Comparing Performances on a Risk
Adjusted Basis
Hedge Funds vs Traditional Asset
Classes
The scope of this study is to give an effective way to compare the performance of various investments:
We are in this study considering the following investments:
- Equity fund, proxy by SP500 future contract with no management or performance fee
- Fixed Income Fund, proxy by a rolling investment in 10 years T-Bonds, with no management
or performance fee
- Commodity Fund, proxy by Gold with no management or performance fee
- Fund of Hedge funds, proxy by HFRI FOF Composite Index, discounted by a management
fee of 1.5% of the AUM and a performance fee of 15%
- Direct investment in Hedge funds, proxy by the HFRX Global investable index
The traditional approach
The traditional approach to compare performances is to compound returns in excess of the risk free
rate, or which is equivalent the evolution of $100 in cash with $100 invested in a given index. Of
course, comparing these performances in such a way is unfair, because it is quite easy to provide high
performances by taking a high level of risk. It is why traditional approaches will compute the ex-post
volatility of each investment, and compute the excess return by unit of volatility: this is the Sharpe
ratio.
On a long term basis, this leads to the conclusion that Equity delivers the highest return.
From January-90 up to June-07
Termination Value
Average Yearly Excess Return vs
Cash
Ex post Yearly Volatility
Sharpe Ratio
FOF (based on
HFR
FOF
Composite (1)) Gold
$
163 $
70
2.8%
4.6%
0.62
-2.0%
13.0%
(0.16)
SP500
$
Hedge
Funds
(Based on HFRX
10YTbonds
GLB (1))
190 $
138
#N/A
3.7%
13.7%
0.27
1.8%
9.7%
0.19
#N/A
#N/A
#N/A
(1) Source: Hedge Fund Research, Inc., © HFR, Inc. 24 July 2007, www.hedgefundresearch.com
But the Fund of Hedge funds have the highest Sharpe ratio – i.e. excess return by unit of ex-post
volatility.
Disclaimer: The information contained in this document is related to proprietary technology and commercial data. By accepting
and reading it, you acknowledge that the content of this document is provided for your sole information. You do not obtain any
ownership interest in such content, nor right to copy, modify or transfer to a third party. Ownership of such all content shall at all
times remain with Riskdata. Riskdata reserves all rights not expressly granted to you
1/5
Comparing Performances on a Risk
Adjusted Basis
Hedge Funds vs Traditional Asset
Classes
Excess Wealth vs Cash from January-90 up to June-07
300
250
FOF (based on HFR FOF Composite (1))
Gold
SP500
10YTbonds
200
150
100
50
(1) Source: Hedge Fund Research, Inc., © HFR, Inc. 24 July 2007, www.hedgefundresearch.com
Ju
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9
nD 90
ec
-9
Ju 0
nD 91
ec
-9
Ju 1
nD 92
ec
-9
Ju 2
nD 93
ec
-9
Ju 3
nD 94
ec
-9
Ju 4
nD 95
ec
-9
Ju 5
nD 96
ec
-9
Ju 6
nD 97
ec
-9
Ju 7
nD 98
ec
-9
Ju 8
nD 99
ec
-9
Ju 9
nD 00
ec
-0
Ju 0
nD 01
ec
-0
Ju 1
nD 02
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-0
Ju 2
nD 03
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-0
Ju 3
nD 04
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-0
Ju 4
nD 05
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-0
Ju 5
nD 06
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-0
Ju 6
n07
0
If we consider the most recent time windows – the last four years, i.e. the equity & commodity rally,
equity seem apparently to be superior both in term of excess return and Sharpe ratio:
From April-03 up to June-07
Termination Value
Average Yearly Excess Return vs
Cash
Ex post Yearly Volatility
Sharpe Ratio
FOF (based on
HFR FOF
Composite (1))
$
118
Gold
$
4.1%
3.1%
1.32
169
13.2%
14.5%
0.91
SP500
$
154
10YTbonds
$
87
Hedge Funds
(Based on
HFRX GLB (1))
$
108
10.7%
8.2%
1.30
-3.3%
9.8%
(0.33)
1.9%
3.2%
0.58
Investing in Gold was what delivers the highest return, but by taking a significantly higher risk.
Investing in Fund of Hedge Funds is a low return / low risk investment, with a Sharpe ratio just below
that of the SP500. It is a significantly better investment than a direct investment in hedge funds. The
fact that the HFR index is not investable – and therefore benefit from the so call “survival bias” –
doesn’t explain the performance gap: the death rate among Fund of hedge funds is very low.
Therefore, the main explanation for this performance gap is the added value FoHF bring in term of
manager selections (they tend to select the best one) and allocation (they actively manage allocations
to take advantage of the trends).
So the conclusion of this approach would be that integrating in the comparison gap in volatilities and
excluding major equity crisis, a traditional equity fund is the best investment, while a fund of hedge
fund is the best “crisis” proof investment.
Why
traditional
sufficient
approaches
are
not
The problem is that it is not at all operational for an investor. It does not give to the investor an
understanding of which amount of money he would have actually make for each unit of risk. Because
Disclaimer: The information contained in this document is related to proprietary technology and commercial data. By accepting
and reading it, you acknowledge that the content of this document is provided for your sole information. You do not obtain any
ownership interest in such content, nor right to copy, modify or transfer to a third party. Ownership of such all content shall at all
times remain with Riskdata. Riskdata reserves all rights not expressly granted to you
2/5
Comparing Performances on a Risk
Adjusted Basis
Hedge Funds vs Traditional Asset
Classes
when something has happened (a crisis, a draw down) it is no longer risk, it is performances. But in
real life situation, risk is what may happen in the future, not what happen in the past.
Let’s take an analogy to illustrate the problem. You have to choose between 2 transportation means to
go from home to the office: motorbike or car. The performance is the time it requires. The risk is the
probability of having an accident. On the one hand, Alicia recommends you to choose the motorbike,
because she uses it every day to get to the office, it takes her 30 min to cover 20 miles, the distance
from home to work, she has been doing that for now 5 years and never got a serious accident. On the
other hand, Alex claims that the car is superior because it takes him 1 hr to cover 20 miles from home
to work, he has been doing that every day for 5 years as well and never had an accident. Looking
backward, Alicia looks correct because the motorbike is faster. However, looking forward, the
probability of an accident and its consequences are far more dramatic with the motorbike than with the
car (considering any statistics). In order for Alicia to reduce her risk to that of the car, she needs to
slow down by at least a factor 3. So, if we compare transportation means with equivalent level of risk,
Alex is now faster than Alicia, who needs 1½ hrs to safely ride her motorbike from home to work.
Using Investable
performances
Strategies
to
compare
The solution is in fact to simulate a looking forward basis, at every time on the period, in order to take
the same level of risk whatever the selected asset class, exactly as a rational investor would actually
behave. It consists in having a risk target (in our case, a 10% ex ante volatility) and then:
- Every month, estimate the forthcoming risk of each index, using an “ex-ante” risk indicator
- Adjust leverage on the index, i.e. leave part of the investment in cash or borrow cash, so that
the “ex-ante” risk indicator is set equal to 10%. Of course, borrowing cash requires paying the
risk free rate + spread (set to 15bps in our study). On the contrary, cash is invested at the risk
free rate – which in fact turns out to penalise low volatility strategies.
Note that, except for the 15 bps spread, leveraging the investment or keeping part of the cash in
money markets has no impact on the Sharpe ratio when the leverage is fixed. However, this is no
longer the case with a varying leverage.
One can now compare the performances of these “automatically leveraged” investment vehicles,
which are what an investor would actually get when investing into risk adjusted strategies.
From January-90 up to June-07
Termination Value
Average Yearly Excess Return vs Cash
Ex post Yearly Volatility
Sharpe Ratio
FOF (based on
HFR FOF
Composite (1))
Gold
$
467 $
9.2%
10.9%
0.85
68
-2.2%
11.0%
(0.20)
SP500
$
204
4.2%
10.5%
0.40
10YTbonds
$
162
2.8%
11.0%
0.25
Hedge Funds
(Based on HFRX
GLB (1))
#N/A
#N/A
#N/A
#N/A
Disclaimer: The information contained in this document is related to proprietary technology and commercial data. By accepting
and reading it, you acknowledge that the content of this document is provided for your sole information. You do not obtain any
ownership interest in such content, nor right to copy, modify or transfer to a third party. Ownership of such all content shall at all
times remain with Riskdata. Riskdata reserves all rights not expressly granted to you
3/5
Comparing Performances on a Risk
Adjusted Basis
Hedge Funds vs Traditional Asset
Classes
Excess Wealth vs Cash from January-90 up to June-07
300
250
FOF (based on HFR FOF Composite (1))
Gold
SP500
10YTbonds
200
150
100
50
(1) Source: Hedge Fund Research, Inc., © HFR, Inc. 24 July 2007, www.hedgefundresearch.com
Ju
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9
nD 90
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-9
Ju 0
nD 91
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-9
Ju 1
nD 92
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-9
Ju 2
nD 93
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-9
Ju 3
nD 94
ec
-9
Ju 4
nD 95
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-9
Ju 5
nD 96
ec
-9
Ju 6
nD 97
ec
-9
Ju 7
nD 98
ec
-9
Ju 8
nD 99
ec
-9
Ju 9
nD 00
ec
-0
Ju 0
nD 01
ec
-0
Ju 1
nD 02
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-0
Ju 2
nD 03
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-0
Ju 3
nD 04
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-0
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0
On the long term, Fund of hedge funds is by far the best choice. Initial investment is multiplied by
4.5, against only double for an equity investment, which comes second, more or less similar to a bond
investment. One can also look at traditional indicators, such as Sharpe ratio. By forcing the “ex-ante”
volatility at a given level, we see that the ex-post volatility is almost the same for the various
investments. Hence the Sharpe ratio ranking coincides with that of the performance.
On a more recent period – during the equity and commodity rally, we again find, based on this
approach, that Fund of Hedge Funds perform similarly to equities and gold and beat other
investments.
From April-03 up to June-07
Termination Value
Average Yearly Excess Return vs Cash
Ex post Yearly Volatility
Sharpe Ratio
FOF (based on
HFR
FOF
Composite (1))
Gold
$
168 $
13.0%
9.6%
1.35
144
9.0%
9.9%
0.91
SP500
$
156
11.0%
9.5%
1.16
10YTbonds
$
85
-3.8%
9.5%
(0.40)
Hedge
Funds
(Based on HFRX
GLB (1))
$
121
4.5%
10.5%
0.43
Disclaimer: The information contained in this document is related to proprietary technology and commercial data. By accepting
and reading it, you acknowledge that the content of this document is provided for your sole information. You do not obtain any
ownership interest in such content, nor right to copy, modify or transfer to a third party. Ownership of such all content shall at all
times remain with Riskdata. Riskdata reserves all rights not expressly granted to you
4/5
Comparing Performances on a Risk
Adjusted Basis
Hedge Funds vs Traditional Asset
Classes
Excess Wealth / Cash for risk adjusted strategies from April-03 up to June-07
180
FOF (based on HFR FOF Composite (1))
Gold
SP500
10YTbonds
Hedge Funds (Based on HFRX GLB (1))
160
140
120
100
80
60
40
20
(1) Source: Hedge Fund Research, Inc., © HFR, Inc. 24 July 2007, www.hedgefundresearch.com
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In conclusion, on a risk-adjusted basis, Fund of Hedge Funds match the best performance of
traditional investments – equities, bonds, commodities – when they rally, and on a long term period,
deliver far superior performances, because they are “crisis proof”.
________________
Disclaimer: The information contained in this document is related to proprietary technology and commercial data. By accepting
and reading it, you acknowledge that the content of this document is provided for your sole information. You do not obtain any
ownership interest in such content, nor right to copy, modify or transfer to a third party. Ownership of such all content shall at all
times remain with Riskdata. Riskdata reserves all rights not expressly granted to you
5/5