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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 [email protected]
Russ Koesterich415 670 2576 phone415 618 1875 [email protected]
EDITOR
Marcia Roitberg850 893 8586 phone415 618 1455 [email protected]
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.
Nu
mb
er o
f p
lan
s
0
5
10
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.
Nu
mb
er o
f p
lan
s
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.
Nu
mb
er o
f p
lan
s
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
rage
An
nu
al T
ran
sact
ion
Cos
ts (%
)
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
rage
An
nu
al T
ran
sact
ion
Cos
ts (%
)
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
rage
An
nu
al T
ran
sact
ion
Cos
ts (%
)
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
Ave
rage
An
nu
al T
ran
sact
ion
Cos
ts (%
)
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
rage
An
nu
al T
ran
sact
ion
Cos
ts (%
)
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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Investment Insights—September 2010
Investment InsightsPublished by BlackRock
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