Executive Summary

• This paper examines the effect of investors' portfolio rebalancing frequency and out-of-balance threshold on scaled return (return/risk ratios).
• Using 1926–2003 data, it examines the return/risk ratio for 19 different bond/stock portfolios with policy weights of 5 percent/95 percent, 10 percent/90 percent, and so on through 95 percent bond/5 percent stock. For each of these 19 portfolios, the authors calculate scaled return (mean return ¸ standard deviation of return) under 60 different time-based policies of rebalancing every 1 month, 2 months, and so on through 60 months.
• The authors then examine 20 threshold-based policies involving rebalancing when portfolio weights deviate from policy weights by 0.5 percent, 1 percent, and so on through 10 percent.
• Finally, the study conducts both analyses again under two distinct Federal Reserve monetary policies: expansionary and contractionary.
• The study finds that rebalancing frequency and threshold have a significant effect on scaled return. Specifically, for many model portfolios examined, deferring rebalancing to even as long as four years was superior to a monthly or quarterly rebalancing policy. For percentage threshold-based policies, the superior (inferior) outcomes were associated with rebalancing only when portfolio weights were 5 percent or more (less than 5 percent) out of balance.
• The best rebalancing policy is dependent on, and can be planned around, the Fed's prevailing monetary policy.

Acknowledgments

The authors are grateful to Bruce Geller for data acquisition, and to Peter Brucato, Indushobha Chengalur-Smith, and Hany Shawky for helpful comments.

David M. Smith, Ph.D., CFA, is associate professor of finance and a research associate at the Center for Institutional Investment Management, University at Albany, SUNY, Albany, New York.

William H. Desormeau, Jr., CFP®, is manager of Strategic Benefit Services in Rensselaer, New York, an affiliate of the Healthcare Association of New York State and provider of employee benefit programs.

Changes in bond and stock prices necessitate periodic restoration of portfolios' asset allocations to their policy weights. This process helps ensure that portfolios remain compatible with the objectives and constraints of beneficiaries. Work by Leibowitz and Hammond (2004) shows that professional investment managers tend to rebalance their portfolios more frequently than do individual investors. The optimal rebalancing frequency and threshold remain open questions for both types of investors. The purpose of this paper is to examine empirically the return-and-risk characteristics of investment portfolios under various rebalancing frequencies and out-of-balance thresholds.
 
Our study takes the following approach. Using large-capitalization U.S. stocks and U.S. government bonds as representative asset classes, we examine the scaled returns for 19 model portfolios between 1926 and 2003, for rebalancing frequencies ranging from 1 month to 60 months, and thresholds ranging from 0.5 percent to 10 percent. We then re-examine the question for two sub-intervals associated with tight versus expansionary monetary policy. In brief, the results show that the common policy of frequent portfolio rebalancing is inferior to a policy characterized by greater patience, and that the Fed's prevailing monetary policy stance should be taken into account in the rebalancing decision.

Literature Review

Many extant studies examine rebalancing frequency for relatively long periods, an extensive range of bond/stock weightings, or taking into account the prevailing stock market or monetary policy environment. To date, none has combined all of these features and also examined both time-based and threshold-based rebalancing policies.
 
Ferguson (1986) demonstrates theoretically and empirically that investors can manage risk effectively by aggressively altering the exposure for two asset classes—one risk-free and the other risky. Ferguson proposes a dynamic asset allocation (DAA) program, which involves manipulating portfolios consisting of one risk-free and one risky investment type: U.S. Treasury bills and securities tracking the S&P 500 Index.
 
The initial allocation to the two asset classes is determined by the investor's minimum acceptable expected return in any given year. Ferguson tests his hypothesis of using only two asset classes to manage risk by replacing the S&P 500 Index security with a security leveraged to 150 percent of the underlying index. The DAA program functions as follows. Over time, DAA will systematically increase exposure to the asset class with superior performance. Using data from 1928 through 1983, Ferguson concludes that the DAA strategy results in a beneficial blend of market upside capture and market downside protection. Ferguson's work focuses on tactical asset allocation; that is, his policy requires frequent portfolio adjustments in response to market trends.
 
Perold and Sharpe (1988) examine dynamic strategies for rebalancing portfolios in response to the tendency of risky assets to increase in value relative to less risky assets, over time. They define a constant-mix strategy as one that buys risky assets (stocks) as they fall in price (and in relative value within the portfolio), and sells them as they rise in price. Perold and Sharpe observe that the popularity of a dynamic strategy tends to eliminate its effectiveness. Specifically, market forces will remove the advantage of a dynamic strategy practiced by more than a minority of market participants.
 
Perold and Sharpe find that a constant-mix strategy would outperform a buy-and-hold strategy in a volatile market, without sustained moves either up or down. The greater the volatility, the greater the advantage for a constant-mix strategy. The constant-mix strategy will underperform the buy-and-hold approach when there are no reversals in market direction; that is, it will underperform during extended bull or extended bear markets. This is a pioneering work in showing that certain market patterns and volatility render some dynamic strategies more effective than others. Nonetheless, some of the strategies cannot easily be applied because investors often fail to realize until afterward whether they are in a bull or bear market.
 
Constant-proportion portfolio insurance and option-based portfolio insurance are two strategies that sell stocks as their prices fall and buy stocks as their prices rise. In effect, they take the opposite actions of the constant-mix strategy. These two forms of portfolio insurance will outperform the buy-and-hold approach during sustained market moves, either up or down. They underperform the buy-and-hold approach in trendless, volatile markets.
 
Using market data from 1963 through 1988, Dennis, Perfect, Snow, and Wiles (1995) examine the effects of rebalancing on portfolios that conform to rigid quantitative criteria. Screening firms using an approach similar to that of Fama and French (1992), they restrict their portfolios to small capitalization firms exhibiting a high book-to-market-equity (BE/ME) ratio. They find that the rebalancing interval producing the highest return was two years. They observe that their optimal portfolios were well diversified, as indicated by the large number of Standard Industrial Classification (SIC) codes represented.
 
Horvitz (2002) promotes the idea that rebalancing costs are substantial, and fall into two broad categories: trading costs and tax costs. He argues that even institutional investors tend to underestimate trading costs. Trading costs are not limited to brokerage commissions, but also include execution inefficiency (slippage) and opportunity costs. Moreover, the tax effects of portfolio turnover are complicated by "the 12-month hurdle,Ó which determines whether a gain is treated as short term or the more favorable long term for tax purposes.
 
Horvitz concludes that in light of rebalancing costs, asset classes move materially off their targets less frequently than many investors realize. Therefore, rebalancing in taxable portfolios can safely be avoided over short periods. The rebalancing of minor asset classes (those making up 10 percent or less of the portfolio) may not contribute meaningfully to the desired risk reduction, and hence may not be warranted. Although our study does not take trading costs and taxes into account explicitly, Horvitz makes clear that frequent rebalancing strategies carry a built-in disadvantage, which must be kept in mind as our results are interpreted.
 
Lynch and Balduzzi (2000) find that the predictability of returns has an effect on the rebalancing behavior of investors. When returns are predictable, investors rebalance more often and bear higher transaction costs. Lynch and Balduzzi show that rebalancing frequency decreases when transaction costs rise beyond a level deemed acceptable by the investor. They also find that, under circumstances where the predictive variable is less persistent (reliable), the investor is less likely to rebalance even when confronted with an extreme value.
 
Tsai (2001) examines the effect of various rebalancing strategies on five model portfolios, each representing a range of risk profiles and consisting of between four and seven asset classes. She compares the return and risk profiles of the portfolios from following a strategy of never rebalancing versus four active alternatives, all between 1986 and 2000. The four alternatives are rebalancing (1) monthly, (2) quarterly, and (3) monthly, or (4) quarterly only if any asset class drifts by more than 5 percent from its policy weight. A buy-and-hold strategy (never rebalancing) produces the lowest risk-adjusted returns, as measured by Sharpe ratio, for all five portfolios tested. For the other four active rebalancing strategies tested, Tsai found small (insignificant) variations in performance and risk. No one strategy outperformed on a risk-adjusted basis across all the portfolios. Tsai concludes that portfolios should be rebalanced because the small additional return associated with not rebalancing fails to compensate for the significantly increased risk. Our study follows in the spirit of Tsai's, but it extends the investment period to 78 years, accounts for 19 portfolio weightings, and considers alternative monetary policy environments.
 
Weiss (2001) examines the portfolio management needs of the retiree who needs to earn a reasonable return and manage risk while taking systematic withdrawals for living expenses. He uses Monte Carlo simulations to test annual and dynamic rebalancing strategies. His hypothesis is that the dynamic rebalancing strategy could either add portfolio life span for a given initial withdrawal rate or increase the portfolio's value for a target longevity.
 
Weiss concludes that the dynamic rebalancing strategy is superior to annual rebalancing because investors do not need to sell equities during market downturns. Instead, they can meet their withdrawal requirements from the fixed income or cash portions of their portfolio and ride out the period of low equity valuation.
 
Jensen and Mercer (2003) show that the return-to-risk ratios of Markowitz-efficient portfolios are improved by basing tactical asset allocation adjustments on turning points in the business cycle. But investors rarely detect such turning points as they occur, making such an investment strategy difficult to apply. Jensen and Mercer propose using changes in the monetary cycle instead of changes in the business cycle as the trigger point for asset re-allocation because monetary policy changes can be readily identified ex-ante.
 
They find that an asset allocation approach based on the monetary cycle resulted in significantly improved risk-adjusted returns (after transaction costs) over both the business-cycle and buy-and-hold approaches. Most of the improvement in returns occurs when the Open Market Committee of the Federal Reserve Board follows a restrictive monetary policy (40 percent of the time), during which time the return-to-risk ratio improves by 82 percent.

Methods

We derived the data for this study from Ibbotson's SBBI Yearbook, 2003. We use monthly returns on the S&P 500 with dividends reinvested, and on the U.S. long-term government bond as reported in the Yearbook.
 
We construct 19 fixed-weight portfolios, from 5 percent bonds/95 percent stock to 95 percent bonds/5 percent stock, at 5 percent intervals, and examine the scaled return for each portfolio. Scaled return is calculated as the ratio of monthly mean return to the standard deviation of monthly returns. Given investors' demonstrated preference for returns and aversion to risk, we assume that all else being equal, they will prefer to maximize scaled return. Our measure is similar to the well-known Sharpe ratio.
 
The analysis consists of three main parts. First, we examine scaled returns for the 19 fixed-weight portfolios under varying rebalancing frequencies during the entire 1926–2003 period and sub-periods. In each case, we allow the portfolios' values to reflect the market's returns in unconstrained fashion, until rebalancing takes place on a fixed schedule. At that time, we return each portfolio's weights to the fixed weights appropriate for that portfolio. For example, a 40/60 percent bond/stock portfolio with a rebalancing frequency of every 60 months is likely to experience large deviations from its model portfolio weights, particularly if the stock and bond markets move very differently from one another in the interim. Only at month 60 will we adjust the bond and stock components to return the portfolio (temporarily) to its policy weights.
 
For each of the 19 portfolios, we observe over the 78-year period the scaled return under 60 separate rebalancing policies (from rebalancing every month to rebalancing every 60 months). We then examine whether an optimum frequency exists, by running the following regression for each of the 19 portfolios:
 

where Scaled Return_p is the ratio of mean monthly return to monthly return standard deviation for portfolio p (for example, 5 percent bond/95 percent stock) and Freq_p is the frequency (in months, ranging from 1 to 60) with which portfolio p is rebalanced. If an optimum or optimal range exists, we expect to observe a positive β₁ coefficient estimate and a negative β₂ coefficient estimate. In equation (1), by taking the first derivative of scaled return with respect to Freq and setting the result equal to zero (which yields Freq = –β₁ / 2β₂) and substituting in the estimates for β₁ and β₂, we obtain a point estimate for the optimal rebalancing frequency.
 
The second part of our analysis examines the same 19 portfolios, but sets aside the time factor. Instead, we consider the effects of rebalancing when a portfolio's market weights deviate from its policy weights by some threshold percentage. For example, whenever the 40/60 percent bond/stock portfolio's weights deviate by some threshold amount from 40/60, the portfolio weights are restored to the policy weights. A "5 percent thresholdÓ would require rebalancing if the bond weights in the portfolio were less than 35 percent or greater than 45 percent. The thresholds we consider are 0.5 percent through 10 percent, at 0.5 percent intervals. Once again, we are searching for the rebalancing policy resulting in the highest level of scaled returns.
 
The third part of our analysis considers the possible effects of Federal Reserve monetary policy on the optimal rebalancing frequency and threshold levels. It has been well established that Fed policy is highly influential in the financial markets, and we seek to determine if that importance extends to the portfolio rebalancing decision. We identify the 32 points, from 1926 to 2003, when the Fed switched the direction of change in the discount rate. For example, one of the 16 contractionary monetary policy periods began on August 24, 1999, when the Fed increased the discount rate from 4.5 percent to 4.75 percent. This increase followed an expansionary period characterized by three discount rate cuts, the first of which was on January 31, 1996, and immediately precedes an expansionary period in which the first cut was on January 3, 2001. Following in the spirit of the Jensen and Mercer (2003) study, we define the start of a period of expansionary (contractionary) monetary policy as the beginning of the month following the first decrease (increase) in the discount rate. We apply the conservative assumption that investors could rebalance by month's end in recognition of the new regime, so the August 24, 1999, rate increase signals the start of a new contractionary period whose returns measurement begins in September 1999 and ends in January 2001.

Findings

Table 1 shows the maximum and minimum scaled returns resulting from various rebalancing policies, along with the time interval associated with maxima and minima. Regardless of the policy weights, the maximum scaled return is achieved at a rebalancing frequency of every 44 months, and the minimum at 1-month frequencies. We generally observe that longer intervals between rebalancing dominate shorter intervals. Between 1926 and 2003, the five best rebalancing intervals are found in the 39- to 44-month range. The lowest scaled returns tend to appear for more frequent rebalancing (one to six months). In the 50/50 percent through 95/5 percent bond/stock portfolios, the results are unambiguous, while portfolios with more than 50 percent stock perform relatively less well under a 30- to 36-month rebalancing policy. Table 1 also shows that the scaled return range is above 0.120 for portfolios with bond/stock weights between 60/40 percent and 40/60 percent, suggesting that the rebalancing frequency decision matters most for these portfolios.


 
Figure 1 provides the same information graphically. Each change of shade represents an increment of 0.04 in the scaled return (mean/standard deviation) ratio. The graphs in Figure 2 show the rebalancing frequency/scaled return relationships for six distinct 13-year periods. Among the notable conclusions from these graphs is that portfolios heavy in bonds outperformed stock-heavy portfolios in five of the six sub-periods. Moreover, for most model portfolios, a longer-term rebalancing interval outperformed monthly or quarterly rebalancing in four out of six sub-periods. The exceptions were 1965–1977 and 1978–1990.

Table 2 shows minimum and maximum scaled returns, for 1926–2003, for the 19 portfolios under various rebalancing threshold policies. In general, less-restrictive thresholds (that is, those allowing higher deviations) perform better than more-restrictive thresholds. Of the 95 situations in which policies are among the five best (19 portfolio weightings x 5 best for each), only 7 involve thresholds below 5 percent. Of the 95 situations in which policies are among the five worst, only 22 involve thresholds above 5 percent. It is interesting to note that the ranges between maximum and minimum scaled returns are lower in Table 2 than in Table 1, suggesting that returns are ultimately less sensitive to threshold-based rebalancing decisions than to frequency-based rebalancing decisions. Figure 3 contains a graph of results for the entire 1926–2003 period.

Figure 4 shows the frequency of rebalancing necessitated by following various threshold policies during the 1926–2003 period. Not surprisingly, low-threshold policies produce over 600 rebalancing events, and this situation is particularly acute for portfolios nearly equally divided between bonds and stocks. Less equally balanced portfolios have only a fraction as many rebalancings, but the disparity among the portfolios diminishes as the threshold rate rises. This graph is particularly instructive as investors attempt to keep in mind the costs and fees associated with trading.


 
Table 3 shows the relationship between scaled returns and rebalancing threshold under expansionary and restrictive monetary policy periods. It contains maximum and minimum scaled returns, along with the threshold levels associated with those maxima and minima. For restrictive monetary periods, all 19 portfolios benefited from a more patient policy involving a higher rebalancing threshold. The lowest-level threshold of 0.5 percent almost always generated the minimum scaled return. In expansionary monetary periods, more patient policies produced a higher scaled return for 15 out of 19 portfolios. For stock-heavy portfolios during expansionary times, it is less clear that low-threshold policies are inferior. Indeed, threshold policy does not appear to matter greatly for stock-heavy portfolios, as the range of scaled returns is quite small.


Figure 5 shows optimal rebalancing frequencies based on regression estimates and 90 percent confidence limits calculated from equation (1), for periods of contractionary monetary policy. The regression estimates are statistically significant at the 10 percent level for all except the 85/15 percent, 90/10 percent, and 05/95 percent bond/stock portfolios. As expected, among the models showing significance, β₁ is positive and β₂ is negative. Optimal frequencies are calculated in the range between 32 and 37 months, with 90 percent confidence limits ranging between 11 and 100 months for the lower-stock portfolios and 21–50 months for the higher-stock portfolios. With such a wide band, the results do not indicate definitively what the optimal rebalancing strategy is. But Figure 5 does provide guidance on strategies that do not work optimally—namely, rebalancing more frequently than every 10 months in the case of lower-stock portfolios and every 20 months in the case of higher-stock portfolios.


 
The totality of our evidence suggests that during most of the past century of market history, following a quick-trigger, mechanistic rebalancing approach would have been much less profitable than a more patient approach. This result applies to a wide array of portfolio allocations and both expansionary and contractionary monetary policy regimes. Although financial advisors may believe that clients need to see them as "taking action" on a frequent basis in order to justify their continued engagement, our study suggests that the frequent activity should generally involve something other than portfolio rebalancing.

Conclusions

Rebalancing frequency and threshold level are associated with significant differences in portfolio scaled returns. We show that this is true across a wide range of policy weights. From the perspective of both frequency and threshold levels, patient rebalancing policies tend to dominate quick-trigger policies, even before trading costs and taxes are considered. If such costs were taken into account, the advantage in favor of patient policies would be even more dramatic.
 
We find that Federal Reserve monetary policy has a discernible impact on scaled returns due to rebalancing, with restrictive monetary periods associated with less ambiguous conclusions. During restrictive periods, rebalancing more frequently than every 10 to 20 months is a suboptimal strategy.
 
Overall, our findings over a 78-year period are consistent with important conclusions of Dennis et al. (1995) and Horvitz (2002). Our basic approach is somewhat in conflict with that of Ferguson (1986), whose dynamic asset allocation strategy would increase exposure to the better performing of two asset classes, while our rebalancing toward a model portfolio would by definition reduce exposure to the better-performing asset class.
 
A question arises about why a relatively long time interval (and higher threshold) for rebalancing outperforms a shorter time period (and lower threshold). One partial explanation comes from the observation by various researchers, including Poterba and Summers (1988) and Fama and French (1988), of positive short-term autocorrelation among stock returns and negative longer-term autocorrelation. To the extent that returns are positively correlated in the short run, investors can take advantage of momentum by sitting tight. In contrast, mean reversion in returns over three to five years suggests a policy of rebalancing about that often.

References

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