Efficient Portfolio Rebalancing in Normal and Stressed Markets

Lydia J. Chan and Sunder R. Ramkumar

Investment Insights THE INVESTMENT RESEARCH JOURNAL from BLACKROCK

September 2010 | Volume 13 Issue 3

9.10

AUTHORS

LYDIA CHAN, CFAVice President

Lydia Chan is a member of the BlackRock Multi-Asset Client Solutions (BMACS) group, which is responsible for developing, assembling and managing investment solutions involving multiple strategies and asset classes. Within BMACS, she is part of the Client Strategy team where

she is responsible for working with clients and prospects to solve their investment chal-lenges through research and analysis, and designing custom solutions across multiple asset classes and strategies.

Ms. Chan’s service with the firm dates back to 2007, including her years with Barclays Global Investors (BGI), which merged with BlackRock in 2009. At BGI, she was a member of the Client Advisory Group, responsible for analyzing and structuring optimal portfolios of managers and asset classes for clients. Prior to joining BGI, she was a bank supervision associate at the Monetary Authority of Singapore.

Ms. Chan earned a BA degree in economics and computer science from Cornell Univer-sity, and an MS degree in management science and engineering with a concentration in finance from Stanford University.

SUNDER RAMKUMAR, CFADirector

Sunder Ramkumar is a member of the BlackRock Multi-Asset Client Solutions (BMACS) group, which is responsible for developing, assem-bling and managing investment solutions involving multiple strategies and asset classes. Within BMACS, he is part of the Client Strategy team

where he advises strategic clients on investment policy, liability-driven investing and manager structure, and designs optimal plan-level investment solutions for clients.

Mr. Ramkumar’s service with the firm dates back to 2003, including his years with Barclays Global Investors (BGI), which merged with BlackRock in 2009. At BGI, he was a senior strategist in the Client Advisory Group advising on total portfolio investment strategy issues. He also conducted research for BGI’s advanced active equity strategies, and advised on new product development for defined contribution plans. His research has been published in financial journals, including the Financial Analysts Journal and The Journal of Fixed Income.

Mr. Ramkumar earned a BE degree in mechanical engineering from Mangalore University in India, and an MS degree in management science and engineering with a concentra-tion in finance from Stanford University.

EXECUTIVE EDITORS

Ronald N. Kahn415 670 2266 phone415 618 1514 facsimileron.kahn@blackrock.com

Russ Koesterich415 670 2576 phone415 618 1875 facsimileruss.koesterich@blackrock.com

EDITOR

Marcia Roitberg850 893 8586 phone415 618 1455 facsimilemarcia.roitberg@blackrock.com

BlackRock

The authors gratefully acknowledge insights provided by their colleagues Duane Whitney, Fred Dopfel, John Pirone, Catherine LeGraw, Dan Ransenberg, Chris Campisano, Kevin Kneafsey, Alex Ulitsky, Marcia Roitberg and three anonymous reviewers.

TABLE OF CONTENTS

Efficient Portfolio Rebalancing in Normal and Stressed Markets

Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Fixed Band Rebalancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Current Rebalancing Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5

Tracking Error Rebalancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1Investment Insights—September 2010

Executive Summary

Most institutional investors use a fixed band rebalancing

policy in which the weight of an asset class is allowed to

drift within specified bands. Investors should select band

sizes based on their tradeoffs between tracking error

control and transaction costs, and trade assets that

breach bands to the midpoint between band edge and

target weight. Other specifications have little impact

on rebalancing efficiency. Overall, in normal market

environments, fixed band rebalancing is relatively inex-

pensive and can control tracking error effectively.

This is not the case in dislocated markets. Higher asset

class volatility in stressed markets implies that the

portfolio is exposed to significantly more tracking error,

even when it stays within its target bands. Similarly,

greater illiquidity in stressed markets implies substan-

tially higher transaction costs, as investors must trade

even illiquid assets if these have breached target bands.

Both factors reduce the effectiveness of fixed band

rebalancing in stressed markets.

Tracking error rebalancing is an alternate approach in which

investors monitor tracking error (rather than asset class

misweights) and ensure that it stays below a specified

threshold using trades that minimize transaction costs.

Instead of trading all assets that breach the target bands,

investors use current estimates of volatilities and costs to

determine the trades that result in the most risk reduction

per unit cost. In stressed markets, this strategy can help

avoid trades in illiquid assets by exploiting asset class

relationships to reduce risk at significantly lower costs.

Investors should build the flexibility into their policies to

switch to tracking error rebalancing in stressed markets,

as volatility and illiquidity rise. The efficiency gains of

tracking error rebalancing are generally more modest in

normal markets. However, investors seeking increased

flexibility in determining opportunistic asset allocation

trades or guidance in liquidity management may benefit

significantly from incorporating tracking error rebalancing

as a part of their ongoing approach to portfolio rebalancing.

The goal of strategic rebalancing is to limit unintended drift, or tracking error, from the strategic policy benchmark without incurring large transaction costs.

2 BlackRock

3

1 We calculate portfolio weights using the S&P 500 Index and Ibbotson Intermediate Bond indexes.

2 Sharpe (2010) suggests that changes in asset class market values imply changes in consensus expected returns, which should be incorporated into the policy portfolio. He proposes that investors should adjust policy weights in proportion to market moves, effectively reducing (but not eliminating) the need to rebalance. This recommendation results in policy portfolios with varying risk levels, which may be inconsistent with individual investor preferences. Furthermore, Leibowitz and Bova (2010) point out that, in addition to changing consensus expected returns, market moves may be driven by a variety of other factors including changing aggregate risk aversion, changing real yields and changing volatility, and therefore can result in conflicting policy recommendations.

IntroductionDuring the credit crisis, as equity mar-kets crashed, many investors found themselves significantly underweight equities and overweight fixed income.

At the same time, illiquidity—particularly in the fixed

income market—made conventional rebalancing prohibi-

tively expensive. This raised several questions. Can

rebalancing policies be improved? What levers are most

important? Should investors adapt their strategies in

stressed markets? In this paper, we evaluate rebalancing

strategies in normal and stressed markets to identify the

most efficient approaches.

Rebalancing is essential in ensuring compliance with

the asset allocation policy. Market moves drive the

portfolio away from the strategic policy weights; over

time, the portfolio tends to drift toward riskier asset

classes. As an example, if a plan invested in a mix of

70% US stocks and 30% US bonds in 1950, by the end

of 2009, absent rebalancing, the portfolio would have

drifted to 99% stocks and 1% bonds.1 The unrebalanced

portfolio can have dramatically different characteristics

than the policy portfolio, which is designed specifically

to meet plan objectives and risk tolerance. In any year,

misweights between the portfolio and policy can cause

underperformance. Rebalancing should be designed to

limit the probability of underperformance, measured by

tracking error.

While rebalancing controls tracking error, frequent

rebalancing can also cause underperformance due to

the transaction costs of buying and selling assets.

Therefore, in designing their rebalancing policy, inves-

tors should balance competing objectives of limiting

tracking error and controlling transaction costs. The most

efficient rebalancing policy will achieve the desired degree

of tracking error control at the lowest possible cost.

The same considerations apply even if the policy weights

change over time. In this case, the problem separates out

into two steps. First, define the new policy weights based

on revised estimates of long-term expected return, risk,

risk tolerance or other considerations.2 Second, determine

the rebalancing strategy relative to the new policy weights

based on tracking error and transaction cost tradeoffs.

Some studies evaluate rebalancing strategies based on

the historical excess returns they would have gener-

ated. See, for example, Arnott and Lovell (1993). This

can yield misleading conclusions based on the study

period. Rebalancing can generate excess returns over

policy in mean-reverting environments when overweight

(underweight) asset classes are sold (bought) before

they subsequently underperform (outperform). However,

it can cause equal underperformance in trending mar-

kets. The excess returns are conditional on tactical

views regarding the future market environment. They

depend on the timing of trades and should be excluded

from the strategic rebalancing decision. In a similar man-

ner, strategic asset class expected returns should also

be excluded. These have already been incorporated in

determining policy allocations and should not influence

the decision to rebalance. Rebalancing is thus an exercise

in risk control and cost control.

We use this framework to examine best practices in

setting rebalancing policy. We begin by evaluating typical

rebalancing strategies in normal markets and then move

on to examine what works in stressed markets, where

rebalancing can be challenging.

Investment Insights—September 2010

4

Fixed Band RebalancingRebalancing Tradeoffs in Normal Market Conditions

The typical institutional investor uses fixed band rebalancing

(see “Current Rebalancing Practices” on page 5). Investors

specify fixed bands around the policy; when bands are

breached, investors simply trade back to within bands.

This is consistent with research that finds that fixed band

rebalancing is more efficient than a periodic approach

where all asset classes are rebalanced back to target

(irrespective of misweights) at fixed calendar intervals (e.g.,

monthly or quarterly). See, for example, Leland (2000)

and Donohue and Yip (2003).

While most plans use fixed band rebalancing policies,

there are four main levers to consider in designing

these policies:

1. Average size of rebalancing bands: How wide should

the rebalancing bands be?

2. Band size variation: How should the size of rebalanc-

ing bands vary for different asset classes?

3. Rebalancing destination: How far back to policy should

investors trade assets that breach bands?

4. Asset class grouping: Should rebalancing bands be set

around broad or narrow definitions of asset classes?

We discuss each lever in turn and calculate how different

choices affect rebalancing efficiency. In each case, we

consider a typical policy and calculate the performance of

alternate rebalancing rules using Monte Carlo simulations

of weekly returns, based on asset class characteristics

in normal markets (Exhibit 1).3 In each simulation, we as-

sume that the portfolio begins on policy and is monitored

monthly relative to static policy weights. We report the

average tracking error and transaction costs of alternate

rebalancing policies over a 10-year time horizon across

1,000 different simulation runs.4

Asset Class Policy (%) ExpectedReturn (%)

ExpectedRisk (%) T-Costs (%)

US Equity 45 7.75 16.00 0.30

Non-US Equity 20 7.75 17.50 0.50

Fixed Income 20 4.50 5.00 0.40

TIPS 5 3.50 5.50 0.30

Private Equity 5 9.00 18.00 N/A

Real Estate 5 6.75 15.50 0.30

Correlations US Equity Non-US Equity

FixedIncome TIPS Private

EquityReal

Estate

US Equity 1.00

Non-US Equity 0.75 1.00

Fixed Income 0.15 0.10 1.00

TIPS 0.20 0.10 0.70 1.00

Private Equity 0.80 0.70 0.45 0.20 1.00

Real Estate 0.65 0.45 0.20 0.35 0.60 1.00

Exhibit 1: Asset Allocation Policy and Normal Market Assumptions

3 Risks and correlations are consistent with long-run historical data. Expected returns are based on a risk premium approach. Transaction costs are estimates based on typical costs for trading active portfolios. Our broad results are robust; alternate specifications of these inputs yield comparable results.

4 For simplicity, we assume no inflows and outflows from the portfolio. This results in conservative estimates of transaction costs because inflows and outflows can be used to reduce asset class misweights without the need for offsetting trades.

Source: BlackRock

BlackRock

5

Current Rebalancing PracticesWhat are the most common rebalancing strategies in

practice today? We surveyed the largest US public defined

benefit pension plans and found that, overall, rebalancing

policies are very similar.

All the plans in our survey used static fixed bands, typically

defined around a set of five to nine asset classes. Most

plans had variable sized bands, but the average band size

clustered between 3% and 5%. Bands were also typically

specified for private equity, though one plan grouped private

and public equity to determine rebalancing trades.

Only a few plans reported their rebalancing destination.

However, a survey from SEI (2009) suggests that 73% of

plans rebalance back to target weights when an asset class

breaches its band. The histograms below summarize the

differences in each rebalancing lever across the 25

largest plans.5

5 Our sample includes the largest 25 public DB plans listed in the Pensions & Investments Survey (2009) that report rebalancing policies on their website.

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5

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2–3% 4–5% 5–6% >6%

1. Average Rebalancing Band Size

There was a wide range of band sizes across different asset classes and plans; however, the average band size across asset classes for each plan clustered around 3–5%.

2. Band Size Variation

The majority of plans had variable sized bands across asset classes. Of these, a large proportion appeared to use bands that were larger for asset classes with larger weights. However, there was no other discernable pattern.

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25

20

15

10

5

0

25

20

15

10

5

0

Equal Variable

3. Asset Class Grouping

Most plans defined bands around the typical asset classes (five to nine asset classes). However, a few used narrow asset class definitions (10 or more asset classes), and one plan only rebalanced around two broad asset class groups. Several plans used a hybrid approach, combining bands around typical asset classes with bands around broad asset groups.

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Narrow Typical Broad

3–4%

Investment Insights—September 2010

6

1. Average Size of Rebalancing Bands: We consider three

rebalancing policies with equal fixed bands of 1.0%, 3.0%

and 5.0% for every asset class. In each case, an asset

class that breaches its band is rebalanced all the way back

to target weight.6 We allow the private equity allocation to

drift, because it is illiquid and hard to trade. Exhibit 2

describes the rebalancing tradeoffs with tracking error on

the x-axis and transaction costs on the y-axis. Transaction

costs are depicted with a negative sign, since they lower

portfolio returns. The goal is to be as far northwest as

possible; that is, to generate the lowest tracking error at

the least possible cost. Exhibit 2 illustrates that 3% bands

imply an average tracking error of 0.32% and average

annual transaction costs of 0.02%. Narrower bands imply

lower tracking error (because they limit large drifts in

portfolio weights) but also higher transaction costs

(because they trigger more frequent rebalancing).

The “right” band size will vary from investor to investor,

based on their individual preferences between tracking

error and transaction costs (i.e., what level of tracking error

is the investor willing to tolerate and how much are they

willing to pay to control it). Exhibit 2 demonstrates that

the slope of the transaction cost/tracking error line can

increase sharply at lower levels of tracking error. Tightening

bands from 5.0% to 3.0% reduces tracking error by the

same amount as moving from 3.0% bands to 1.0% bands.

In the latter case, however, the incremental costs are

almost three times higher. This implies that it may not be

cost effective to reduce tracking error to very low levels.7

The average band size is a key driver of rebalancing

performance. Investors must understand the implications

of alternate band sizes and select bands consistent with

their tracking error and transaction cost preferences.

6 We use a simple heuristic to determine offsetting trades in other asset classes and select trades that reduce asset class misweights in proportion to the size of the misweights.

7 For plans with active management, the rebalancing tracking error tolerance can be selected relative to the degree of manager selection risk in the portfolio (i.e., the tracking error of the portfolio relative to policy due to active manager bets). The overall tracking error relative to policy is a combination of these two uncorrelat-ed risks. While very high levels of rebalancing tracking error would cause incidental policy “misfit” returns to dominate the alpha from manager bets, modest levels of rebalancing tracking error do not increase overall tracking error significantly. As a simple heuristic, plans with active management might set their rebalancing tracking error between one quarter and one half of the manager selection risk. Since rebalancing tracking error and manager selection risk are uncorrelated, this would increase overall tracking error by 3% and 12%, respectively.

Exhibit 2: Impact of Average Rebalancing Band Size on Rebalancing Efficiency

0.00

–0.02

–0.04

–0.06

–0.08

1% Bands

3% Bands

5% Bands

Ave

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Cos

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)

Average Annual Tracking Error (%)

0.100.00 0.20 0.30 0.40 0.50 0.60 0.70 0.80

Source: BlackRock

BlackRock

7

2. Band Size Variation: The band size variation specifies

how band sizes should differ depending on the asset class.

There are typically three types of band designs:

a) Equal bands (as in the previous section): Ignore

differences in asset class characteristics and assign

the same band to every asset class.

b) Proportional bands: Assign proportionately larger

bands to asset classes that have higher policy weights.

All else equal, asset classes with greater weights are

likely to deviate from policy more than those with lower

weights. Proportional bands are designed to limit the

amount of trading required, by having wider bands for

these assets.

c) Risk- and cost-adjusted bands: Assign variable bands

with an eye to controlling transaction costs and tracking

error. This typically involves wider bands for asset

classes that are more expensive to trade and narrow

bands for more volatile assets. For example, Masters

(2003) proposes bands for asset classes that are

proportional to their rebalancing transaction costs and

inversely proportional to tracking error squared.8

Exhibit 3 compares the characteristics of equal bands

(1%, 3% and 5% equal bands) with proportional bands (5%,

15% and 25% of policy weight) and risk- and cost-adjusted

bands proposed by Masters (using risk tolerances of 1.0%,

2.5% and 4.0%). The graph demonstrates that there is little

discernable difference in rebalancing efficiency between

the different rebalancing band designs.

Risk- and cost-adjusted bands are appealing in principle

but difficult to design, because the tracking error and

transaction cost implications of different bands are

difficult to predict. The tracking error caused by an asset

class misweight depends on the positions of all the other

assets. A 1% overweight to fixed income with a corre-

sponding underweight to TIPS might imply a low tracking

error, but a 1% overweight to fixed income with a corre-

sponding underweight to equity would imply a much larger

tracking error. Similarly, the transaction costs of trading

an asset class also depend on the offsetting trades

required. For example, the cost of rebalancing a large-

cap equity overweight is relatively low but may also require

offsetting purchase of expensive assets.

Exhibit 3: Impact of Band Size Variation on Rebalancing Efficiency

0.00

–0.02

–0.04

–0.06

–0.08

Equal

Proportional

Risk- and Cost-Adjusted

Ave

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Cos

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)

Average Annual Tracking Error (%)

0.100.00 0.20 0.30 0.40 0.50 0.60 0.70 0.80

Source: BlackRock

8 Masters calculates the tracking error for an asset class assuming that the asset class overweight (or underweight) is offset by underweights (overweights) in all other assets in proportion to policy weights. Similarly, expected transaction costs are calculated assuming that when an asset class breaches its band, it is traded back to target, and offsetting trades are made in all the other asset classes in proportion to their policy weights.

Investment Insights—September 2010

8

Since the efficiency gains from variable bands are modest,

some investors may prefer the simplicity of equal bands.

These require few assumptions and control tracking error

effectively at a low cost in normal markets.

3. Rebalancing Destination: The destination defines how

far back to policy to trade asset classes that have trig-

gered a rebalance. There are three typical choices:

a) Trade the asset class all the way back to target

(as in the previous sections),

b) Trade only to the edge of the band, or

c) Trade back to the midpoint between target and edge.

Exhibit 4 contrasts the characteristics of fixed band

rebalancing policies with the three different rebalancing

destinations. In each case, we consider three rebalancing

policies with equal rebalancing bands for every asset

class of 1.0%, 3.0% and 5.0%. The line representing

trading back to target is below the other two rebalancing

alternatives, indicating that this approach is least efficient.

Investors can achieve the same tracking error at a lower

cost by trading to the edge (or to the midpoint) of a band

that is slightly tighter. For example, Exhibit 4 illustrates

that an investor can design a set of bands between 3%

and 5%, rebalanced to edge (or to the midpoint), that have

the same tracking error as 5.0% bands rebalanced to

target, but with lower transaction costs. These findings

are consistent with results in Brown, Ozik and Scholz

(2007) and Leland (2000).

The inefficiency of trading back to target stems from

two sources. First, trading back to target locks in larger

up-front transaction costs than trading to the edge, where

there is a possibility that the misweights will be naturally

corrected by market moves. Second, the additional

degree of tracking error control from being back at target

can be modest, as there are other asset classes that are

still misweighted.

Trading to the edge is efficient but typically requires

frequent (small) trades, because an asset that is traded

to the edge of the band might require a rebalance in the

very next period. In our simulations for 3.0% bands,

trading to edge requires a trade every 4 months as

opposed to every 15 months for trading to target. Instead,

plans may choose to rebalance to the midpoint between

target and band. As Exhibit 4 indicates, this efficiency is

similar to trading to the edge but with much less frequent

trading (every 12 months for 3.0% bands).

Exhibit 4: Impact of Rebalancing Destination on Rebalancing Efficiency

0.00

–0.02

–0.04

–0.06

–0.08

Trade to Target

Trade to Edge

Trade to Midpoint

Ave

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)

Average Annual Tracking Error (%)

0.100.00 0.20 0.30 0.40 0.50 0.60 0.70 0.80

Source: BlackRock

BlackRock

4. Asset Class Grouping: Grouping determines the defini-

tion of an asset class for the purpose of setting bands. We

consider two alternatives:

a) No grouping: Uses asset class definitions consistent

with the asset allocation policy (US equity, interna-

tional equity, US fixed income, etc.).

b) Broad grouping: Sets rebalancing bands around broad

asset categories (e.g., around the total equity portfolio

and the total fixed income portfolio rather than on the

individual asset classes within these groupings).

Narrow asset class definitions provide better tracking

error control in environments where correlated asset

classes behave differently. For example, in an inflationary

environment, nominal bonds and inflation-linked bonds

typically have significantly lower correlations than in

normal environments; simply focusing on the aggregate

bond allocation may provide a misleading measure of

tracking error. However, narrow asset class definitions

may also create situations in which a plan must sell an

overweight asset class (e.g., small-cap growth) despite

the fact that it has an underweight in another highly

correlated asset class (e.g., small-cap value) that essen-

tially offsets the tracking error. The net result, illustrated

in Exhibit 5, is that alternate asset class groupings do not

change rebalancing efficiency materially. Most investors

may simply default to asset class definitions consistent

with their policy, while investors with tactical views on

return opportunities of different asset classes may prefer

broader groupings that provide more flexibility in deter-

mining trades.

A small portion of plans group only private equity with

public equity and retain other asset class definitions.

Since private equity is illiquid, this strategy effectively

uses public equity as a proxy trade, and is an alternative

to leaving the private equity allocation unrebalanced.

Investors should consider grouping private and public

equity; this generally results in a modest reduction in

tracking error, compared with allowing private equity to

drift, with similar transaction costs (Exhibit 5).

Rebalancing Efficiency in Stressed Market Conditions

Our analysis so far—and practically every study of rebal-

ancing policy—has focused on normal market conditions.

Fixed band rebalancing is effective in controlling tracking

error and transaction costs in normal markets. However,

as we saw during the credit crisis of 2008–2009, market

conditions can change dramatically over time. In 2008,

we saw volatility spike. The VIX index of equity volatility

hit an all-time high, and real estate volatility was three

times as high as its long-term average. Liquidity was also

a significant concern, particularly in segments of the

Exhibit 5: Impact of Asset Class Grouping on Rebalancing Efficiency

Typical Grouping

Broad Grouping Grouping Private Equity with Public Equity

0.00

–0.02

–0.04

–0.06

–0.08

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)

Average Annual Tracking Error (%)

0.100.00 0.20 0.30 0.40 0.50 0.60 0.70 0.80

Source: BlackRock

9Investment Insights—September 2010

10

fixed income market, and drove up the costs of trading.

The cost of trading securitized and credit bonds moved to

250 basis points or more, while in typical markets the

same bonds traded for just 20 bps.

Both volatility and illiquidity reduce the effectiveness

of fixed band rebalancing. Higher volatility exposes the

portfolio to more tracking error, even when it stays within

target bands. Illiquidity implies substantially higher trans-

action costs, since the investor must trade even illiquid

assets when they breach target bands. Exhibit 6 contrasts

the performance of fixed band rebalancing (with equal

bands, rebalancing to midpoint between band and edge,

no grouping) in stressed markets against normal markets

using Monte Carlo simulations. The stressed market

simulations use assumptions consistent with data from

2008, with higher asset class volatility and correlations

and transaction costs that are substantially higher for fixed

income. The graph illustrates how the tracking error from

fixed band rebalancing can effectively double in stressed

markets with substantially higher transaction costs.

Exhibit 7 provides a historical perspective on volatility and

liquidity. Since historical transaction costs are difficult to

obtain, we use credit spreads to proxy periods of illiquid-

ity. The graph demonstrates that markets go through

periodic dislocations. Three stress periods stand out:

1987, 2001–2003 and 2008–2009, each of which is

associated with a market crash. Market crashes cause the

biggest portfolio dislocations and generate the greatest

need to rebalance. However, they are also followed by an

environment of higher volatility and illiquidity in which fixed

band rebalancing is least effective. This suggests that

fixed band rebalancing fails plan investors precisely when

rebalancing is most critical. Investors need a more respon-

sive rebalancing policy that adapts to market conditions.

Tracking Error RebalancingTracking error rebalancing is a market-aware alternative to

rebalancing that explicitly focuses on reducing tracking

error at the lowest possible cost. Instead of using bands

as a proxy, investors specify a tracking error tolerance

directly.9 As the portfolio drifts from policy, investors

Exhibit 6: Fixed Band Rebalancing and Tracking Error Rebalancing in Alternate Markets

–0.20

–0.18

–0.16

–0.14

–0.12

–0.10

–0.08

–0.06

–0.04

–0.02

0.00

Fixed Band –Normal

Fixed Band –Stressed

Tracking Error–Normal

Tracking Error–Stressed

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Ave

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Average Annual Tracking Error (%)

Source: BlackRock

9 The tracking error tolerance is generally a constant, but investors may retain the flexibility to change it over time based on tactical views (e.g., reducing tracking error if there is conviction that misweights will lead to underperformance) and/or cost considerations (e.g., allowing greater tracking error if the cost of reducing tracking error is found to be prohibitive).

BlackRock

calculate the expected tracking error based on current

estimates of asset class volatility and correlation.10 If the

expected tracking error is greater than the specified

tracking error tolerance, investors use a mean-variance

optimization to determine the lowest-cost trades11 required

to bring tracking error within threshold.12

Tracking error rebalancing can help investors identify key

sources of tracking error. Rather than trading all assets that

breach threshold bands, investors can use tracking error

rebalancing to optimize trades, focusing on trades that may

reduce risk the most per unit cost. In dislocated markets,

it helps investors avoid trades in illiquid asset classes and

instead exploit asset class relationships to reduce risk at a

fraction of the cost of fixed band rebalancing.

Exhibit 6 highlights the differences between fixed band

rebalancing and tracking error rebalancing in both stressed

and normal market environments, based on Monte Carlo

simulations. To facilitate a comparison, we examine track-

ing error rebalancing policies with triggers designed to

yield the same tracking error as corresponding fixed band

rebalancing policies. In typical market environments, when

transaction costs are similar across asset classes, fixed

band rebalancing (solid dark blue line) works well. It

controls tracking error and transaction costs, and it is only

marginally less efficient than tracking error rebalancing

(dotted dark blue line). In contrast, tracking error rebalanc-

ing creates significant efficiency gains in stressed markets

(dotted light blue line), achieving the same tracking error

as fixed band rebalancing (solid light blue line) at about

half the cost.

Tracking error rebalancing produces efficiency gains

relative to fixed band rebalancing by exploiting differences

in relative asset class volatilities and transaction costs to

reduce risk inexpensively. While precise volatility forecasts

can be difficult to make, relative asset class volatilities are

generally stable. Equities have consistently been more

volatile than bonds, and emerging market equities have

consistently been more volatile than developed market

10 There is a large body of work on forecasting volatilities and correlations based on historical data. See Litterman and Winkelmann (1998) for a summary. In our work, we find that an exponentially weighted covariance matrix using monthly data with a 12-month half-life provides a reasonable balance of responsiveness without causing excessive trading.

11 See Grinold and Kahn (2000) for an overview of transaction cost models. In practice, estimates of asset class transaction costs are available from brokers and portfo-lio managers.

12 The ideal optimization would also consider expected transaction costs and expected tracking error for future periods. Practically, however, this makes the optimization computationally intensive and difficult to solve. See Kritzman, Myrgren and Page (2009). In the absence of time-varying forecasts of returns, covariances and transac-tion costs, the single-period optimization used here is an effective proxy. We simulated performance of the single-period optimization using the same assumptions of Kritzman et al. and found that single- and multi-period optimizations produce similar tracking error and transaction cost characteristics.

Exhibit 7: Historical Market Volatility and Liquidity

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0 110

100

90

80

70

60

50

40

30

20

10

01985

Cre

dit

Sp

read

s (%

)

Equ

ity

Ris

k (%

)

Equity Risk Credit Spreads

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

Source: Bloomberg. Equity risk based on annualized daily volatility of S&P 500 (12/85–12/89) and VIX (1/90–4/09); Credit spreads based on Barclays Capital U.S. Credit Bond Index.

11Investment Insights—September 2010

12

equities. Similarly, relative asset class transaction costs

can be estimated fairly accurately based on recent

transactions and market quotes. Therefore, despite the

fact that precise volatility estimates are hard to develop,

and correlations can be unstable over time, tracking error

rebalancing produces robust results. In a historical

backtest (described in the Appendix on page 16), we find

that tracking error rebalancing would have produced

efficiency gains relative to fixed band rebalancing in each

of the three stress periods that occurred from 1985

through 2009.

Not only is tracking error rebalancing more efficient, it is

relatively easy to implement and produces intuitive results.

To see how tracking error rebalancing works, we consider

the following simple case study based on market condi-

tions at the beginning of 2009.

Tracking Error Rebalancing Case Study

Consider an investor with a typical 70/30 policy alloca-

tion. If the portfolio began on policy weights at the start of

2008, market moves through the year would have driven

the portfolio to be underweight equities by 10% and

overweight fixed income by 9% by year-end, as illustrated

in Exhibit 8.

Based on updated estimates of asset class volatilities and

correlations, we can calculate the tracking error relative to

the policy associated with these misweights. For example,

volatilities and correlations derived using an exponentially

weighted time series of asset class data with a 12-month

half-life (Exhibit 9) imply an annualized tracking error of

2.3%. Without a view on relative asset class performance,

there is a 1-in-10 chance that the portfolio will underper-

form the policy by 2.9% or more in the following year. This

is significant and highlights the need for rebalancing.

Exhibit 8: Example Portfolio Misfits and Sources of Misfit Risk

Fixed Income

TIPS

Private Equity

Real Estate

US Equity

Non-US Equity

4.3%

0.2%

0.3%

1.9%

54.3%

39.1%

–5.8%

–4.2%

9.3%

1.8%

–0.4%

–0.7%

US Equity

Non-US Equity

Fixed Income

TIPS

Private Equity

Real Estate

Example Portfolio Misfits (%) Sources of Tracking Error

Expected Tracking Error 2.3%

Source: BlackRock

–10 –5 0 5 10

BlackRock

While considering options to reduce risk, it is instructive to

examine the sources of tracking error in the portfolio. This

is illustrated in Exhibit 8. Equities are the largest source of

tracking error, due to their high observed volatility. Despite

the fact that fixed income has a misweight that is two

times as large as US equities, the contribution to tracking

error is less than 5.0%. This foreshadows why a fixed

band rebalancing approach, which focuses only on

misweights and ignores the tracking error implications,

is likely to be inefficient.

We consider three rebalancing options, illustrated in

Exhibit 10:

1. Fixed band rebalancing to +/–3% bands,

2. Tracking error rebalancing trading physicals, and

3. Tracking error rebalancing using derivatives.

An investor using a conventional fixed band rebalancing

policy (option 1) must sell 6.3% of fixed income to get

back within the 3% band and buy the corresponding

amount of equities (5.1% US and 1.2% non-US). This

reduces tracking error by over 50%, from 2.3% to 1.0%.

However, based on asset class transaction cost estimates

consistent with market conditions in 2008–2009 (Exhibit

9), these trades entail an estimated one-time cost of

17.8 bps. This cost, which is about 10 times higher than

typical rebalancing costs in normal markets, is chiefly

driven by the high cost of trading credit and securitized

bonds during the illiquid fixed income markets of 2009.

Alternatively, the investor can use tracking error rebalanc-

ing by determining the cheapest trades required to reduce

tracking error to the desired level (option 2), represented

by the dark blue efficient frontier in Exhibit 10.

Asset Class Policy (%) ExpectedRisk (%) T-Costs (%)

US Equity 45 19.75 0.30

Non-US Equity 20 24.00 0.50

Fixed Income 20 5.25 2.50

TIPS 5 9.75 0.30

Private Equity 5 24.00 N/A

Real Estate 5 37.00 0.30

S&P 500 Futures 19.00 0.10

10-year Treasury Futures 10.25 0.10

Exhibit 9: Input Assumptions for Case Study

13

Correlations US Equity Non-US Equity

FixedIncome TIPS Private

Equity Real Estate S&P 500 Futures

10-yearTreasuryFutures

US Equity 1.00

Non-US Equity 0.95 1.00

Fixed Income 0.15 0.30 1.00

TIPS 0.45 0.55 0.80 1.00

Private Equity 0.95 0.85 0.15 0.45 1.00

Real Estate 0.80 0.70 0.20 0.50 0.90 1.00

S&P 500 Futures 0.99 0.90 0.15 0.45 0.95 0.80 1.00

10-year Treasury Futures 0.00 0.00 0.75 0.50 0.00 0.25 0.00 1.00

Source: BlackRock

Investment Insights—September 2010

14

The frontier is calculated using a mean variance optimiza-

tion similar to that used in asset allocation (the tradeoffs

are between transaction costs and tracking error instead

of expected return and risk). The optimization suggests

that if the investor buys 1.8% US equity, 4.3% non-US

equity and 0.7% REITs, and also sells 6.8% TIPS, the

portfolio would achieve the same tracking error reduction

as option 1 at a fraction of the cost (4.9 bps compared

with 17.8 bps). While the fixed income overweight remains

outside the 3% bands, these transactions reduce the

largest source of tracking error by reducing the equity

underweight, and avoid trades in illiquid fixed income by

funding the equity purchase with TIPS. We find that the

decision to trade TIPS is independent of the correlation

between TIPS and nominal bonds. TIPS are sold because

they are liquid and can fund the equity purchase easily,

not because they represent a proxy for nominal bonds.

Exhibit 10: Rebalancing Options

Option 1

Option 2

CurrentPortfolio

Option 3

–0.20

–0.15

–0.10

–0.05

0.000.00 0.40 0.80 1.20 1.60 2.00 2.40 2.80

Ex

pec

ted

Cos

ts (%

on

e ti

me)

Option 1: Fixed Band Rebalancing to +/–3%Buy 5.1% US equity, 1.2% non-US equitySell 6.3% fixed income

Option 2: Tracking Error Rebalancing Trading PhysicalsBuy 1.8% US equity, 4.3% non-US equity, 0.7% REITsSell 6.8% TIPS

Option 3: Tracking Error Rebalancing Using DerivativesLong 7.8% S&P 500 futuresShort 4.7% 10-yr Treasury futuresSell 3.1% TIPS for cash collateral

–10 –5 0 5 10 –10 –5 0 5 10–10 –5 0 5 10

–4.0%

0.1%

9.3%

–5.0%

–0.4%

0.0%

2.1%

–4.2%

4.5%

–1.3%

–0.4%

–0.7%

–0.7%

–3.0%

3.0%

1.8%

–0.4%

–0.7%

US Equity

Non-US Equity

Fixed Income

TIPS

Private Equity

Real Estate

Option 1: Fixed BandRebalancing to +/–3%

Option 2: Tracking ErrorRebalancing Trading Physicals

Option 3: Tracking ErrorRebalancing Using Derivatives

Option 1 Option 2 Option 3

Costs 17.8 bps 4.9 bps 4.7 bps

Expected Tracking Error (%) 1.0 1.0 1.0

Expected Annual Tracking Error (%)

Source: BlackRock

Misfits Relative to Policy (%) Misfits Relative to Policy (%)Misfits Relative to Policy (%)

BlackRock

15

Our analysis thus far has focused on strategic rebalanc-

ing. The tracking error rebalancing approach also allows

investors to incorporate tactical views in determining

rebalancing trades. Rather than optimizing tracking error

against transaction costs, investors with high-conviction

tactical views would instead optimize tracking error against

expected “alpha” from misweights net of transaction

costs. For example, if an investor in 2009 was convinced

that TIPS would outperform in the months following the

crisis, the optimization would suggest selling nominal

Treasuries or other liquid assets in the portfolio.

Portfolios with limited liquidity can benefit from the use

of derivatives for rebalancing (option 3). Derivatives are

capital efficient and can help investors rebalance their

asset class exposures without buying and selling large

amounts of physical assets. The derivatives market is also

typically liquid and provides tremendous flexibility in

controlling asset class misweights. The light blue efficient

frontier in Exhibit 10 illustrates how trading just two

simple futures—the S&P 500 and 10-year Treasury—can

reduce the largest sources of tracking error. By taking a

7.8% long position in S&P 500 futures and 4.7% short

position in 10-year Treasury futures, while selling 3.1% of

TIPS for margin requirements, the investor can achieve

the same tracking error reduction as option 1 at a much

lower cost.

Tracking Error Rebalancing: Sometimes or All the Time?

Our analysis demonstrates that investors can benefit

from switching to tracking error rebalancing in stressed

market conditions. Should investors also use it as the

core rebalancing philosophy? While tracking error

rebalancing produces a more modest improvement in

normal market conditions, this approach can have three

important advantages. First, the tracking error rebalanc-

ing framework can provide guidance for liquidity

management. When investors are looking for liquidity

and considering trade options, tracking error and

transaction costs should be the key decision factors.

Second, it can help investors monitor the risk exposures

of their portfolio and flag large sources of tracking error.

Finally, it may provide investors with the flexibility to

make opportunistic asset allocation trades without being

constrained by fixed asset class bands. This flexibility

may yield higher returns for skillful investors, without

increasing portfolio tracking error. Tracking error rebal-

ancing is based on a core philosophy of optimizing risks,

returns and costs. Since most investment problems

incorporate these elements at some level, it can be a

valuable addition to a plan’s asset allocation toolbox.

ConclusionsMost discussions on rebalancing tend to focus on rebal-

ancing levers such as size of rebalancing bands and

whether to trade all the way back to target or not. While

there are modest differences across rebalancing levers,

overall, typical rebalancing policies are effective and

control tracking error inexpensively in most markets. In

normal markets, what matters most is designing a rebal-

ancing policy that is consistent with the investor’s ability

to tolerate tracking error and then sticking with it.

The choice of rebalancing policy becomes significant in

stressed markets. Investors who use a tracking error

rebalancing approach (or build in the flexibility to switch

to tracking error rebalancing in stressed markets) can

rebalance effectively despite higher volatility and illiquidity.

This requires investors to change their mind-set to focus on

risk rather than misweights, and to adopt a new approach

for determining rebalancing trades. As we saw in 2009, a

systematic process for analyzing rebalancing trades can go

a long way toward improving plan performance.

Investment Insights—September 2010

16

AppendixWe use a historical backtest13 to examine the sensitivity

of tracking error rebalancing to forecast errors in asset

class volatilities and correlations. Three stress periods

are evaluated, defined by elevated volatilities and credit

spreads: the market crash of 1987 (10/87–9/89), the

dot-com crash (02/01–12/03) and the credit crisis

(01/08–09/09). We compare the performance of

tracking error rebalancing with a fixed band rebalancing

policy that has 3.0% equal bands across all public asset

classes. The policy weights are taken from Exhibit 1. In

each case, we assume that the portfolio begins on policy

at the beginning of the period.

In the fixed band approach, we trigger a rebalance if any

asset class breaches the 3.0% fixed band, and continue

to rebalance the portfolio throughout the stress period

as needed. In the tracking error approach, we monitor

the portfolio tracking error based on an exponentially

weighted covariance matrix that has a 12-month half-life

using monthly data. To facilitate a comparison, we only

begin the rebalancing in the same month that the fixed

band policy first rebalances, and we calculate the lowest-

cost trades required to bring down the tracking error to

the same level as with fixed band rebalancing after its

trades. In other words, the tracking error trigger is simply

the tracking error of the fixed band rebalanced portfolio

after its first trade.

We continue to monitor the portfolio tracking error and

calculate lowest-cost trades based on this tracking error

trigger. Since historical transaction cost data are not

readily available, we assume that the transaction costs

in each of the stressed periods are equal and consistent

with the costs we observed during the 2008 credit crisis

(see Exhibit 9).

The graph below tabulates the realized tracking error

and total realized transaction costs in each stress

period. It illustrates that tracking error rebalancing would

have been more efficient than fixed band rebalancing in

each of the periods, providing lower transaction costs

at similar or lower realized tracking error levels. The

magnitude of improvement was the highest during the

2008 credit crisis, when the dislocations were severe

and prolonged. The improvement in efficiency was less

during the 1987 market crash, when the market recov-

ered soon after and conditions improved.

Tota

l Rea

lize

d T-

Cos

ts (%

)

Realized Annualized Tracking Error (%)

Fixed Band Rebalancing

Tracking Error Rebalancing

–0.40

–0.35

–0.30

–0.25

–0.20

–0.15

–0.10

–0.05

0.000.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Credit Crisis(2008–2009)

Dot-Com Crash(2001–2003)

Stock Market Crash (1987–1989)

13 We used the historical returns of Russell 3000, MSCI World ex-US, Barclays Capital US Aggregate, Barclays Capital US TIPS, Russell 2000 and FTSE US NAREIT indexes to represent the US equity, non-US equity, fixed income, TIPS, private equity and real estate asset classes respectively.

BlackRock

17

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ing: Why? When? How Often?” The Journal of Investing 2,

no. 1 (Spring).

Brown, David T., Gideon Ozik, and Daniel Scholz. 2007.

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Analysts Journal 63, no. 5 (September/October).

Donohue, Christopher, and Kenneth Yip. 2003. “Optimal

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Grinold, Richard C., and Ronald N. Kahn. 2000. Active

Portfolio Management. 2nd ed. New York: McGraw-Hill.

Kritzman, Mark, Simon Myrgren and Sebastien Page. 2009.

“Optimal Rebalancing: A Scalable Solution.” Journal of

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Leibowitz, Martin, and Anthony Bova. 2010. “Policy

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Portfolio Strategy Note, March 3. New York: Morgan

Stanley Research North America.

Leland, Hayne E. 2000. Optimal Portfolio Implementation

with Transactions Costs and Capital Gains Taxes. Unpub-

lished manuscript, Haas School of Business, University of

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Masters, Seth. 2003. “Rebalancing.” The Journal of

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Investment Insights—September 2010

Investment InsightsPublished by BlackRock

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