10 CTAsBridgewaterAssociatesCampbell &Co., Inc.Vega AssetManagement(USA) LLCGrossman AssetManagementUBS O’ConnorCrabel CapitalManagement,LLCFX Concepts,Inc.GrinhamManagedFunds Pty.,Ltd.Rotella CapitalManagementInc.SunriseCapitalPartnersAverage
6,831.00
11.88
9.75
−0.10
−0.60
119.38
5,026.00
14.16
13.70
−0.40
0.10
148.53
2,054.68
9.21
4.60
−1.50
5.00
87.28
1,866.001,558.00
15.648.31
15.288.54
−0.100.30
−0.300.70
170.8173.02
1,511.00
7.74
6.31
1.10
3.70
68.29
1,480.00
10.79
15.26
0.30
−0.10
94.63
1,280.00
11.69
10.01
0.50
−0.10
116.34
1,227.95
11.63
12.19
0.30
0.30
112.10
1,080.96
13.77
13.75
0.90
0.50
142.03
2,391.62
11.48
10.94
0.13
0.92
113.24
Panel B: Subsample 2: Middle 10 CTAsCompucomFinance, Inc.MarathonCapital GrowthPtnrs., LLCDynexCorp Ltd.ARA PortfolioManagementCompany
53.00
9.90
22.18
0.50
0.50
68.12
50.1050.00
13.737.47
14.7812.17
0.000.10
1.30−0.70
139.1159.25
47.70
7.05
17.24
−0.10
0.90
47.08
382
PROGRAM EVALUATION, SELECTION, AND RETURNS
TABLE 22.1 (continued)
FundName
AverageAverageAssets Annualized AnnualizedCompounded(EndingReturnStd. Dev.ExcessReturnMillions $)(%)(%)Skewness Kurtosis(%)
Panel B: Subsample 2: Middle 10 CTAs (continued)Blenheim CapitalMgmt., LLC46.50Quality CapitalManagement,Ltd.46.00Sangamon Trading,Inc.46.00WillowbridgeAssociates, Inc.45.80Clarke CapitalManagement,Inc.43.20Millburn RidgefieldCorporation42.94Average47.12
21.66
37.22
−0.10
−0.20
181.17
13.06
16.34
0.20
−0.40
124.74
9.06
7.30
1.80
6.70
83.40
14.38
42.44
0.90
4.80
48.89
16.19
17.41
0.60
0.90
175.78
5.9111.84
17.4720.46
1.000.49
0.701.45
36.0496.36
Panel C: Subsample 3: Bottom 10 CTAsMuirlands CapitalManagement LLC 0.40Minogue InvestmentCo.0.40Shawbridge AssetMgmt. Corp.0.22International TradingAdvisors, B.V.B.A. 0.20Be Free Investments,Inc.0.20Lawless Commodities,Inc.0.10District CapitalManagement0.10Venture I0.10Marek D.Chelkowski0.10Robert C. Franzen0.10Average0.19
16.10
24.11
0.20
-0.70
149.13
9.27
41.88
1.70
8.30
8.10
15.66
33.88
1.00
3.00
102.94
−6.33
12.22
−1.10
8.10
−38.83
14.95
20.49
−1.50
5.70
140.79
−11.10
43.02
−1.70
7.80
−77.22
13.80−1.42
34.6821.19
−0.50−2.50
1.2011.80
67.73−22.91
−15.91−8.942.61
78.2915.7932.56
−0.30−2.00−0.67
0.504.705.04
−95.98−50.8118.29
383
Risk-Adjusted Returns of CTAs
TABLE 22.2 Performance ResultsFundName
NormalVaR (%)
ModifiedVaR (%)
NormalModifiedSharpe Ratio Sharpe Ratio
Panel A: Subsample 1: Top 10 CTAsBridgewater AssociatesCampbell & Co., Inc.Vega Asset Management(USA) LLCGrossman AssetManagementUBS O’ConnorCrabel CapitalManagement, LLCFX Concepts, Inc.Grinham ManagedFunds Pty., Ltd.Rotella CapitalManagement Inc.SunriseCapital PartnersAverage
−6.42−8.17
−6.28−9.13
0.090.13
0.100.12
−1.33
−2.64
0.60
0.30
−8.99−3.91
−8.94−3.75
0.110.25
0.110.26
−2.85−9.22
−2.33−8.09
0.240.10
0.290.11
−5.66
−4.23
0.16
0.22
−7.33
−6.54
0.12
0.14
−8.08
−4.89
0.11
0.18
−6.20
−5.68
0.19
0.18
Panel B: Subsample 2: Middle 10 CTAsCompucom Finance, Inc.Marathon CapitalGrowth Ptnrs., LLCDynexCorp Ltd.ARA PortfolioManagement CompanyBlenheim CapitalMgmt, LLCQuality CapitalManagement, Ltd.Sangamon Trading, Inc.WillowbridgeAssociates, Inc.Clarke CapitalManagement, Inc.MillburnRidgefield CorporationAverage
−11.07
−12.66
−0.03
−0.03
−10.69−6.83
−9.36−7.60
0.110.01
0.100.02
−12.24
−10.98
0.06
0.05
−21.76
−21.49
0.08
0.08
−8.81−2.19
−9.85−4.01
0.110.23
0.130.12
−3.54
−32.94
0.03
0.02
−8.32
−9.94
0.12
0.10
−7.21
−12.67
0.07
0.04
−9.27
−13.15
0.08
0.06
384
PROGRAM EVALUATION, SELECTION, AND RETURNS
TABLE 22.2 (continued)FundName
NormalVar (%)
ModifiedVar (%)
NormalSharpe Ratio
ModifiedSharpe Ratio
Panel C: Subsample 3: Bottom 10 CTAsMuirlands CapitalManagement LLCMinogue Investment Co.Shawbridge AssetMgmt. Corp.International TradingAdvisors, B.V.B.A.Be Free Investments, Inc.Lawless Commodities, Inc.DistrictCapital ManagementVenture IMarek D. ChelkowskiRobert C. FranzenAverage
−13.90−24.62
−15.98−29.99
0.03−0.01
0.03−0.01
−18.66
−22.18
0.03
0.04
−21.31−24.37−52.03
−10.86−14.15−29.80
−0.010.06−0.11
−0.000.03−0.06
−29.99−26.46−44.79−11.90
−24.05−13.79−40.25−8.34
0.02−0.06−0.10−0.09
0.02−0.03−0.09−0.06
−26.80
−20.94
−0.02
-0.01
CONCLUSIONIt is of critical importance to understand that complications will arise whena traditional measure of risk-adjusted performance, such as the Sharperatio, is used on the nonnormal returns of CTAs. Institutional investorsmust use the modified Sharpe ratio to measure the risk-adjusted returns correctly. The modified VaR is better in the presence of extreme returnsbecause the normal VaR considers only the first two moments of a distribution, namely mean and standard deviation. The modified VaR, however,takes into consideration the third and fourth moments of a distribution,skewness and kurtosis. Using both the modified Sharpe and modified VaRwill enable investors to more accurately assess CTA performance. In manycases, if the modified Sharpe ratio is used to examine normally distributedassets, they will be ranked in the same exact order as if the traditionalSharpe ratio was used. This occurs because the modified VaR converges tothe classical VaR if skewness equals zero and excess kurtosis equals zero.The statistics presented can be applied to all CTA classifications displaying nonnormal returns. We believe many institutional investors wanting to add CTAs to traditional stock and bond portfolios must requestadditional and more appropriate statistics, such as the modified Sharperatio, to analyze the returns of CTAs.
CHAPTER
23
Time Diversification:The Case of Managed FuturesFrançois-Serge Lhabitant and Andrew Green
here is a long-standing debate in the financial literature as to whetherstocks are more risky over the long term than over the short term. In thischapter, we use an approach based on historical data and analyze the ex-postperformance of managed futures over different time periods. We observe thatin terms of capital preservation, managed futures seem less risky over the longterm than over the short term. However, this superiority is at risk as soon asthe benchmark return increases. This fact, combined with the correlationproperties of managed futures with traditional asset classes, tends to promotetheir use as portfolio diversifiers rather than as stand-alone investments.
T
INTRODUCTIONAdam and Eve, as originally created, were biologically capable of living forever. Unfortunately, eating the forbidden fruit forced them to realize thataging also could mean a process of decay that leads finally to death. Severalexpressions—vita brevis (life is short), sic transit gloria mundi (thus passesaway the glory of the world), carpe diem (seize the day), tempus fugit (timeflies)—remind us of time’s inevitability as well as men’s foolish attempts totranscend it or, at least, find an antidote to it.To our knowledge, the only field where the passage of time actuallymay provide growth rather than decay is the investment arena, particularlywhen one takes into account the power of compounding. The latter simplymeans earning interest on interest, a principle that Einstein used to describeas being the “most powerful force in the universe” and the “ninth wonderof the world.” Its consequences are straightforward: The longer you stayinvested and reinvest your earnings, the faster your money will grow. Thekey is therefore to be patient and let time do the work for you.
385
386
PROGRAM EVALUATION, SELECTION, AND RETURNS
The power of compounding is universally recognized. Another important theory linked to the passage of time in portfolios is called time diversification. It is well entrenched in the practices of asset management, butraises a healthy dose of skepticism from some in the academic community.Simply stated, it claims that investing for a longer time horizon decreasesthe risk of an investment. As all experienced investors know, the market isa roller-coaster ride when looked at from a day-to-day perspective. An assetthat moves up by 2 percent one day may well drop 5 percent the followingday. However, over the long run, the common belief is that markets shouldtend to move in an upward direction, simply because their returns mustinclude a risk premium to convince risk-averse investors that they shouldparticipate. This wisdom advises investors to take a long-term view of themarkets and not focus too much on short-term gyrations. With this outlook, the chances are better that investors’ portfolios ultimately willincrease in value. It follows from this argument that the longer an investor’stime horizon is, the more money he or she should place in riskier investments—assuming, of course, that taking more risk implies obtaining ahigher risk premium, or rate of return.Time diversification as a hedge against risk has been widely applied inequity markets and retirement fund planning. However, we have not yetfound any research devoted to the validity of time diversification for alternative investments, and more specifically to commodity trading advisors(CTAs). This is rather surprising, as CTAs are well known for their diversification benefits from a portfolio standpoint—what some people call spacediversification. With practically a zero correlation to stocks, one of themost attractive features of CTAs is their ability to add diversification to aninvestment portfolio. As an illustration, a study published by the ChicagoBoard of Trade (2002) concluded that “portfolios with as much as 20 percent of assets in managed futures yielded up to 50 percent more than a portfolio of stocks and bonds alone.” But how long should one wait to observethese benefits? And, ideally, should CTAs be part of portfolios for a longtime period or a short one?In this chapter, we explore the effects of time diversification on portfolios of CTAs. Rather than construct an argument based on financial toolsor theoretical concepts, we choose to look at the historical data. We areinterested in two questions:1. How does the terminal value of a CTA’s portfolio evolve as the holdingperiod increases?2. How does the value of a CTA’s portfolio evolve within a given holdingperiod when the length of the latter increases?
Time Diversification
387
In the next section we briefly introduce CTAs and their key features.Then we review the various arguments for time diversification as presentedfor the equity markets. Next we describe the methodology and discuss themajor findings. In the last section we draw conclusions and open the wayfor further research.
COMMODITY TRADING ADVISORSCommodity trading advisors, also known as managed futures or tradingadvisors, are individuals or organizations that trade derivative instrumentssuch as futures, forward contracts, and options on behalf of their clients.Investors have been using the services of CTAs for more than 30 years. Theystarted their activities in the late 1970s with the regulatory separationbetween the brokerage and investment management functions of the futuresbusiness. Their group expanded significantly in the early 1980s with theproliferation of nontraditional commodity futures contracts. As their nameimplies, initially they started trading in commodity markets, but have sinceevolved to trade in all the markets. Today, contrarily to hedge funds, mostof them are regulated. They are federally licensed by the CommodityFutures Trading Commission (CFTC) and periodically audited by theNational Futures Association (NFA) in the United States. They are supervised by the Provincial Securities Commission in Canada and by theAutorité des Marchés Financiers in France.CTAs may use a broad spectrum of different trading strategies. However, their primary investment style is systematic trend following. That is,they use computer programs to perform some sort of technical analysis(moving averages, breakouts of price ranges, etc.), identify trends in a set ofmarkets, and generate buy and sell signals accordingly. These signals thenare executed on an automated basis to create a portfolio that strives to bepositioned in the direction of any trend that is in place.Most CTAs follow a disciplined and systematic approach by prioritizing capital preservation, controlling potential losses, and protecting potential gains. The risk they initially take for each trade is usually small, but thesize of positions may increase progressively if the detected trends are stableand verified. However, in adverse or volatile markets, automated stops areexecuted to limit losses.The basic trend-following programs are relatively simple. One exampleis an envelope breakout system. If a market is trading sideways in a fairlynarrow range, the program might suggest no position. A breakout on theupside or the downside could trigger an entry. Another example is based onthe crossing of different moving averages. For instance, if a rising short-
388
PROGRAM EVALUATION, SELECTION, AND RETURNS
term moving average crosses a long-term moving average, this constitutesa buy signal. Inversely, if a declining short-term moving average crosses along-term moving average, this constitutes a sell signal. Of course, the largetrend-following advisors, such as Dunn Capital Management, John W.Henry & Co., and Campbell, simultaneously use multiple models thatemploy different strategies for entering and exiting trends in markets, oftenusing short, intermediate, and long time frames.Trend following typically generates strong returns in times when themarkets are trending (upward or downward), and will lose money at the endof a trend or during sideways markets. This is precisely where risk management should step in to try to limit the losses. Good trend followers haveto inure many small losses. They also may have more losing trades thanwinning ones, but the average size of the winners is typically two or moretimes the average of losing trades. To reduce their overall risk, most CTAsalso diversify themselves by using their programs to make investment decisions simultaneously across several markets, such as stocks, bonds, foreignexchange, interest rate, commodities, energy, agricultural and tropicalproducts, and precious metals. If they lose money in one market, they hopeto make money in another. Over some longer periods of time, say one yearor more, a good trend follower should net 10 percent to 20 percent on abroadly diversified program.
TIME DIVERSIFICATIONThe conventional wisdom in the professional investment community is thatclassic one-period diversification (space diversification) across risky securities such as equities handles the static risk of investing and that time diversification handles the intertemporal dynamic aspects of that risk.The advocates of time diversification point out that fluctuations insecurity returns tend to cancel out through time, thus more risk is diversified away over longer holding periods. As a consequence, apparently riskysecurities such as stocks are potentially less risky than previously thought ifheld for long time periods yet their average returns are superior to low-risksecurities such as treasury bills. Empirically, it can be observed thatThe distribution of annualized returns converges as the horizonincreases. If returns are independent from one year to the next, thestandard deviation of annualized returns diminishes with time whilethe expectation of annualized returns remains constant.■ The probability of incurring a loss (shortfall probability) declines as thelength of the holding period increases. If we determine the likelihood ofa negative return by measuring the difference in standard deviation■
Time Diversification
389
units between a 0 percent return and the expected return, we see thatas the length of the holding period lengthens, the probability of facinga negative return decreases very rapidly.Those who challenge the time diversification argument, most notablyBodie (1995), Merton (1969), and Samuelson (1969, 1971, 1972, 1979,1994), contend that the choice of risk measurement used by time diversification advocates is erroneous. They believe that what is important to aninvestor is not the probability of a loss or the annualized variance of a portfolio but rather how large the potential shortfall might be and how aninvestor might avoid it. They argue that in using the probability of shortfall, no distinction is made between a loss of 20 percent and a loss of 99percent in an investment. While it may be less likely, a loss of 99 percent isobviously more painful to the investor, should it actually occur. Although itis true that annualized dispersion of returns converges toward the expectedreturn with the passage of time, the dispersion of terminal wealth divergesfrom the expected terminal wealth as the investment horizon expands. Solosses can be very large in spite of their low probability of occurrence. Asinvestors should be concerned with terminal wealth, not change in wealthover time, and although one is less likely to lose money after a long duration, the magnitude of the loss, if it does occur, increases with duration. So,from a utility of terminal wealth point of view, the reduction in the possibility of loss is just offset by the larger possible size of loss.Bodie (1995) makes this point quite dramatically by illustrating that thepremium for insuring against a shortfall in performance of stocks versusbonds is actually an increasing function of the time horizon over which theinsurance is in force instead of a decreasing one, which would be expectedwith declining risk.1 Insurance premiums are a particularly appealing measure because they represent the economic cost of neutralizing undesirablereturns. However, Bodie’s argument is circular, as the same observationapplies to the premiums for insuring against a shortfall in performance ofbonds versus stocks.Kritzman (1994) provides a comprehensive review of the time diversification debate and illustrates the delicate balance that exists between one’sassumptions and the conclusions that necessarily derive from those assumptions. However, more recently, Merrill and Thorley (1996) reignited thedebate by noting that “the differences between practitioners and theo-
1Samuelson (1971, 1972, 1979) addressed a similar fallacy involving the virtues of
investing to maximize the geometric mean return as the “dominating” strategy forinvestors with long horizons.
390
PROGRAM EVALUATION, SELECTION, AND RETURNS
rists . . . are often rooted in semantic issues about risk” (p. 15). In addition,the two camps do not really focus on the same problem. Time diversificationadvocates are concerned with the impact of increasing the time horizon fora buy and hold strategy, while their opponents are looking at a dynamicinvestment problem in which a given time horizon is chopped up into several periods. Hence, their divergent opinions are not really surprising.In our view, CTAs provide a more interesting testing field for the theory of time diversification than equities. The reason is that the majority ofthem are trend followers and that in the long run, trends are likely toemerge (upward or downward). CTAs should then be able to capture thesetrends and extract profits from them as long as they last. However, in thepresence of trend reversals or trendless markets, their performance is likelyto decrease. Remember that trend followers do not know that a trend isover until the market has reversed somewhat, so they actually give back aportion of their accumulated profits, which leads to sizable drawdowns.Their performance, of course, is cyclical or mean reverting because itdepends on suitable market environments for the trading strategy. This isparticularity interesting when one remembers that Samuelson (1991), Kritzman (1994), and Reichenstein and Dorsett (1995) have shown that the timediversification principle can be justified only if there is mean reversion inthe returns.
EMPIRICAL TESTFor the purposes of this exercise, we use the Credit Suisse First BostonTremont Managed Futures Index to represent the universe of CTAs. Thisindex is asset-weighted and includes 29 of the world’s largest audited managed futures funds (see Table 23.1).The index is only intended as a rough approximation of how a fund ofCTAs would behave in reality. Funds of CTAs typically include a substantially smaller number of managers than those represented in the index, andwould seek to implement some kind of selection strategy from among thedifferent managers/programs. In addition, the smallest CTAs tend to have anaverage return significantly larger than the average return of the largestCTAs. Thus, by focusing on larger funds, we may unwittingly cause a downward bias in returns by eliminating some of the small high-return funds.Table 23.2 summarizes the performance of the CSFB Tremont Managed Futures Index for the period January 1994 to December 2003. CTAsappear to be positioned close to bonds in terms of returns (7.07 percent versus 6.79 percent per annum), but with a much higher volatility (12.84 percent versus 6.76 percent per annum). Their performance is far below thatof stocks (11.07 percent per annum), but stocks also have a much higher
Time Diversification
391
TABLE 23.1 Commodity Trading Advisors Included in the CSFB-TremontManaged Futures IndexAspect Diversified Fund (USD) Ltd.AXA FuturesCampbell Global Assets FundChesapeake Select LLCD.QUANT Fund/Ramsey Futures TradingDexia Systemat (Euro)Eckhardt Futures LPEpsilon Futures (Euro)Epsilon USDFTC Futures Fund SICAVGraham Global Investment Fund (Div 2XL Portfolio)Graham Global Investment Fund (Div Portfolio)Graham Global Investment Fund (Fed Policy)Graham Global Investment Fund (Prop Matrix Portfolio)Hasenbichler Commodities AGJWH Global StrategiesLegacy Futures Fund LPLiberty Global Fund LPMillburn International (Cayman) Ltd.—DiversifiedMLM Index Fund Leveraged (Class B)Nestor PartnersQuadrigaRivoli International Fund (Euro)Rotella Polaris FundRoy G. Niederhoffer Fund (Ireland) PlcSMN Diversified Futures Fund (Euro)Sunrise FundSysteia Futures Fund (Euro)Systeia Futures Ltd. (USD)
volatility (17.29 percent per annum). On average, the index experienced 56percent of positive months, with a better absolute performance in positivemonths (+2.95 percent) than in negative months (−2.30 percent). Stockshave a higher ratio of positive months (63 percent), but they lose the advantage by having on average a much worse performance during negativemonths (−3.91 percent).Although they do not seem to be very good stand-alone investments,CTAs are likely to be good portfolio assets. This is evidenced by their lowcorrelation with stocks (−0.23) and bonds (0.35). As evidenced in Figure23.1, when the stock market has declined through all of the negative
392
PROGRAM EVALUATION, SELECTION, AND RETURNS
months, the CSFB Tremont Managed Futures Index has generated anattractive performance.Interestingly enough, there is, in a sense, positive correlation when thestock market is up and, in effect, negative correlation when the stock market is down. This is particularly visible on the drawdown diagram, whichconsiders losing periods only (see Figure 23.2).The worst periods for futures markets coincide with winning periodsfor equity markets, and vice versa. Once again, this illustrates the dangersof using a linear correlation coefficient to measure nonlinear relationships.Contrarily to the majority of hedge fund strategies, the histogram of
TABLE 23.2 Statistics of the CSFB-Tremont Managed Futures IndexCSFB/TremontManaged FuturesIndexReturn (% p.a.)Volatility (% p.a.)SkewnessKurtosisNormality(Bera Jarque test, 95%)
S&P 500
SSB World Gvt.Bond Index
7.0712.840.030.58
11.0717.29−0.600.29
6.796.760.470.37
Yes
Yes
Yes
−0.23
0.35
56
63
58
9.95
9.78
5.94
2.95
3.8126
1.79−64
44
37
43
−9.35
−14.46
−3.44
−2.30
−3.91−22
−1.09315
−17.74−8.37
−44.73−10.54
−7.94−3.26
Correlation% of positive monthsBest monthperformance (%)Avg. of positivemonths returns (%)Upside capture (%)% of negative monthsWorst monthperformance (%)Avg. of negativemonths returns (%)Downside capture (%)Max. drawdown (%)VaR (1M, 99%)
393
Time Diversification
6050
Performance over12 Months (%)
403020100–10–20–30–4012/94
S&P 50012/95
CSFB/Tremont Managed Futures12/96
12/97
12/98
12/99
12/00
12/01
12/02
12/03
FIGURE 23.1 Rolling 12-Month Performance of the CSFB-Tremont ManagedFutures Index Compared to the S&P 500
01/940
01/95
01/96
01/97
01/98
01/99
01/00
01/01
01/02
01/03
–5–10
Drawdown (%)
–15–20–25–30–35–40–45–50
S&P 500
CSFB/Tremont Managed Futures
FIGURE 23.2 Maximum Drawdown of the CSFB-Tremont Managed Futures IndexCompared to the S&P 500
394
PROGRAM EVALUATION, SELECTION, AND RETURNS
monthly returns displays no fat tails compared to a normal distribution,and no clear asymmetry (see Figure 23.3).As mentioned, a large number of CTAs capitalize on market trends,that typically are associated with an increase in volatility. Hence, an