MULTIPLE TIME SCALE ATTRIBUTION for COMMODITY TRADING ADVISOR (CTA) FUNDS∗ Brian T
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Journal Of Investment Management, Vol. 9, No. 2, (2011), pp. 35–72 © JOIM 2011 JOIM www.joim.com MULTIPLE TIME SCALE ATTRIBUTION FOR COMMODITY TRADING ADVISOR (CTA) FUNDS∗ Brian T. Hayes a,b Commodity trading advisors (CTAs) make directional investments in liquid futures and forward markets. Since CTAs generally do not engage in security selection or relative value trades, their performance depends to a large extent on funds’ ability to “time” market exposures. We analyze CTA return attribution, splitting returns into contributions from asset class (beta) factors and market timing factors. For each asset, we use timing factors at several frequencies. The highest frequency (e.g., daily) timing factors are absolute values of asset returns, while lower frequency (e.g., weekly or monthly) timing factors also use high-frequency returns. Average fund returns net of beta and market timing contributions are called residual alpha. For CTAs, the market timing contribution varies by frequency. By combining timing factors at different frequencies, we estimate aggregate market timing alpha and residual alpha; this latter quantity is around −8% per year for CTA indexes, with transaction costs being a potential contributor. Commodity trading advisors (CTAs) are funds commodities. They are often referred to as man- that invest in liquid futures and forward mar- aged futures funds or trend followers, although kets for equities, fixed income, currencies, and the latter term does not apply to all managers in the space. By taking long or short positions in these markets, CTAs make bets on market direc- ∗The views and opinions expressed in this article are those tion. Generally, trading signals for these funds are of the author and do not necessarily represent those of Lom- produced by systematic models. The directional bard, Odier, Darier, Hentsch & Cie, or any of its affiliates. approach of most CTAs differs from that of rel- a I thank Troy Buckner, Alan Dorsey, Martin Estlander, ative value hedge funds that seek to profit from Mila Getmansky, Cedric Kohler, Alexey Medvedev, Rafael Molinero, and Roy Niederhoffer for helpful their com- the spread between two quantities, regardless of ments, as well as Lombard, Odier, Darier, Hentsch & Cie whether their respective markets rise or fall. for supporting this research. bCurrent address: Morgan Stanley, 1585 Broadway, New While CTA fund returns tend to be correlated with York, NY 10036, USA; Brian.T.Hayes@morganstanley. each other,1 funds differ in their size, the markets com they trade, the holding period of their investments, Second Quarter 2011 35 Not for Distribution 36 Brian T. Hayes and the models that they use to forecast market skill in less-liquid markets could appear as resid- direction. CTAs range in size from under $10 mm ual alpha; this effect should be more pronounced to over $10 bn in assets2; smaller funds typically in smaller funds, however. For the minority of trade in the same markets as large funds, but CTAs that trade individual equities or emerg- may be overweight smaller markets (e.g., cot- ing markets, gains from these activities would ton). Holding periods for CTAs can range from also show up as residual alpha. Fees are a possi- minutes to several months, but most assets are in ble (negative) contributor; however, management the multi-month category, due to capacity lim- and incentive fees exert opposing influences on itations of short-term trading. Most CTAs use residual alpha,4 and their combined impact is systematic trend-following models (i.e., continu- smaller than our estimated residual alphas. A ation or momentum) to predict market direction, remaining contributor to residual alpha is trans- although some funds use mean reversion or pat- action cost. Since funds incur these costs on all tern recognition as signals.3 Funds also differ in trades, successful or not, they will be uncorre- their leverage, often expressed as a margin to lated with market timing factors. Due to such equity. costs, we expect to see negative residual alpha in many CTAs, after extracting beta contri- We focus on attribution analysis of CTA funds butions and market timing alpha. Indeed, we in this paper. If a fund has net exposure to mar- find residual alphas of around −8% for CTA kets over the measurement period (e.g., long indexes. bonds), a portion of its returns are attributable to directional (beta) contributions. Consistent with Our analysis of market timing alpha in CTA funds Fung and Hsieh (2001), however, we find that is motivated by their trading approach. A man- these contributions are relatively small. The aver- ager who can predict the market direction over age return net of beta contributions is called some horizon would be long the market when it excess return or alpha. For many hedge funds, rises and short the market when it falls5; i.e., her alpha comes from selection of stocks or bonds. returns associated with this market would be the Since CTAs do not generally invest in individ- absolute value of market returns.6 While some ual stocks or bonds, their alpha comes mainly CTAs forecast the magnitude and direction of from market timing gains; that is, from tactical market returns, many focus solely on direction; adjustments in asset exposure that are coordi- at these funds, the allocation to an asset is inde- nated with market movements. We use a model pendent of the signal strength and only the sign to estimate the contribution from directional matters. This motivates our choice of absolute (beta) exposure, as well as the alpha due to values of index returns as proxies for market tim- market timing skill; the average return net of ing skill. Therefore, instead of simply including beta contribution and market timing alpha is equity, fixed income, currency, and commod- called the residual alpha. Absent market tim- ity returns in our model, we also include their ing skill, residual alpha is just the usual excess absolute values. Positive and significant coeffi- return. cients on absolute value factors are evidence of market timing ability. Since the absolute value For CTA funds, what comprises residual alpha? factors have positive averages, their presence in a Since we use liquid indexes in each asset class regression model accounts for some of a fund’s to measure the beta contribution and market tim- positive average return. In fact, we find that ing alpha, gains from exposure to and timing this estimated contribution exceeds CTA index Journal Of Investment Management Second Quarter 2011 Not for Distribution Multiple Time Scale Attribution for Commodity Trading Advisor (CTA) Funds 37 average returns, resulting in negative residual obtain market timing variables at different time alphas. scales. CTA funds differ in their forecast horizons (e.g., For a given fund, the time scales used in attribu- long-term or short-term) and some funds use mod- tion analysis depend on its strategy, the frequency els with multiple horizons.7 This mixing of time and length of available data, and the correlations scales is compounded in CTA indexes, which among timing factors during the fund’s history. combine the returns of many funds. In fact, we For short-term traders, it is more important to observe market timing alpha at a range of fre- include daily and weekly timing factors, whereas quencies for CTAindexes. Market timing skill at a these may be less relevant for longer term CTAs. range of time scales complicates attribution anal- To get meaningful results from long-term timing ysis. For asset class returns (beta factors), absent factors, such as quarterly or annual timing, several the effects of compounding or serial correlation,8 years of fund data are necessary—otherwise, low- contributions are independent of time scale of frequency timing ability may appear as beta. Also, measurement.9 This is not necessarily so for the if timing factors for an asset are highly correlated, nonlinear factors we use to measure market tim- only one or two time scales may ultimately appear ing ability, as the sum of absolute values of in a multi-factor model for the fund. Since timing daily returns within a month can be equal to or factors for an asset may be correlated at differ- much larger than the absolute value of monthly ent frequencies, and timing factors for different returns.10 Consequently, contributions from mar- assets may also be correlated, analysts must con- ket timing at different time scales may either duct due diligence to ensure that the timing factors be additive or redundant.11 To compute a fund’s included in the model are truly relevant to the aggregate market timing alpha, we need to sum fund’s strategy. the orthogonal contributions from different time Isolating market timing contributions and com- scales. puting residual alpha can provide useful insights into CTA funds. Investors may prefer funds that To estimate the combined market timing skill of exhibit consistent market timing ability at a given a fund at multiple time scales, we introduce vari- time scale, seeing this as evidence of a proprietary ables that express low-frequency timing ability advantage.Also, in studying a fund’s performance through high-frequency data. Suppose a manager over time, a more-negative residual alpha or ratio 12 has monthly market timing skill ; i.e., she can of residual alpha to market timing alpha could predict whether a market will be up or down indicate higher trading costs, possibly associ- for the month, but not at daily or weekly time ated with greater assets. Our results also indicate scales, and only trades at month-end. During the potentially large role that transaction costs the month, she will be long (short) the market play even in ostensibly liquid and low-frequency each day, depending on whether it will be up CTAs.