Fulcrum Research Papers – October 2012 Risk Parity Portfolios: A Practitioner’s Guide Suhail Shaikh, CFA and Athanasios Bolmatis, PhD At the core of most pension fund investment portfolios is an allocation to equities and government bonds, with risk typically dominated by the former. Recognizing this lack of diversification, some plans have moved to a more balanced risk allocation by directly adopting a risk budget based approach or by allocating to externally managed risk parity funds. At Fulcrum, we have been building risk parity portfolios for many years, and this paper summarises our approach, along with the key lessons we have learned. Risk parity portfolios have generally outperformed equity/bond balanced portfolios in Sharpe ratio terms over the past two decades, and this has continued to be the case since the financial market shocks in 2008. In this paper, we comment on the selection of assets to include in risk parity portfolios, their performance, the appropriate treatment of volatility and correlations in building these portfolios, and the relationship between risk parity portfolios and traditional portfolios. We believe that the risk parity approach represents a valuable addition to traditional investment management techniques, especially if risk parity portfolios are combined with alpha seeking trading strategies, and are hedged against severe losses using a permanent options based overlay. We will analyse these alpha generators, and hedging strategies, in future research papers.
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Fulcrum Research Papers – October 2012
Risk Parity Portfolios: A Practitioner’s Guide
Suhail Shaikh, CFA and Athanasios Bolmatis, PhD
At the core of most pension fund investment portfolios is an allocation to equities and
government bonds, with risk typically dominated by the former. Recognizing this lack
of diversification, some plans have moved to a more balanced risk allocation by directly
adopting a risk budget based approach or by allocating to externally managed risk
parity funds.
At Fulcrum, we have been building risk parity portfolios for many years, and this paper
summarises our approach, along with the key lessons we have learned. Risk parity
portfolios have generally outperformed equity/bond balanced portfolios in Sharpe ratio
terms over the past two decades, and this has continued to be the case since the
financial market shocks in 2008. In this paper, we comment on the selection of assets
to include in risk parity portfolios, their performance, the appropriate treatment of
volatility and correlations in building these portfolios, and the relationship between
risk parity portfolios and traditional portfolios.
We believe that the risk parity approach represents a valuable addition to traditional
investment management techniques, especially if risk parity portfolios are combined
with alpha seeking trading strategies, and are hedged against severe losses using a
permanent options based overlay. We will analyse these alpha generators, and hedging
strategies, in future research papers.
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 2
Introduction
Risk parity1 portfolios have delivered strong returns over the past twenty years, with a
Sharpe ratio that has been higher than traditional portfolios of equities and bonds.
Figure 1: Historical Excess2 Performance (Jan-93 to Sep-12)
Figure 2: Cumulative Excess Performance Since 1993
1 In Figures 1 to 4, we include the following premia in the risk parity portfolio: Equity Premium, Bond Premium, EM $ Debt Spreads, High Yield Spreads, Commodity Beta, Emerging Equities (EM - DM), Equity Style (Value - Growth), Equity Size (Small - Large), Fixed Income Carry, Commodity Carry, Developed Market Currency Carry and Emerging Market Currency Carry. 2 Performance is expressed on an unfunded basis, i.e. without including the return on cash.
Even since the financial crisis began in early 2007, risk parity portfolios have continued
to generate attractive risk-adjusted returns.
Figure 3: Historical Excess Performance (Jan-07 to Sep-12)
Figure 4: Cumulative Excess Performance Since 2007
In our opinion, it is likely that risk parity portfolios will continue to outperform
traditional portfolios over the long term, but there are many issues related to their
construction that need to be carefully addressed.
Equities Bonds 60/40 Risk Parity
Annual Excess Return -2% 4% 1% 7%
Volatility 17% 3% 10% 8%
Sharpe Ratio -0.1 1.3 0.1 0.9
Correlation with:
Equity Premium 0.9 -0.1 0.9 0.5
Bond Premium -0.4 0.8 -0.3 -0.1
Equity/Bond 0.4 0.7 0.5 0.3
Source: Fulcrum Asset Management
Global Equities
Global Bonds
GlobalBalanced
60/40
Risk Parity
50
60
70
80
90
100
110
120
130
140
150
Dec-06 Dec-07 Dec-08 Dec-09 Dec-10 Dec-11 Dec-12
Source: Fulcrum Asset Management
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 4
The philosophy behind risk parity
At its core, the risk parity approach to asset allocation seeks to improve diversification
versus traditional portfolios of equities and bonds. More specifically, its philosophy can
be summarised as follows:
Maximise diversification at each point in time by equalising risk across a
variety of return sources, each of which has a positive expected Sharpe ratio and
a less than perfect correlation with other return sources; and
Maximise diversification through time by maintaining a relatively stable
volatility profile that prevents long-term performance being overly dependent
on periods of high volatility.
Under the assumption that all investments offer the same risk-adjusted return, the
optimal portfolio is one that equalises risk across investments. This portfolio represents
the special case of risk parity within a broader risk budgeting framework. Approaches
that maintain a focus on risk contributions but deviate from risk parity – for example
based on differences in expected Sharpe ratios – are more accurately described as risk
budget portfolios. Our approach to risk parity falls into this latter category.
The issues addressed in this paper
The paper outlines our thoughts on the following questions that are of interest to risk
parity investors:
Which risk premia do you include in risk parity portfolios?
How have these risk premia performed historically?
Are you confident these risk premia will perform in the future?
Which risk premia do you exclude?
How does volatility targeting impact return distributions?
Can you control the volatility of your risk parity portfolio?
What correlations do you assume between the premia?
How correlated are risk parity portfolios with equities and hedge funds?
How have portfolios of risk premia performed historically?
What are the main pitfalls of risk parity approaches?
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 5
Which risk premia do you include in risk parity portfolios?
Risk parity based portfolio construction techniques can be used to combine a wide
variety of investments, including risk premia – both traditional and alternative – as
well as alpha strategies. At Fulcrum we focus on liquid risk premia. These can be
classified in many ways, including by asset class, economic regime and the need for
leverage.
In the table below, we classify risk premia as either traditional, which are typically
present in long only portfolios, or alternative, which form the building blocks of many
hedge fund portfolios.
Figure 5: The Liquid Risk Premia
The main criteria on which we judge whether these return sources should be included
in risk parity portfolios are as follows:
Have they provided positive Sharpe ratios historically?
Do they offer a genuine risk premium?
Do they exploit a behavioural anomaly?
Do they provide diversification benefits to portfolios dominated by equity risk?
Asset Class
Traditional (Long Only)
1 Equity Premium Equity
2 Bond Premium Fixed Income
3 EM $ Debt Spreads Fixed Income
4 High Yield Spreads Fixed Income
5 Commodity Beta Commodity
Alternative (Long Short)
6 Emerging Equities (EM - DM) Equity
7 Equity Style (Value - Growth) Equity
8 Equity Size (Small - Large) Equity
9 Fixed Income Carry Fixed Income
10 Commodity Carry Commodity
11 Developed Market Currency Carry Currency
12 Emerging Market Currency Carry Currency
13 Volatility Equity & FI
Return Source
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 6
How have these risk premia performed historically?
Figure 6 shows the realised Sharpe ratio from October 1997 to September 2012 for each
of the risk premia listed in Figure 5, as well as a more recent period beginning in 2007.
Due to data limitations, the volatility premium has been excluded from this analysis3.
Figure 6: Realised Sharpe Ratios
The key highlights are as follows:
Over the full sample period, all risk premia have generated positive Sharpe
ratios, with the exception of the equity style premium.
The long term performance of credit premia (high yield bonds and emerging
market debt) is disappointing, especially given the fall in credit spreads and
high yields offered by these assets. (We explain some of the reasons behind this
later.)
The bond, fixed income carry and commodity carry premia have performed best
and most consistently.
3 The volatility premium has a very high historical Sharpe ratio. However, the Sharpe ratio can be a misleading way of evaluating short volatility strategies.
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Eq
uity P
rem
ium
Bo
nd
Pre
miu
m
EM
$ D
eb
t
Hig
h Y
ield
Co
mm
od
ity B
eta
EM
-DM
Eq
uitie
s
Eq
uity S
tyle
Eq
uity S
ize
FI C
arr
y
Co
mm
od
ity C
arr
y
DM
FX
Ca
rry
EM
FX
Ca
rry
Oct-97 to Sep-12
Jan-07 to Sep-12
Source: Fulcrum Asset Management
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 7
Risk-adjusted returns delivered by currency carry premia have dropped versus
their prior history, but remain positive.
Since 2007, only the equity and equity style premia have generated negative
Sharpe ratios.
Are you confident these risk premia will perform in the future?
Identifying genuine risk premia is a challenging exercise that requires judgement. Of
the thirteen premia listed in Figure 5, we are confident that ten will compensate
investors for assuming specific forms of risk, such as real interest rates, inflation,
default, growth and insurance (see Figure 20). The remaining three premia exploit
behavioural biases, for example those that stem from leverage aversion (currency carry
premia) or information asymmetry (equity size premium).
Although we believe that all thirteen premia have a valuable role within liquid risk
parity portfolios, our confidence in three of the premia is slightly lower than in the
others. As a result, we deviate from strict risk parity and allocate moderately lower risk
budgets to them. These risk premia are as follows:
Commodity beta; by investing in commodity futures it is possible to gain
exposure to changes in commodity spot prices and the return associated with
carry, which relates to potential gains made from owning commodities for
which forward prices are lower than current spot prices. Over the very long
term, returns from commodity futures have been dominated by the carry return
while spot prices have generally provided an insignificant contribution,
especially in real terms. Currently, most commodities are in contango (forward
prices are higher than current spot prices), which puts a downward bias on the
return to commodity futures and reduces our confidence in this source of
returns. Nevertheless, we include commodities in risk parity portfolios, given
the likely diversification they will provide (versus equities and bonds) if
agricultural or energy commodities suffer from supply shocks.
Equity style; the recent underperformance of value stocks could signify the
erosion of a historic behavioural anomaly that has seen value stocks outperform
growth stocks over many decades. Alternatively, it may represent a highly
attractive opportunity for mean reversion. Given the robust performance of this
premium over the very long term, we still believe this risk premium belongs in
risk parity portfolios. However, we are investigating ways of broadening the
value premium across other asset classes.
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 8
Developed market currency carry; with interest rates close to zero across most
developed economies, higher yielding carry currencies offer only a marginal
yield pick-up versus lower yielding funding currencies. At the same time, the
former are generally more overvalued. Although we expect developed market
currency carry to generate a positive Sharpe ratio, our confidence in this
potential return source is lower than it has been historically. Meanwhile,
emerging market currency carry strategies continue to be underpinned by
significant interest rate differentials between currencies, giving us relatively
more confidence in the potential returns from this risk premium.
Which risk premia do you exclude?
In our risk parity portfolios, we include all suitable liquid risk premia. There are,
however, several risk premia that offer compensation for investing in illiquid assets,
such as convertible bonds, commercial mortgage backed securities (CMBS) and event
driven strategies. While it may be logical for long-term investors to allocate part of their
portfolios to these assets and extract the illiquidity premia, we exclude them for a
number of reasons:
First, risk parity approaches require regular rebalancing to reflect changes in
volatility forecasts; as volatility forecasts rise, positions are typically reduced
and vice versa. Rebalancing exposures can be challenging if investments are
made in illiquid assets that cannot be readily liquidated, as was the case during
the financial crisis.
Secondly, illiquid assets can behave in highly unpredictable ways during periods
of market turmoil, when liquidity typically dries up. In order to capture the
liquidity premium, investors need to be willing to provide liquidity during these
times, i.e. not reduce positions in line with the surge in volatility. A risk parity
approach, however, is biased towards selling assets at exactly the time when the
liquidity premium is at its highest4.
Finally, our risk parity approach offers high liquidity to investors, which makes
it unsuitable for the fund to invest in any illiquid return streams that would
create a dangerous liquidity mismatch.
4 While the related problem of buying high and selling low applies to all assets within a risk parity portfolio (since volatility typically rises after price declines, and vice versa), it has historically been of much less significance to liquid premia. In addition, this problem can be moderated for liquid assets through option based hedging strategies, which we utilize in all of our risk parity portfolios. It is much more difficult to hedge illiquidity risk.
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 9
How does volatility targeting impact return distributions?
If we ignore the impact of correlations, it is possible to construct a risk parity portfolio
by allocating a weight to each premium that is inversely proportional to its forecasted
volatility, thereby allocating each premium with an equal risk budget5. This process of
volatility targeting helps normalise return distributions for most premia since dynamic
(real-time) volatility forecasts are generally better at estimating future volatility than
static (long-term) forecasts, which do not reflect changing market conditions. In
addition, it also tends to improve risk-adjusted returns. The main driver behind these
improvements relates to better diversification; volatility targeting allows risk premia
(and portfolios) to be more diversified through time, i.e. equally influenced by periods
of high and low volatility. In contrast, static volatility assumptions tend to result in
portfolios that are disproportionately dependent on market outcomes during periods of
high volatility.
Figure 7: Monthly Return Distribution of S&P 500 Index Futures
5 An equivalent approach is to first scale each asset (using leverage or cash) such that it targets the same level of risk and then allocate fixed weights across them. If the premia’s volatility is below the target, as tends to be the case with the bond premium, for example, leverage can be used to achieve the volatility target. On the other hand, if the premia’s volatility is above the target, as tends to be the case for the commodity premium, for example, exposure can be cut in favour of cash to reduce volatility.
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
-18% -14% -10% -6% -2% 2% 6% 10% 14% 18%
S&P 500 Index Return, without Volatility Target
S&P 500 Index Return, with 8% Volatility Target
Source: Fulcrum Asset Management
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 10
For example, Figure 7 shows the distribution of monthly returns for S&P 500 Index
futures, both before and after volatility targeting. To target 8% volatility, we use
standard volatility estimates (σ) that are based on recent realised returns and allocate a
weight (w) to the S&P 500 Index, such that w*σ = 8%6. As can be seen, adopting a
volatility target for the S&P 500 Index has historically improved skewness (the
distribution is less negatively skewed) and kurtosis (the distribution is less fat-tailed).
In addition, it has also increased the Sharpe ratio from 0.3 to 0.5.
Figure 8 goes on to show how the volatility of returns for the S&P 500 Index is also
much more stable after a volatility targeting approach has been adopted. Again, similar
results can be shown for the majority of risk premia listed in Figure 5, including all the
alternative risk premia.
Figure 8: 3 Year Realised Volatility of S&P 500 Index Futures
The only notable exceptions are with credit premia, such as high yield corporate bonds
and emerging market debt. Here, estimating volatility is a much more challenging task.
6 This is the methodology used in constructing the risk premia component of Fulcrum Alternative Beta Plus (FAB+). For example, if the volatility estimate for the S&P 500 Index is 20% at the beginning of a month, we invest 40% in the S&P 500 Index future and generate 40% of its return for that month. Correspondingly, if the volatility estimate is 10%, we invest 80% in the S&P 500 Index future.
S&P 500 Index Futures, without Volatility Target
S&P 500 Index Futures, with 8% Volatility Target
0%
5%
10%
15%
20%
25%
1995 1997 1999 2001 2003 2005 2007 2009 2011
Source: Fulcrum Asset Management
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 11
Approaches that use realised volatility as a guide to future volatility have tended to
worsen the overall return distribution (Figure 9) and done little to stabilise the overall
volatility profile. This is because they tend to be over exposed to credit before the onset
of financial panics (reflecting artificially depressed volatility levels) and under exposed
during the ensuing recovery (reflecting the sharp rise – often by many multiples – in
realised volatility levels). The implication is that applying standard risk budget
approaches to credit premia can result in a tendency to buy high and sell low.
Figure 9: Monthly Return Distribution of US High Yield Corporate Bonds
Overall, volatility targeting helps normalise return distributions and improve risk-
adjusted returns for all premia listed in Figure 5, except for the credit premia.
Importantly, once these (normalised) premia have been combined into a risk parity
portfolio, the overall portfolio’s return distribution and risk-adjusted returns are also
improved.
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
-18% -14% -10% -6% -2% 2% 6% 10% 14% 18%
US High Yield Index Return, without Volatility Target
US High Yield Index Return, with 8% Volatility Target
Source: Fulcrum Asset Management
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 12
Can you control the volatility of your risk parity portfolio?
Risk parity approaches, especially those consisting of many uncorrelated premia, tend
to result in stable realised volatility profiles. In order to illustrate this, we create four
risk parity portfolios using the premia listed in Figure 5 (each with a volatility of 8%):
1. Bond and equity risk premia only (“BERP”);
2. All traditional risk premia (“TRP”);
3. All alternative risk premia (“ARP”); and
4. All risk premia (“RP”).
When constructing these portfolios, we size allocations such that each premium
contributes the same level of risk under the assumption of perfect correlation.
Figure 10: 3 Year Volatility of Risk Parity Portfolios (BERP, TRP, ARP and RP)
As can be seen in Figure 10, TRP, ARP and RP have all delivered relatively stable
realised volatility profiles that are generally close to the 8% target. The two asset BERP
portfolio has seen a less stable volatility profile, reflecting the unstable correlation
between equities and bonds. Overall, however, the volatility of diversified risk parity
portfolios can be controlled effectively.
Equity/Bond (BERP)
Traditional (TRP)Alternative
(ARP)
All Risk Premia (RP)
4%
5%
6%
7%
8%
9%
10%
11%
12%
1995 1997 1999 2001 2003 2005 2007 2009 2011
Source: Fulcrum Asset Management
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 13
What correlations do you assume between the premia?
When modelling correlations, there is a trade-off between reacting to perceived
changes in correlations and exposing portfolios to sudden correlation breaks. There is
no perfect solution since conservative assumptions (for example, zero or perfect
correlations) that result in more robust portfolios during times of crisis are sub-optimal
in normal times, while dynamic correlations can have the reverse problem.
Figure 11 shows the correlation between each traditional risk premium and the overall
TRP portfolio; with the exception of the bond premium, all are highly correlated with
TRP. As a result, we assume that equities, commodities and credit (emerging market
debt and corporate high yield) are perfectly correlated with each other.
Figure 11: 3 Year Rolling Correlations with TRP
For the bond premium, however, correlations vary significantly over time. As a result,
we assume a zero correlation between major government bonds and other traditional
risk premia. Over the last two years, this assumption has resulted in lower bond
exposure than more traditional risk parity approaches. Going forward, we believe that
10 year bond yields will not sustainably remain below 1%, which limits the likely upside
in bonds. Meanwhile, our approach is likely to be less vulnerable to rising bond yields.
Equity Premium
Commodity Beta
Bond Premium
EM $ Debt
High Yield
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1995 1997 1999 2001 2003 2005 2007 2009 2011 2013
Source: Fulcrum Asset Management
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 14
Figure 12: 3 Year Rolling Correlations with BERP
Figure 13: 3 Year Rolling Correlations with BERP
EM-DM Equities
Equity Size
Equity Style
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
1995 1997 1999 2001 2003 2005 2007 2009 2011 2013
Source: Fulcrum Asset Management
CommodityCarry
DM FX Carry
EM FX Carry
FI Carry
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1995 1997 1999 2001 2003 2005 2007 2009 2011 2013
Source: Fulcrum Asset Management
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 15
Turning to alternative risk premia, Figures 12 and 13 show their low average correlation
with a BERP portfolio. Importantly, this diversification benefit has increased since the
financial crisis, reinforcing the valuable role played by alternative risk premia within
risk parity portfolios. The tendency of these correlations to fluctuate in fairly wide
bands around zero, leads us to assume a zero correlation between them and other risk
premia.
How correlated are risk parity portfolios with equities and hedge
funds?
Since the risk in most pension fund portfolios tends to be dominated by equities,
approaches that are less correlated with equities are more valuable to most investors.
As can be seen in Figure 14, TRP portfolios tend to be highly correlated (0.8) with
equities while ARP portfolios tend to be uncorrelated (0.1).
Figure 14: 3 Year Rolling Correlation with Equities
As shown in Figure 15, TRP and RP are more correlated with hedge funds than they are with
equities. Nevertheless, we believe that investors considering risk parity funds should allocate from
existing equity exposure, reflecting the dominance of equity risk in most portfolios.
Equity/Bond (BERP)
Traditional (TRP)
Alternative (ARP)
All Risk Premia
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1995 1997 1999 2001 2003 2005 2007 2009 2011 2013
Source: Fulcrum Asset Management
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 16
Figure 15: 3 Year Rolling Correlation with Hedge Funds (HFRI Fund of Funds Index)
How have portfolios of risk premia performed historically?
Figure 16 shows the performance characteristics of the four risk parity portfolios
(BERP, TRP, ARP and RP) and Figure 17 illustrates their cumulative returns.
Figure 16: Historical Excess Performance (Jan-93 to Sep-12)
Equity/Bond (BERP)
Traditional (TRP)
Alternative (ARP)
All Risk Premia(RP)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1995 1997 1999 2001 2003 2005 2007 2009 2011 2013
Source: Fulcrum Asset Management
BERP TRP ARP RP
Annual Excess Return 8% 6% 10% 10%
Volatility 8% 8% 8% 8%
Sharpe Ratio 1.0 0.7 1.3 1.3
Correlation with:
Equity Premium 0.7 0.8 0.1 0.6
Bond Premium 0.7 0.0 0.0 0.0
Equity/Bond 1.0 0.6 0.1 0.5
Source: Fulcrum Asset Management
Risk Parity Portfolios: A Practitioner’s Guide
Fulcrum Research Papers – October 2012 17
Figure 17: Historical Excess Performance (Jan-93 to Sep-12)
The key highlights are as follows:
Between 1993 and 2012, a risk parity portfolio of equities and bonds (BERP) has
been highly correlated with both equity (0.7) and bond (0.7) premia.
A portfolio of traditional risk premia (TRP) has underperformed BERP,
reflecting its lower exposure to the bond premia. Meanwhile, rising correlations
between credit, commodities and equities have resulted in a high correlation of
TRP with the equity premium (0.8).
A portfolio of alternative risk premia (ARP) has strongly outperformed BERP
and has been uncorrelated with both equity (0.1) and bond (0.0) premia.
A portfolio of all risk premia (RP), which combines ARP with TRP, has also
performed well, with a moderately high correlation with the equity premium
(0.6).
Figure 18 shows the relative ranking of calendar year excess returns for each of the risk
premia (excluding volatility). For example, so far in 2012, the best performing risk
premium is high yield, while the worst performing is the equity style premium. While
we continue to investigate ways of systematically timing risk premia, our current