In Theory: Hasanhodzic and Lo

Attack By Jasmina Hasanhodzic

and Andrew W. Lo

of
the Clones
Hedge funds are considered by many investors to be an attractive investment, thanks in
large part to their diversification benefits and distinctive risk profiles. The major drawbacks
are their high fees and lack of transparency. Research by Jasmina Hasanhodzic and Andrew
W. Lo of the Massachusetts Institute of Technology raises the possibility of creating passive
portfolios that provide similar risk exposures to those of hedge funds at lower costs and with
greater transparency. Hasanhodzic and Lo find that for certain hedge fund strategies, these
hedge fund “clones” perform well enough to warrant serious consideration.

A
s institutional investors take a more active in- Plan sponsors require a certain degree of liquidity in their
terest in alternative investments, a signifi- assets to meet their pension obligations and also desire sig-
cant gap has emerged between the culture nificant capacity because of their limited resources in man-
and expectations of those investors and aging large pools of assets; hedge fund managers routinely
hedge fund managers. Pension plan impose lockups of one to three years, and the most success-
sponsors typically require transparency from their managers ful managers have the least capacity to offer, in many cases
and impose numerous restrictions on their investment man- returning investor capital once they make their personal for-
dates because of regulatory requirements such as ERISA tunes. And as fiduciaries, plan sponsors are hypersensitive to
rules; hedge fund managers rarely provide position-level the outsize fees that hedge funds charge and are concerned
transparency and bristle at any restrictions on their invest- about misaligned incentives induced by performance fees;
ment process, saying that restrictions can hurt performance. hedge fund managers argue that their fees are fair compen-

00 • INSTITUTIONAL INVESTOR’S ALPHA • JUNE 2006 Illustrations by Edel Rodriguez for Alpha
Hasanhodzic and Lo

sation for their unique investment acumen — and at least suggests that for certain classes of hedge fund strategies,
for now, the market seems to agree. portable beta may be an even more important source of
This cultural gap raises the natural question of untapped expected returns and diversification.
whether it is possible to obtain hedge-fund-like returns
without investing in hedge funds. In other words, can BEFORE TURNING TO OUR empirical analysis, we
hedge fund returns be cloned? provide two concrete examples that span the extremes of
In a series of recent papers, Harry Kat and Helder Palaro the hedge fund replication problem. For one hedge fund
of the Cass Business School at City University in London strategy, we show that replication can be accomplished
show that sophisticated dy- easily; for another strategy
namic trading strategies in- we find replication to be
volving liquid futures
Table 1: Capital Decimation Partners* almost impossible using
contracts can replicate many The monthly returns of fictitious Capital Decimation Partners’ simulated linear models.
of the statistical properties of short-put-option strategy handily beat the Standard & Poor’s 500 index. The first example is a
hedge fund returns. In fact, Standard & Capital hypothetical strategy we
in a 2001 paper with Dim- Poor’s 500 Decimation proposed several years ago
Statistic index Partners*
itris Bertsimas and Leonid called “Capital Decimation
Kogan of the Massachusetts Monthly mean 1.4% 3.6% Partners,” or CDP, which
Institute of Technology, we Monthly standard deviation 3.6% 5.8% yields an enviable track
show that the risk/return Minimum month –8.9% –18.3% record that many investors
characteristics of securities Maximum month 14.0% 27.0% would associate with a suc-
with very general payoff Annual Sharpe ratio 0.98 1.90 cessful hedge fund: a 43.1
functions (like hedge funds Number of negative months 36 6 percent annualized mean
or complex derivatives) can Correlation to S&P 500 index 100% 61% return and 20.0 percent an-
be synthetically replicated to Growth of $1 since inception $4 $26 nualized volatility, implying
an arbitrary degree of accu- * January 1992 through December 1999. Source: Lo (2001). a Sharpe ratio of 1.90, and
racy by dynamic trading with only six negative
strategies — called epsilon-arbitrage strategies — involving months over the 96-month simulation period from January
more liquid instruments. Although these results are encour- 1992 through December 1999 (see Table 1).
aging for the hedge fund replication problem, the strategies So what is CDP’s secret? The investment strategy in-
are quite complex and not easily implemented by the typi- volves shorting out-of-the-money S&P 500 put options
cal institutional investor. on each monthly expiration date for maturities less than
In this article we take a slightly different tack: We con- or equal to three months, and with strikes approximately
struct “linear clones” — buy-and-hold portfolios of com- 7 percent out of the money.
mon risk factors like the Standard & Poor’s 500 and U.S. The essence of this strategy is the provision of insur-
dollar indexes, with portfolio weights estimated by a lin- ance. CDP investors receive option premiums for each op-
ear regression of a fund’s historical returns on market fac- tion contract sold short, and as long as the option contracts
tors — of a large number of individual hedge funds in the expire out of the money, no payments are necessary. From
TASS Hedge Fund Database. We then compare their this perspective the handsome returns to CDP investors
characteristics to those of the corresponding funds from seem more justifiable: In exchange for providing downside
which the clones are derived. protection, CDP investors are paid a risk premium in the
If a hedge fund generates part of its expected return same way that insurance companies receive regular pay-
and risk profile from certain common risk factors, it may ments for providing earthquake or hurricane insurance.
be possible to design a low-cost, buy-and-hold portfolio Given the relatively infrequent nature of 7 percent
— not an active, dynamic trading strategy — that cap- losses, CDP’s risk/reward profile can seem very attractive
tures some of that fund’s risk/reward characteristics by in comparison to more traditional investments, but there
taking on just those risk exposures. For example, if a par- is nothing unusual or unique about CDP. Investors will-
ticular long-short equity hedge fund is 40 percent long ing to take on “tail risk” — the risk of rare but severe
growth stocks, it may be possible to create a passive port- events — will be paid well for this service (consider how
folio that has similar characteristics through a long-only much individuals are willing to pay each month for their
position in a passive growth portfolio coupled with a 60 homeowner’s, auto, health and life insurance policies).
percent short position in stock index futures. CDP involves few proprietary elements and can easily be
The magnitude of hedge fund alpha that can be cap- implemented by most investors; it is one example of a
tured by a linear clone depends, of course, on how much hedge-fund-like strategy that can readily be cloned.
of a fund’s expected return is driven by common risk fac- Now for the bad news. Consider the case of “Capital
tors versus manager-specific alpha. This can be measured Multiplication Partners,” or CMP, a hypothetical fund
empirically. Although portable-alpha strategies have be- based on a dynamic asset-allocation strategy between the
come fashionable lately among institutions, our research S&P 500 and one-month U.S. Treasury bills, where the

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 Hasanhodzic and Lo

fund manager can correctly forecast which of the two ve- which we have complete data for all of our factors (the TASS
hicles will do better in each month and invests the fund’s database goes back to 1977). Of these funds, we drop those
assets in the higher-yielding instrument at the start of the that do not report net-of-fee returns, those that report re-
month. (This example was first proposed by Robert Mer- turns in currencies other than the U.S. dollar, those that re-
ton in his 15.415 Finance Theory class at the MIT Sloan port returns less frequently than monthly, those that do not
School of Management in the 1970s.) The monthly re- provide assets under management or provide only estimates
turn of this perfect-market-timing strategy is simply the and those that have fewer than 36 monthly returns. These
larger of the monthly returns of the S&P 500 and T-bills. filters yield a final sample of 1,610 funds.
The source of alpha is clear. Merton observes that this For each fund we estimate a linear regression of its
strategy is equivalent to a long-only investment in the monthly historical returns on the following six risk factors:
S&P 500 plus a put option on the S&P 500 with a strike the U.S. dollar index return, the return on the Lehman
price equal to the T-bill return. The economic value of Brothers corporate AA intermediate bond index, the spread
this perfect market-timing is equal to the sum of monthly between the Lehman BAA corporate bond index and the
put-option premiums over the life of the strategy. Lehman Treasury index, the S&P 500 total return, the
There is little doubt that such a strategy contains signifi- Goldman Sachs commodity index return and the first-dif-
cant alpha indeed: A $1 investment in CMP in January ference of the end-of-month value of the VIX Chicago
1926 would have grown to more than $23 billion by the Board Options Exchange volatility index. (Throughout this
end of December 2004! Table 2 provides a more detailed article all statistics, except for those related to the first-order
performance summary of CMP, whose Sharpe ratio exceeds autocorrelation, have been annualized to facilitate interpre-
that of Warren Buffett’s Berkshire Hathaway, arguably the tation and comparison.)
most successful pooled investment vehicle of all time. We choose these six risk factors for two reasons: They
It should be obvious to even the most naive investor provide a reasonably broad cross-section of risk exposures
that CMP is a fantasy because no one can time the market for the typical hedge fund (stocks, bonds, currencies, com-
perfectly. Therefore, attempting to replicate such a strate- modities, credit and volatility), and each of the factor re-
gy with exchange-traded instruments seems hopeless. But turns can be realized through relatively liquid instruments
suppose we try anyway. How close can we come? In par-
ticular, suppose we attempt to relate CMP’s monthly re-
turns to the monthly returns of the S&P 500 by fitting a
Table 2: Capital Multiplication Partners*
straight line through a graph of their paired monthly re- Based on a series of simulated monthly returns going back to 1926, the aptly named
turns, that is, a linear regression. The option-like nature of Capital Multiplication Partners’ perfect-market-timing strategy easily beats its clone’s.
CMP’s perfect-market-timing strategy, which is inherently Standard & Capital
nonlinear, cannot be captured by a straight line. However, Poor’s 500 Treasury Multiplication
the formal statistical measure of how well the linear regres- Statistic index bills Partners Clone
sion fits the data — the R2, a number between 0 and 100 Monthly mean 1.0% 0.3% 2.6% 0.7%
percent that implies a perfect linear relationship at 100 Monthly standard deviation 5.5% 0.3% 3.6% 3.0%
percent and no relationship at all at 0 — is 70.3 percent in Minimum month –29.7% –0.1% –0.1% –16.3%
this case, which suggests a very strong linear relationship Maximum month 42.6% 1.4% 42.6% 23.4%
indeed. But when the estimated linear regression is used to Annual Sharpe ratio 0.63 4.12 2.50 0.79
construct a buy-and-hold portfolio of the S&P 500 and Number of negative months 360 12 10 340
one-month T-bills, the results are not nearly as impressive Correlation to S&P 500 index 100% –2% 84% 100%
as CMP’s returns, as Table 2 shows. Growth of $1 since inception $3,098 $18 $2.3 x 1010 $429
This example underscores the difficulty of replicating * January 1926 through December 2004. Source: Authors’ calculations.
certain strategies that have genuine alpha with linear clones,
and it cautions against using the R2 as the only metric of so that the returns of linear clones may be achievable in
success. Despite the high R2 achieved by the linear regres- practice. In particular, there are forward contracts for each
sion of CMP’s returns on the market index, the actual per- of the component currencies of the U.S. dollar index and
formance of the linear clone falls far short of the strategy futures contracts for the stock and bond indexes and for the
because a linear model will never be able to capture the components of the commodity index. Futures contracts on
option-like payoff structure of the perfect market-timer. the VIX index were introduced by the CBOE in March
2004 and are not as liquid as the other index futures, but
TO EXPLORE THE FULL RANGE of possibilities for the over-the-counter market for variance and volatility
replicating hedge fund returns illustrated by the two extremes swaps is quite well developed.
of CDP and CMP, we investigate the performance of linear The linear-regression model provides a simple but use-
clones for a sample of individual hedge funds drawn from ful decomposition of a hedge fund’s expected return into
the TASS Hedge Fund Live Database over the sample period two distinct components — beta coefficients multiplied
from February 1986 through September 2005. We start our by the risk premiums associated with various risk factors,
analysis in February 1986 because this is the earliest date for and manager-specific alpha. The intuition for this decom-

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Hasanhodzic and Lo

position is straightforward. Hedge funds generate their ex- spread (27.1 percent), and the average contribution of
pected returns by taking on certain generic risks for which manager-specific alpha is –33.3 percent.
they are compensated, like market or credit risk, and also This implies that convertible-arbitrage funds, on aver-
by taking advantage of insights and opportunities that are age, earn more than all of their mean returns from the risk
specific to the manager. premiums associated with the six factor exposures, and that
By “manager-specific alpha,” we do not mean to imply the average contribution of other sources of alpha is nega-
that a hedge fund’s unique source of alpha is without risk. tive. Of course, this does not mean that convertible-arbitrage
We are simply distinguishing this source of expected return managers are not adding value. The results are averages
from those that have clearly iden- across all funds in the sample; hence, the positive manager-
tifiable risk factors associated specific alphas of successful managers will be dampened and,
“For certain types with them. In particular, it may in some cases, outweighed by the negative manager-specific
well be the case that manager- alphas of the unsuccessful ones. Moreover, all of the statistics
of hedge fund specific alpha arises from factors reported in our study are estimates only and therefore sub-
other than the six we have pro- ject to a certain amount of estimation error.
strategies, a posed, and a more refined list of In contrast to the convertible-arbitrage funds, for the
factors — one that reflects the ten funds in the dedicated short-bias category, manager-
passive buy-and- particular investment style of the specific alpha accounts for 225.6 percent of the total mean
manager — may yield a better- return, while the contribution of the S&P 500 factor is
hold approach performing linear clone. negative. This result is not as anomalous as it may seem.
A similar decomposition for The bull market of the 1990s implies a performance drag
may yield some of a hedge fund’s return variance for any fund with negative exposure to the S&P 500.
can be derived that is the sum of Thus, dedicated short-bias managers that have generated
the same benefits three distinct components: the positive performance during this period must have done
variances of the risk factors mul- so through other means.
as hedge funds.” tiplied by the squared beta coef- A concrete illustration of this intuition is given by the
ficients, the variance of the decomposition of the annualized average return of the
— JASMINA HASANHODZIC
fund-specific sources of ran- two most successful funds in the dedicated short-bias cat-
AND ANDREW W. LO
domness or “residual” (which egory. From 1997 through 2005 these two funds posted
may be related to the specific annualized net-of-fee returns of 15.56 percent and 10.02
economic sources of alpha) and the weighted covariances percent, respectively, but the contribution of the S&P
among the factors. This decomposition highlights the fact 500 factor to these annualized returns was negative in
that a hedge fund can have several sources of risk, each of both cases. In fact, the six factors account for very little of
which should yield some risk premium — that is, risk- the two funds’ performance; hence, the manager-specific
based alpha — otherwise, investors would not be willing alphas are particularly significant for these two funds.
to bear such risk. By taking on exposure to multiple risk Between the two extremes of convertible-arbitrage and
factors, a hedge fund can generate attractive expected re- dedicated short-bias funds, there is considerable variation
turns from the investor’s perspective, as we saw with Capi- in the importance of manager-specific alpha for the other
tal Decimation Partners. strategy categories. For the entire sample of 1,610 funds,
Using the linear-regression model to decompose a 61.0 percent of the average total return is attributable to
fund’s expected returns, we can now reformulate the ques- manager-specific alpha, implying that, on average, the re-
tion of whether a hedge fund strategy can be cloned by maining 39.0 percent is due to the risk premiums from
asking how much of a hedge fund’s alpha is due to risk our six factors. These results suggest that for certain types
premiums from identifiable factors. If it is a significant of hedge fund strategies, a passive buy-and-hold approach
portion, then a passive portfolio with just those risk expo- may yield some of the same benefits as hedge funds, but
sures — created by means of liquid instruments such as in a transparent, scalable and lower-cost vehicle.
index futures, forwards and other contracts — may be a
reasonable alternative to a direct investment in the fund. HOW CLOSE CAN WE COME to replicating hedge
Table 3 summarizes the empirical results of the expected- fund returns? To answer this question, we construct linear
return decomposition for our sample of funds, grouped ac- clones of each fund in our sample by regressing the fund’s re-
cording to their style categories. Each row contains the turns on five of the six factors we considered above (we drop
average total mean return of funds in a given category, and the DVIX volatility factor because its returns are not as easily
averages of the percent contributions of each of the six fac- realized with liquid instruments) and no intercept, and then
tors and the manager-specific alpha to that average total rescaling the fitted regression equation so that the resulting
mean return. For example, the most significant contributors buy-and-hold portfolio has the same sample volatility as the
to the investment return of convertible-arbitrage funds are original fund’s return series. We omit the intercept because
the dollar index (67.1 percent), the bond index (34.9 per- our objective is to estimate a weighted average of the factors
cent), the commodity index (31.8 percent) and the credit that best replicates the fund’s returns. The motivation for

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 Hasanhodzic and Lo

rescaling the volatility of the clones is to create a fair compar- for the event-driven funds. This large gap is understand-
ison between the buy-and-hold portfolio and the fund, and able, given the idiosyncratic and opportunistic nature of
is equivalent to changing the leverage of the clone portfolio. most event-driven strategies. Moreover, a significant
Table 4 contains a comparison of the performance of source of the profitability of event-driven strategies is the
these linear clones and that of the original funds from which illiquidity premium that managers earn through their
the clones are derived. The results are striking — for several willingness to provide capital in times of distress. This
strategy categories the average mean return of the clones is illiquidity premium will clearly be missing from a clone
only slightly lower than that of their fund counterparts, and portfolio of liquid securities; therefore, we should expect
in some categories the clones outperform. For example, the a significant performance gap in this case.
average mean return of the convertible-arbitrage clones is For dedicated short-bias funds, the average mean return
8.15 percent, and the corresponding figure for the actual of the clones and the funds is 3.58 and 5.98 percent, respec-
funds is 8.41 percent. For long-short equity hedge funds, tively. This may seem somewhat counterintuitive in light of
the average mean return for clones and funds is 13.94 and the expected-return decomposition in Table 3, where we
14.59 percent, respectively. And in the multistrategy catego- observed that dedicated short-bias funds were responsible
ry, the average mean return for clones and funds is 10.10 for more than 100 percent of the average total returns of
and 10.79 percent, respectively. funds in this category. The fact that dedicated short-bias
In three cases the average mean return of the clones is clones have positive average performance is due entirely to
higher than that of the funds: global macro (14.43 percent the clone of a single fund, No. 33735 in the TASS database,
versus 11.38 percent), managed futures (23.47 percent ver- and when this outlier is dropped from the sample, the aver-
sus 13.64 percent) and fund of funds (8.63 percent versus age mean return of the remaining nine clones drops to –0.35
8.25 percent). However, these differences are not statisti- percent. The underperformance of the clones in this catego-
cally significant because of the variability in mean returns ry is also intuitive — given the positive trend in the U.S.
across funds within each category. Even in the case of man- stock market during the 1980s and ’90s, a passive strategy
aged futures, the difference in average mean return between of shorting the S&P 500 is unlikely to have produced at-
clones and funds — almost 10 percentage points — is not tractive returns when compared to the performance of more
statistically significant because of the large fluctuations in nimble discretionary short-sellers.
average mean returns of the managed-futures clones. Nev- Another metric of comparison is the average Sharpe ratio,
ertheless, these results suggest that for certain categories, which adjusts for the volatilities of the respective strategies.
the performance of clones may be within shouting distance Given our rescaling process, the standard deviations for the
of their corresponding funds. clones are identical to their fund counterparts, so a compari-
One category of hedge funds that seems particularly son of Sharpe ratios reduces to a comparison of mean re-
difficult to replicate is event-driven strategies. The aver- turns. However, the average Sharpe ratio of a category is not
age performance of the event-driven clones, at 9.60 per- the same as the ratio of that category’s average mean return
cent, is considerably lower than the 13.03 percent average to its average volatility, so the Sharpe ratio statistics in Table

Table 3: Breaking Down Hedge Fund Returns by Strategy

Not all alpha is created equal. An analysis of the total mean returns for more than 1,600 hedge funds in the TASS database from February 1986 to September 2005
shows which asset classes and factors make the biggest contribution to their investment performance.

Average of percentage contribution of factors to total expected return (%)

Average
No. of expected Credit Dollar S&P 500 Bond VIX Commodity
Category description funds return (%) spread index index index index index Alpha

Convertible arbitrage 82 8.4% 27.1% 67.1% –19.3% 34.9% –8.4% 31.8% –33.3%
Dedicated short-bias 10 6.0 12.2 19.4 –108.2 7.0 8.9 –64.9 225.6
Emerging markets 102 4.9 –0.3 –3.2 19.3 0.1 –0.4 6.2 78.3
Equity market-neutral 83 20.4 0.2 3.6 4.0 3.9 1.3 6.3 80.8
Event-driven 169 8.1 2.1 3.0 4.3 9.4 –0.7 3.1 79.0
Fixed-income arbitrage 62 13.0 –1.4 3.3 2.7 18.5 –0.5 4.4 73.1
Global macro 54 9.5 2.0 8.1 9.7 25.0 –3.3 10.0 48.6
Long-short equity hedge 520 11.4 1.1 1.9 17.8 2.1 –1.8 8.4 70.5
Managed futures 114 14.6 1.9 23.4 –3.4 53.8 –1.5 53.2 –27.5
Multistrategy 59 13.6 0.5 3.5 5.7 10.1 –1.9 3.2 78.9
Fund of funds 355 10.8 0.5 5.4 9.7 8.8 –2.8 7.3 71.1
All funds 1,610 8.3 2.3 7.8 8.5 11.3 –1.9 10.9 61.0
Source: Authors’ calculations.

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Hasanhodzic and Lo

4 do provide some incremental information. The average The clones have much lower average autocorrelations than
Sharpe ratio of the funds in the convertible-arbitrage cate- their fund counterparts, with the exception of the managed-
gory is 2.70, which is almost twice the average Sharpe ratio futures category, for which both clones and funds have very
of 1.54 for the clones, a significant risk-adjusted perform- low average autocorrelations. For example, the average auto-
ance gap between the funds and their clones. However, there correlation of convertible-arbitrage funds is 42.2 percent,
is virtually no difference in average Sharpe ratios between and the corresponding average value for convertible-
clones and funds for equity market-neutral, long-short arbitrage clones is only 10.4 percent. A more formal statisti-
equity hedge and fund-of-funds categories. As we discussed cal analysis shows that for every single category the average
above, the apparent similarity of dedicated short-bias clones level of autocorrelation in the funds is higher than that in
to their funds is the result of a single outlier. And for global the clones, confirming our intuition that, by construction,
macro and managed futures, the average Sharpe ratios of the clones are more liquid than their fund counterparts.
clones are, in fact, higher than those of the funds.
Table 4 provides one more comparison worth noting: the A PORTION OF EVERY HEDGE FUND’S expect-
average first-order autocorrelation coefficients of clones and ed return is risk premiums — compensation to investors
funds. The first-order autocorrelation, ρ^ 1, is the correlation for bearing certain risks. One of the most important
between a fund’s current return and the previous month’s re- benefits of hedge fund investments is the nontraditional
turn, and in our previous studies we show that a positive val- types of risks they encompass, such as tail risk, liquidity
ue for ρ^ 1 in hedge fund returns is a proxy for illiquidity risk. risk and credit risk. Most investors would do well to take

Table 4: A Comparison of Hedge Funds and Their Clones

The promise of replicating hedge fund returns varies greatly by strategy. As shown by the following performance comparison of linear clones with the corresponding
hedge funds in the TASS database, the technique is very effective for convertible-arbitrage, global macro, long-short equity hedge and managed-futures strategies.

STANDARD DEVIATION FIRST-ORDER

AVERGE MEAN RETURN SHARPE RATIO AUTOCORRELATION (ρ^ 1)
RETURN
No. of Standard Standard Standard Standard
Category description funds Mean (%) deviation (%) Mean (%) deviation (%) Mean deviation Mean (%) deviation (%)

LINEAR CLONES
Convertible arbitrage 82 8.15% 5.15% 6.20% 5.28% 1.54 0.62 10.4% 10.7%
Dedicated short-bias 10 3.58 13.09 28.27 10.05 0.16 0.54 1.2 4.4
Dedicated short-bias* 9 –0.35 4.40 28.75 10.53 0.00 0.17 1.9 4.2
Emerging markets 102 17.91 16.51 22.92 15.16 0.97 0.61 0.7 8.8
Equity market-neutral 83 7.45 6.81 7.78 5.84 1.14 0.76 1.8 9.6
Event-driven 169 9.60 6.79 8.40 8.09 1.39 0.52 3.5 11.3
Fixed-income arbitrage 62 8.55 6.04 6.56 4.41 1.43 0.64 2.5 8.2
Global macro 54 14.43 9.65 11.93 6.10 1.25 0.55 3.9 8.9
Long-short equity hedge 520 13.94 10.34 15.96 9.06 0.96 0.59 0.1 9.5
Managed futures 114 23.47 15.94 21.46 12.07 1.11 0.46 5.7 8.5
Multistrategy 59 10.10 7.66 8.72 9.70 1.50 0.68 1.8 10.0
Fund of funds 355 8.63 5.88 6.36 4.47 1.46 0.48 –0.3 11.2

ACTUAL FUNDS
Convertible arbitrage 82 8.41% 5.11% 6.20% 5.28% 2.70 5.84 42.2% 17.3%
Dedicated short-bias 10 5.98 4.77 28.27 10.05 0.25 0.24 5.5 12.6
Dedicated short-bias* 9 4.92 3.58 28.75 10.53 0.20 0.20 3.4 11.3
Emerging markets 102 20.41 13.01 22.92 15.16 1.42 2.11 18.0 12.4
Equity market-neutral 83 8.09 4.77 7.78 5.84 1.44 1.20 9.1 23.0
Event-driven 169 13.03 8.65 8.40 8.09 1.99 1.37 22.2 17.6
Fixed-income arbitrage 62 9.50 4.54 6.56 4.41 2.05 1.48 22.1 17.6
Global macro 54 11.38 6.16 11.93 6.10 1.07 0.58 5.8 12.2
Long-short equity hedge 520 14.59 8.14 15.96 9.06 1.06 0.58 12.8 14.9
Managed futures 114 13.64 9.35 21.46 12.07 0.67 0.39 2.5 10.2
Multistrategy 59 10.79 5.22 8.72 9.70 1.86 1.03 21.0 20.1
Fund of funds 355 8.25 3.73 6.36 4.47 1.66 0.86 23.2 15.0
* Fund No. 33735 has been dropped from this sample of dedicated short-bias funds. Source: Authors’ calculations.

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 Hasanhodzic and Lo

on small amounts of such risks if they are not already nonlinearities in a buy-and-hold portfolio. In fact, an ear-
doing so because these factors usually yield attractive lier study by Lo and Martin Haugh shows that a judi-
risk premiums, and many of these risks are not highly ciously constructed buy-and-hold portfolio of simple put
correlated with those of traditional long-only invest- and call options can yield an excellent approximation to
ments. Although talented hedge fund managers are al- certain dynamic trading strategies, and this approach can
ways likely to outperform passive buy-and-hold also be used to create better clones.
portfolios, the challenges of manager selection and mon- Finally, a number of implementation issues remain to
itoring, the lack of transparency, the limited capacity of be resolved before hedge fund clones become a reality: the
such managers and the high fees may tip the scales for estimation methods for computing clone portfolio
the institutional investor in favor of clone portfolios. In weights, the implications of the implied leverage required
such circumstances, portable beta may be a reasonable by our volatility rescaling process, the optimal rebalanc-
alternative to portable alpha. ing interval, the types of strategies to be cloned and the
Our empirical findings suggest that the possibility of best method for combining clones into a single portfolio.
cloning hedge fund returns is real. For certain hedge fund We are cautiously optimistic that the promise of our ini-
categories, the average performance of clones is compara- tial findings will provide sufficient motivation to take on
ble — on both a raw-return and a risk-adjusted basis — these practical challenges.
to that of their hedge fund counterparts. For other cate-
gories, like dedicated short-bias and event-driven, the
clones are less successful.
As encouraging as these results may be, several qualifi-
cations must be kept in mind. First, we have used the
entire sample of return histories to construct our clones,
which is a particularly naive approach to replicating a
dynamic strategy and also imparts a “look-ahead bias” to
the results. Any practical cloning process must employ
rolling or expanding windows to estimate the portfolio
weights. This allows the clone-portfolio weights to change
over time and in response to changing market conditions,
a particularly important feature in the hedge fund con-
text. Although the look-ahead bias may not be that severe
in this case because we did not select the best-performing
clone among many trials, nevertheless, a more realistic
simulation is an important extension of our analysis.
Second, despite the promising properties of linear clones
in several style categories, it is well known that certain hedge
fund strategies contain inherent nonlinearities that cannot
be captured by linear models (for example, Capital Multi-
plication Partners). Therefore, more sophisticated nonlinear
methods — including nonlinear regression, regime-switch-
ing processes, stochastic volatility models and Kat and
Palaro’s copula-based algorithm — may yield significant
benefits in terms of performance and goodness-of-fit. How-
ever, there is an important trade-off between goodness-of-fit
and the complexity of the replication process, and this trade- Jasmina Hasanhodzic is a Ph.D. candidate in the Department of Electrical Engi-
off varies from one investor to the next. As more neering and Computer Science at the Massachusetts Institute of Technology. Andrew
sophisticated replication methods are used, the resulting W. Lo is the Harris & Harris Group Professor of Finance at the MIT Sloan School
clone becomes less passive, requiring more trading and risk- of Management and founder and chief scientific officer of AlphaSimplex Group, a
management expertise, and eventually becoming as com- quantitative investment management company based in Cambridge, Massachusetts.
plex as the hedge fund strategy itself. The views and opinions expressed in this article are those of the authors only and do
Third, the replicating factors we proposed are only a not necessarily represent the views and opinions of AlphaSimplex Group, MIT or
small subset of the many liquid instruments that are avail- any of their affiliates and employees. The authors make no representations or war-
able to the institutional investor. By expanding the uni- ranty, either expressed or implied, as to the accuracy or completeness of the informa-
verse of factors to include options and other derivative tion contained in this article, nor are they recommending that this article serve as
securities and customizing the set of factors to each hedge the basis for any investment decision. For a complete list of references used in prepar-
fund category (and perhaps to each fund), it should be ing this article, as well as a more detailed explanation of the analyses and addition-
possible to achieve additional improvements in perform- al results and tables, please refer to Lo’s home page, web.mit.edu/alo/www.
ance, including the ability to capture tail risk and other

JUNE 2006 • INSTITUTIONAL INVESTOR’S ALPHA • 00