environment that may be difficult for traditional strategies, particularly in thepresence of down trends, actually presents an ideal trading environment forCTAs. In a sense, they follow long-volatility strategies, whereas most traditional strategies and hedge fund strategies are termed “short volatility” andview an increase of volatility as a risk factor. This qualifies them as interesting portfolio diversifiers to yield better risk-adjusted returns, over thelong run . . . or maybe the short run.To test the impact of the holding period on the performance of CTAs,we first use overlapping blocks of N consecutive months, where N variesfrom 1 to 120. Because we have 120 returns in our historical data set, weobtain 120 possible blocks of one month and only one block of 120months. For each block, we calculate the return obtained at the end of theconsidered period. Figure 23.4 shows the evolution of this terminal annualized return of the CSFB Tremont Managed Futures Index as a function ofthe block size.Figure 23.5 shows the evolution of the annualized volatility of thisreturn as a function of the block size. Both figures tend to confirm that the
0.16
CSFB/Tremont Managed Futures
Normal
0.14
Probability
0.120.100.080.060.040.02
Return (%)0.00–18% –15% –12% –9%
FIGURE 23.3Returns
–6%
–3%
0%
3%
6%
9%
12%
15%
18%
Distribution of the CSFB-Tremont Managed Futures Index Monthly
395
Time Diversification
87
AnnualizedReturn (%)
65432100
10
20
30
40
50
60
70
80
90
100
110
Number of Months in Holding Period
FIGURE 23.4 Annualized Holding Period Return Expressed as Function of theNumber of Months in the Holding Period
141312
AnnualizedVolatility (%)
111098765432100
10
20
30
40
50
60
70
80
90
100
110
Number of Months in Holding Period
FIGURE 23.5 Annualized Volatility of the Holding Period Return Expressed as aFunction of the Number of Months in the Holding Period
396
PROGRAM EVALUATION, SELECTION, AND RETURNS
longer the investor’s holding period, the smaller the standard deviation ofthe annualized rate of return on the managed futures portfolio, while thereturn itself remains relatively stable. These results are so convincing thatone is left with the impression that over a very long time horizon, investingwith CTAs is a sure thing.2However, there does not necessarily exist genuine diversification in thissituation. Although the basic argument that the standard deviations ofannualized returns decrease as the time horizon increases is true, it is alsomisleading. In fact, it may fatally miss the point, because for an investorconcerned with the value of the portfolio at the end of a period of time, itis the total return that matters, not the annualized return. And because ofthe effects of compounding, the standard deviation of the total return actually increases with time horizon. Thus, if we use the standard deviation ofreturns as the traditional measure of uncertainty over the time period inquestion, uncertainty increases with time. However, in the case of managedfutures, some additional elements should be considered.We all agree that investors should care about the amount of wealth atthe end of the period, and more particularly about the severity of a potential shortfall. We therefore need to consider both the severity of a shortfalland its likelihood to conclude anything. Figure 23.6 shows the evolution ofthe worst historical holding period return of the CSFB Tremont ManagedFutures Index as a function of the length of the holding period. This provides a new and interesting perspective. We clearly see that the worst-caseholding period return is initially negative (−9.35 percent) and tends toworsen as the holding period lengthens. However, it stabilizes after a fewmonths of holding and starts decreasing in intensity. After 45 months ofholding, the shortfall probability is nil, and the worst-case holding periodreturn is positive. This tends to confirm the fact that even in the worst case,managed futures are less risky in the long run than in the short run.Of course, one may argue that the preserving the initial capital is not avery aggressive target, particularly over the long run. What happens if wehave a target rate of return of, say, 3 percent or 5 percent a year? Figure23.7 provides the answer. The shortfall is the amount by which target goalsfail to be achieved. Clearly, the cyclical nature of managed futures penalizesthem in the long run when compared to safe investments. Note that we are
2One could object that our observation periods are strongly overlapping, so that the
resulting rollover returns have a high degree of correlation, which results in a serious estimation bias. To assess statistical significance would require independentreturns based on nonoverlapping periods. The existing horizon of experience, however, is too short to obtain enough data of these kinds.
397
Time Diversification
8070
Worst HoldingPeriod Return (%)
6050403020100–10–20–300
10
20
30
40
50
60
70
80
90
100
110
Number of Months in Holding Period
FIGURE 23.6 Worst-Case Holding Period Return Expressed as a Function of theNumber of Months in the Holding Period
40
Worst-Case Shortfall(%, nonannualized)
30
Target rate:3% p.a.
20100–10
Target rate:5% p.a.
–20–30–400
10
20
30
40
50
60
70
80
90
100
110
Number of Months in Holding Period
FIGURE 23.7 Worst-Case Shortfall Expressed as a Function of the Number ofMonths in the Holding Period
398
PROGRAM EVALUATION, SELECTION, AND RETURNS
only looking at the worst case here, but this is what matters from a riskmanagement perspective.
CONCLUSIONThe impact of the time horizon on the risk of stock investments is still asubject of intense and controversial debate within the academic and investment communities. Although it is true under the assumption of normallydistributed returns that the volatility increases with the square root of time,the standard deviation of mean returns decreases with longer time intervals.Whether this can be interpreted as stocks being less risky over the long termis still an issue. In this chapter, we use an approach based on historical dataand analyze the worst case ex-post performance of managed futures overdifferent time periods. Our results tend to suggest that a diversified portfolio of managed futures is a relatively safe investment over the long run, butremains risky from a shortfall perspective as soon as the minimum requiredreturn increases above zero.
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