with a $100 Christmas club account to lose.  Although this type of utility curve may seem counterintuitive, nevertheless, it is characteristic of certain groups of investors. ⁷²  Many investors have utility curves that exhibit decreasing absolute risk aversion and constant relative risk aversion [CRRA]. ⁷³  Finally, there are investors with “kinked” risk aversion curves.  They may feel comfortable with investment risk above a specified portfolio value (an investment “surplus”), but may become highly risk averse below the threshold value. ⁷⁴  The important point to note is that some investors are highly affected by shifts in wealth while others may remain largely unaffected.  Returns measured in dollar space are no longer adequate gauges of portfolio performance.  Rather, performance is best measured in utility space. 

For investors who exhibit a high degree of sensitivity to shifts in wealth (increased risk tolerance when wealth increases and decreased tolerance when wealth declines) a passive or drifting portfolio management strategy may be appropriate.  For a two-asset class portfolio (stocks and bonds), when stocks increase in value (i.e. assume a greater proportion of weight in the portfolio), the investor can tolerate the increased risk.  However, when stocks decline in value (i.e., the portfolio loses wealth), they constitute a lower percentage of portfolio weight relative to the safer bonds.  But this is exactly what the investor may wish.  Along the spectrum of possible risk aversion curves, investors exhibiting higher risk aversion as the portfolio approaches a floor value may prefer an insured portfolio strategy; while, at the other end of the spectrum, an investor with low risk aversion may wish to employ a strict contrarian strategy.  Between these two extremes lie a series of portfolio management elections that include (1) the tactical asset allocation strategy ⁷⁵ (appropriate for investors that do not exhibit quite the extreme reaction to wealth changes as the highly risk-averse investor who may prefer portfolio insurance); and, (2) the elections to rebalance towards the strategic asset allocation targets.  Rebalance elections are appropriate for investors that exhibit risk aversion curves more in line with the “average” within the population of investors. ⁷⁶   However, for some investors, it may be prudent to drift! ⁷⁷ 

Conclusion

Beneficiaries and fiduciaries would like to know the probable consequences of portfolio management elections prior to their implementation.  This is especially the case for decisions to incur voluntarily extra costs and taxes by electing to rebalance the portfolio to its asset allocation targets.  A naïve and difficult to defend decision making process is based on data mining historical results to find the “best” combination of asset allocation / rebalancing strategies; where “best” is defined as the combination that, by happenstance, produced the most money or the most favorable Sharpe ratio.  Academic research indicates that both utility of wealth and utility of consumption affect asset management policy with respect to both choice of portfolio management approach (drift, fixed mix, insured) and design of rebalance policy.  Ultimately, the prudence and suitability of the trust’s rebalance policy is a function of its ability to reduce the present value of expected utility loss over the applicable planning horizon.  However, given the heterogeneity of trust types, settlor objectives and beneficiary preferences, it is difficult to advocate a “one-size-fits-all” rule for rebalancing especially when such a rule is a product of mere empiricism.  

Rebalancing elections have economic consequences; and, therefore, should receive the requisite degree of care, skill and caution by trustees.  This is especially the case for taxable portfolios operating under distributional regimes (net income or total return trusts) where cash flow requirements create path dependencies.  If, as this essay argues, rebalancing policy is a critical bridge between a trustee’s choice of (1) trust portfolio management approach and (2) trust distribution policy, then written investment policy guidelines should make explicit a prudent and suitable rebalancing policy.  Indeed, the trustee may find that the rebalance strategy optimal for a net income trust distribution regime is not optimal for a total return unitrust distribution regime, or a total return indexed annuity distribution regime. 

The right strategy depends primarily on investor utility.  This is especially true for asset decumulation regimes.  If unspent terminal wealth (final portfolio value) has value because of bequest preferences or remainder interest considerations, then the trustee will select distribution policies and rebalance strategies that will augment the utility of final dollar values.  If however, the settlor does not have these preferences, the unspent money may merely represent lost consumption opportunities for the current beneficiary and may produce disutility.  In this case, asset management and rebalance strategies may give way to actuarial solutions such as immediate annuities.  This is a complex extension of this paper, however, and, given the current transaction-biased and commission-oriented marketplace--which is replete with potential counterparty risk--for actuarial instruments, is itself a solution that may bear considerable risk. 

Rebalance strategies appropriate for wealth accumulation trusts may not be appropriate for decumulation trusts.  At the limit, for trusts operating under long-term inter-generational planning horizons, rebalancing may not be preferred.  In such cases, the rebalancing policy may devolve into a no-rebalance policy.  In other cases, the rebalance policy must not only be appropriate to the purposes, terms, distribution requirements, and other circumstances of the trust, but must also match the skill sets of the trustee or the money manager to whom the trustee delegates investment responsibilities.  The high dimensionality of the problem argues for simulation analysis so that the trustee can “test drive” various asset management approaches (including asset allocations) and rebalance elections within the distributional constraints and limits of discretion established in the governing instrument.