This document discusses asset allocation perspectives under changing market conditions. It provides an analysis of average returns, volatilities, and correlations for various asset classes over different time periods from 2003-2014. Benchmark Implied Returns (BIR) are also estimated for different periods, which show how implied returns for asset classes vary as volatilities and correlations change. The analysis finds that higher volatility assets require higher returns to justify inclusion in a portfolio, while assets with better diversification potential require lower returns. The BIR estimates provide a reality check on return assumptions used by investors when deviating from benchmark weights.

1. ASSETALLOCATION
PERSPECTIVES UNDER CHANGING
CONDITIONS
ERIC J. WEIGEL
February 2015
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2. Motivation
• Asset allocation is the most important decision that investors face both in terms of
determining the risk as well as the long-term return of their portfolio
• Much of the daily news flow in the capital markets is specific to an asset class (with an
overwhelming focus on equities) and short-term in nature yet sound asset allocation
decisions require an integrated perspective on the long-term prospects and risks facing the
major asset categories
• Therefore, arriving at an asset allocation strategy that properly balances risk and return
prospects of the major asset classes in the context of ever-evolving capital markets is of
great importance to investors
• For a significant segment of investors, the starting and ending point of their allocation
process is an assessment of expected returns. Frequently only lip service is paid to asset
class risks and correlations
• Assessing prospective asset class returns is important, but not sufficient when dealing with
changing levels of risk and asset class inter-relationships
• In this note we provide investors unaccustomed to incorporating changing asset class risks
and correlations an approach that effectively summarizes such effects into a metric
expressed in the more commonly used language of returns
• We refer to this metric as Benchmark Implied Returns (BIR)
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3. Methodology
• We include ten categories of investments in our benchmark
• Equities: US Large Cap (30%), US Small Cap (10%), International Developed (15%), Emerging
(5%)
• Fixed Income: US Bonds (25%), International Developed (5%), Emerging (0%)
• Alternatives: Commodities (5%), Real Estate (5%)
• Cash (0%)
• We use monthly return data to estimate average returns, volatilities and
correlations over the 2003-2014 period
• Given our asset classes and the benchmark weights we calculate
Benchmark Implied Returns (BIR)
• In general, more volatile and highly correlated asset classes require higher Implied Returns
• Conversely, lower volatility assets with low correlations to other assets exhibit lower Benchmark
Implied Returns
• For purposes of interpretability we scale our BIR estimates to a benchmark return of 8% per year
and a risk-free rate of 0.5%
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4. Benchmark Implied Returns (BIR)
• Idea borne out of the mean/variance framework whereby “optimal” portfolio
allocations are found by maximizing expected returns with respect to risk
• However, instead of searching for the “optimal” asset class weights we reverse engineer the process,
apply the benchmark weights as given, and solve for those returns implied by the benchmark
• Specifically, we use asset class volatilities and correlations along with the benchmark weights to find
the implied asset class returns
• As asset class volatilities and correlations change so do the implied returns
• We assume that the status quo position for an investor is the benchmark. Any asset
class deviations from the benchmark should only be justified by return assumptions
significantly at odds with the Benchmark Implied Returns
• The BIR estimates serve as an “anchor” or “reality” check to investor return
assumptions that may ignore the effects of changing volatilities and correlations. In
general,
• As an asset becomes more volatile relative to others, the implied returns should increase
• As an asset becomes less correlated, the implied returns should decrease
• BIR estimates are specific to the benchmark and scaled to a long-term expected return
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5. LOOKINGAT CHANGING AVERAGE RETURNS,
VOLATILITIESAND CORRELATIONS
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An Analysis of Three Year
Calendar Returns
2014-2003

6. 6
MEAN 1.59% 1.55% 0.99% 0.43% -0.76% 1.34% 0.18% -0.22% 0.46% 0.02%
STD DEV 2.63% 3.84% 3.80% 4.39% 3.66% 3.84% 1.45% 1.53% 2.22% 0.00%
CORRELATIONS
201412-201201 US LCAP US SCAP INTL EQ EM EQ COMM RE US BD INTL BD EM BD CASH
US LCAP 1 0.83 0.79 0.67 0.49 0.45 -0.17 0.21 0.47 0.07
US SCAP 0.83 1 0.63 0.56 0.38 0.43 -0.15 0.24 0.25 0.10
INTL EQ 0.79 0.63 1 0.81 0.61 0.44 -0.10 0.43 0.67 0.21
EM EQ 0.67 0.56 0.81 1 0.54 0.44 0.05 0.48 0.72 0.22
COMM 0.49 0.38 0.61 0.54 1 0.24 -0.07 0.50 0.52 0.22
RE 0.45 0.43 0.44 0.44 0.24 1 0.42 0.47 0.60 0.06
US BD -0.17 -0.15 -0.10 0.05 -0.07 0.42 1 0.42 0.41 0.00
INTL BD 0.21 0.24 0.43 0.48 0.50 0.47 0.42 1 0.59 0.20
EM BD 0.47 0.25 0.67 0.72 0.52 0.60 0.41 0.59 1 0.23
CASH 0.07 0.10 0.21 0.22 0.22 0.06 0.00 0.20 0.23 1
MEAN 1.25% 1.48% 0.86% 1.81% 0.66% 2.05% 0.49% 0.44% 1.26% 0.02%
STD DEV 5.48% 7.32% 6.57% 7.54% 5.30% 9.27% 2.12% 2.72% 2.05% 0.01%
CORRELATIONS
201112-200901 US LCAP US SCAP INTL EQ EM EQ COMM RE US BD INTL BD EM BD CASH
US LCAP 1 0.95 0.93 0.86 0.70 0.84 -0.26 0.49 0.61 0.17
US SCAP 0.95 1 0.85 0.82 0.62 0.85 -0.35 0.30 0.56 0.16
INTL EQ 0.93 0.85 1 0.90 0.74 0.81 -0.30 0.61 0.71 0.24
EM EQ 0.86 0.82 0.90 1 0.76 0.71 -0.32 0.51 0.79 0.40
COMM 0.70 0.62 0.74 0.76 1 0.48 -0.26 0.59 0.52 0.10
RE 0.84 0.85 0.81 0.71 0.48 1 -0.16 0.41 0.63 0.13
US BD -0.26 -0.35 -0.30 -0.32 -0.26 -0.16 1 0.33 -0.03 -0.12
INTL BD 0.49 0.30 0.61 0.51 0.59 0.41 0.33 1 0.62 0.03
EM BD 0.61 0.56 0.71 0.79 0.52 0.63 -0.03 0.62 1 0.36
CASH 0.17 0.16 0.24 0.40 0.10 0.13 -0.12 0.03 0.36 1
Directionally these two correlation structures are similar, but the specific estimates can exhibit large
changes from period to period.
The average returns and volatilities show even greater variability from period to period.

7. MEAN -0.62% -0.54% -0.43% -0.05% -0.53% -0.55% 0.84% 0.77% 0.17% 0.37%
STD DEV 4.41% 5.81% 5.64% 8.39% 6.59% 8.90% 2.05% 2.36% 3.38% 0.11%
CORRELATIONS
200812-200601 US LCAP US SCAP INTL EQ EM EQ COMM RE US BD INTL BD EM BD CASH
US LCAP 1 0.91 0.91 0.82 0.41 0.76 -0.25 -0.12 0.71 0.30
US SCAP 0.91 1 0.82 0.75 0.34 0.84 -0.29 -0.09 0.66 0.12
INTL EQ 0.91 0.82 1 0.95 0.56 0.65 -0.14 0.11 0.75 0.26
EM EQ 0.82 0.75 0.95 1 0.61 0.55 -0.15 0.12 0.69 0.27
COMM 0.41 0.34 0.56 0.61 1 0.28 -0.10 0.18 0.44 0.25
RE 0.76 0.84 0.65 0.55 0.28 1 -0.14 0.10 0.64 0.08
US BD -0.25 -0.29 -0.14 -0.15 -0.10 -0.14 1 0.67 0.39 -0.27
INTL BD -0.12 -0.09 0.11 0.12 0.18 0.10 0.67 1 0.37 -0.08
EM BD 0.71 0.66 0.75 0.69 0.44 0.64 0.39 0.37 1 -0.02
CASH 0.30 0.12 0.26 0.27 0.25 0.08 -0.27 -0.08 -0.02 1
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MEAN 1.16% 1.77% 1.87% 2.82% 1.47% 2.07% 0.25% 0.52% 1.26% 0.17%
STD DEV 2.65% 4.42% 3.34% 4.81% 4.12% 4.49% 1.91% 2.34% 2.17% 0.09%
CORRELATIONS
200512-200301 US LCAP US SCAP INTL EQ EM EQ COMM RE US BD INTL BD EM BD CASH
US LCAP 1 0.88 0.84 0.74 0.08 0.45 -0.10 0.20 0.28 -0.11
US SCAP 0.88 1 0.73 0.73 0.11 0.51 -0.14 0.16 0.21 -0.13
INTL EQ 0.84 0.73 1 0.82 0.25 0.38 0.00 0.39 0.35 -0.04
EM EQ 0.74 0.73 0.82 1 0.37 0.46 -0.04 0.20 0.39 0.06
COMM 0.08 0.11 0.25 0.37 1 -0.08 0.03 0.11 0.10 -0.03
RE 0.45 0.51 0.38 0.46 -0.08 1 0.30 0.47 0.44 -0.11
US BD -0.10 -0.14 0.00 -0.04 0.03 0.30 1 0.60 0.75 0.02
INTL BD 0.20 0.16 0.39 0.20 0.11 0.47 0.60 1 0.59 -0.25
EM BD 0.28 0.21 0.35 0.39 0.10 0.44 0.75 0.59 1 -0.03
CASH -0.11 -0.13 -0.04 0.06 -0.03 -0.11 0.02 -0.25 -0.03 1
The average returns during the 2008-2006 period are all negative for riskier asset classes and the
volatilities are several magnitudes higher compared to the 2005-2003 period

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201412-201201 US LCAP US SCAP INTL EQ EM EQ COMM RE US BD INTL BD EM BD CASH
US LCAP
US SCAP -0.12
INTL EQ -0.13 -0.22
EM EQ -0.19 -0.27 -0.09
COMM -0.22 -0.24 -0.13 -0.22
RE -0.40 -0.42 -0.37 -0.27 -0.24
US BD 0.09 0.20 0.21 0.37 0.18 0.58
INTL BD -0.28 -0.06 -0.18 -0.02 -0.09 0.05 0.09
EM BD -0.14 -0.31 -0.04 -0.06 0.00 -0.03 0.45 -0.03
CASH -0.10 -0.06 -0.03 -0.17 0.13 -0.07 0.13 0.17 -0.13
Comparing the last three years to the 2011-2009 period shows significant drops in volatility,
lower average monthly returns for most asset classes, significant drops in correlation
among equity markets and commensurate increases in correlation within fixed income
Changing asset class return prospects, volatilities and correlations imply different target
asset allocation weights

9. Benchmark Implied Return Estimation
• The BIR estimates assume a benchmark portfolio return of 8% and a
0.5% risk-free rate for each period (all of our estimates are scaled to
these numbers which admittedly are arbitrary)
• The benchmark weights are held static over our whole sample, but the
asset class volatilities and correlations are estimated over three-year
calendar windows
• Differences in Benchmark Implied Returns are solely a function of
changing asset class volatilities and correlations
• As illustrated by the previous correlation and volatility displays, changing
asset allocation conditions represent the norm
• At a minimum changing volatility and correlation conditions suggest
exploring potential commensurate changes in asset mix weights
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10. Benchmark Implied Returns estimated over four distinct periods show
that, in general, higher volatility assets require higher returns and assets
with superior diversification potential require lesser returns
Considerable variability in implied returns exists across time periods as
volatilities and correlations change dynamically
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11. Insights Gained
• Given the lower volatility and low correlation of bonds relative to
equities it is not surprising to see low implied returns to fixed income
• What this means is that the hurdle rate for including fixed income at benchmark
weights is significantly lower than that of equities
• As the volatility of fixed income increases and its diversification
capabilities diminish, the implied returns must increase thus requiring
higher hurdle rates for benchmark weighted fixed income positions
• This has been the situation over the last few years as equity market volatility has
dropped significantly more than that of fixed income markets and correlations
between stocks and especially US bonds have risen
• The Benchmark Implied Returns are useful as reality check on the
assumptions used by active managers to deviate from benchmark
weights
• Over-weight positions in an active portfolio should be associated with manager
views of prospective relative asset class returns higher than those corresponding to
the estimated relative implied returns ( as a reminder, our estimates are scaled to a
benchmark return of 8%)
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12. Insights Gained
• Not surprisingly the benchmark implied returns to emerging market
equities and real estate are high given their above-average volatility and
high correlations to equities
• The volatility of real estate has been quite variable over these three year
periods as have correlations to equities and bonds resulting in big
jumps in Benchmark Implied Returns
• Using the most recent three year period, the implied returns to real estate are only slightly
higher than those of US large cap equities
• Lastly, the implied returns of commodities clearly illustrate their
changing volatility and correlation structure especially in relation to
equities
• As commodities have become more mainstream their diversification benefits have
diminished significantly resulting in higher implied returns for benchmark allocations
• Higher hurdle rates are necessary under current capital market conditions for
considering commodity allocations
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13. Summary
• A significant portion of investors ignore the effects of changing
volatilities and correlations in constructing asset allocation
portfolios
• While a focus on estimating expected asset class returns is a key component of any
strategy, it is insufficient in the face of ever evolving and changing capital markets
• Moreover, the hurdle rate for including an asset in a portfolio should vary with its
volatility and diversification ability
• Constructing portfolios simply based on including the highest expected return assets
is most likely to lead to much higher volatility portfolios and by-pass clear
diversification opportunities
• We believe that as capital market conditions change so should
target asset class weights
• One way to adjust to changing asset class volatilities and correlations is to anchor
one’s expectations around Benchmark Implied Returns
• Variability in asset class volatilities and correlations remains the norm in capital
markets and asset allocation strategies should incorporate such changing conditions
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14. FOR FURTHER INFORMATION ON OUR
RESEARCH PRODUCTSAND/OR ASSET
MANAGEMENT STRATEGIES PLEASE
CONTACT:
Eric J. Weigel at eweigel@gf-cap.com
617-529-2913
www.gf-cap.com
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