概述 Abstract
This paper studies the relationship between idiosyncratic volatility and expected returns in
commodity futures markets. Measuring idiosyncratic volatility relative to traditional pricing
models that fail to account for backwardation and contango leads to the puzzling conclusion
that idiosyncratic volatility is negatively priced. In sharp contrast, idiosyncratic volatility is not
priced when the fundamental backwardation and contango cycle of commodity futures markets is
factored in an appropriate benchmark. Further evidence suggests that the idiosyncratic volatility
inferred from traditional benchmarks acts as proxy for the risk associated with contangoed
contracts.
Keywords: Commodity futures; Idiosyncratic volatility; Backwardation; Contango.
本文研究了商品期貨市場(chǎng)特異波動(dòng)率與預(yù)期收益之間的關(guān)系。如果使用傳統(tǒng)定價(jià)模型對(duì)特異波動(dòng)率進(jìn)行定價(jià)，由于沒有考慮到升水和貼水，將會(huì)導(dǎo)致特異波動(dòng)率定價(jià)為負(fù)這一令人困惑的結(jié)論。與此形成鮮明對(duì)比的是，如果將商品期貨市場(chǎng)基本的貼水與升水周期歸因到一個(gè)合適的基準(zhǔn)，那么特異波動(dòng)率的定價(jià)應(yīng)當(dāng)為零。進(jìn)一步的證據(jù)表明，從傳統(tǒng)的基準(zhǔn)導(dǎo)出的特異波動(dòng)率代表了與升水合約相聯(lián)系的風(fēng)險(xiǎn)。
關(guān)鍵詞：商品期貨、奇異波動(dòng)率、升水、貼水
1，簡(jiǎn)介 Introduction
The link between idiosyncratic volatility and mean returns has been the subject of intense scrutiny
in the equity markets literature. Theoretical arguments rule out any such link since idiosyncratic
volatility can be diversified away and thus should not be priced (Sharpe, 1964) or maintain
that the link is positive since agents who hold poorly-diversified portfolios demand incremental
returns for bearing idiosyncratic volatility (Merton, 1987; Malkiel and Xu, 2002). The empirical
evidence is mixed. A number of studies support the contention that idiosyncratic volatility is not
priced (Fama and McBeth, 1973; Bali et al., 2005; Bali and Cakici, 2008; Fink et al., 2012; Huang
et al., 2010; Han and Lesmond, 2011) but others report evidence in favor of a positive (Malkiel and
Xu, 2002; Goyal and Santa-Clara, 2003; Fu, 2009; Garcia et al., 2011) or an anomalous negative
link (Guo and Savickas, 2008; Ang et al., 2006, 2009) between idiosyncratic volatility and average
returns in equity markets.
在股票市場(chǎng)相關(guān)的文獻(xiàn)中，特異波動(dòng)率和平均回報(bào)率之間的關(guān)聯(lián)已經(jīng)認(rèn)真地研究過了。理論上的觀點(diǎn)要么認(rèn)為特異波動(dòng)率和平均回報(bào)率之間不存在任何關(guān)聯(lián)，因?yàn)樘禺惒▌?dòng)率可以通過分散化消除掉（Sharpe，1964）。要么持有特異波動(dòng)率定價(jià)為正的觀點(diǎn)，因?yàn)槌钟蟹稚⒒^差資產(chǎn)組合的客戶將要求額外的風(fēng)險(xiǎn)補(bǔ)償以承擔(dān)特異波動(dòng)率（Merton, 1987; Malkiel and Xu, 2002）。實(shí)證上的觀點(diǎn)則比較混亂。許多的研究支持特異波動(dòng)率定價(jià)為0的觀點(diǎn)（(Fama and McBeth, 1973; Bali et al., 2005; Bali and Cakici, 2008; Fink et al., 2012; Huang et al., 2010; Han and Lesmond, 2011）。另外一些則提供證據(jù)支持特異波動(dòng)率定價(jià)為正的觀點(diǎn)（Malkiel and Xu, 2002; Goyal and Santa-Clara, 2003; Fu, 2009; Garcia et al., 2011）。還有一些很奇怪的觀點(diǎn)認(rèn)為在股票市場(chǎng)上特異波動(dòng)率和平均回報(bào)率之間存在著一種負(fù)的關(guān)聯(lián)(Guo and Savickas, 2008; Ang et al., 2006, 2009)。
This article studies the relation between idiosyncratic volatility and mean returns in commodity
futures markets. The role of idiosyncratic volatility as driver of commodity futures risk premia
was first conceptualized by Hirshleifer (1988) in a theoretical model that accounts for trading
costs and non-marketability of producers claims. The commodity futures risk premium can then
be decomposed into two components: the first one, in the spirit of the CAPM, depends on the
co-movement of the futures contract with a broad equity index; the second one depends on the
idiosyncratic volatility of the contract and net hedging which is positive when hedgers are net
short and negative when they are net long. Bessembinder (1992) validates the predictions of
Hirshleifer (1988) by showing that idiosyncratic volatility conditional on net hedging commands
a positive risk premium in agricultural commodity and foreign currency markets.
本文研究了商品期貨市場(chǎng)中特異波動(dòng)率和平均回報(bào)率的關(guān)系。特異波動(dòng)率作為驅(qū)動(dòng)商品期貨風(fēng)險(xiǎn)溢價(jià)的角色這一概念最早是由 Hirshleifer 在1988年的一個(gè)理論模型中提出的，這個(gè)模型考慮了交易成本和生產(chǎn)者缺乏他們需要的銷售市場(chǎng)的情況。商品期貨的風(fēng)險(xiǎn)溢價(jià)于是可以分解成兩個(gè)組成部分。按照CAPM的理論范式，第一個(gè)是取決于期貨合約與其它一系列股票指數(shù)之間的共同運(yùn)動(dòng)情況，第二個(gè)取決于特異波動(dòng)率和持有裸露頭寸的情況。當(dāng)持有多頭頭寸時(shí)，它是正的，當(dāng)持有空頭頭寸時(shí)，它是負(fù)的。Bessembinder (1992)證實(shí)了Hirshleifer (1988) 的預(yù)測(cè)，他發(fā)現(xiàn)在農(nóng)產(chǎn)品商品期貨市場(chǎng)和外匯市場(chǎng)中，當(dāng)持有裸露頭寸時(shí)，特異波動(dòng)率將導(dǎo)致正的風(fēng)險(xiǎn)補(bǔ)償收益。
While studying the pricing of idiosyncratic volatility in commodity futures markets, the first
thorny issue we face relates to the choice of an appropriate asset pricing model or benchmark
upon which to model idiosyncratic volatility. Traditional risk factors from equity and fixed income
markets or emanating from the APT have been proven to be unsuccessful for pricing commodity
futures contracts (Dusak, 1973; Bodie and Rosansky, 1980; Kolb, 1996; Erb and Harvey, 2006; or,
more recently Daskalaki et al., 2012). Commodity-specific risk factors (Carter et al., 1983; Chang,
1985; Bessembinder, 1992; De Roon et al., 2000; Basu and Miffre, 2012; Daskalaki et al., 2012;
Gorton et al., 2012) have fared somewhat better, but not unanimously so, inasmuch as they
capture the fundamentals of backwardation and contango put forward in the theory of storage
of Kaldor (1939) and Working (1948, 1949) and in the hedging pressure hypothesis of Cootner
(1960) and Hirshleifer (1988). Given the lack of consensus on a suitable asset pricing model or
benchmark for commodity futures, the first objective of this paper is to provide evidence on
the ability of various risk factors to explain the cross-sectional variation in commodity futures
returns. The second objective is to test, through the various asset pricing models considered, the
nature of the relation between idiosyncratic volatility and mean returns both in a cross-sectional
framework and in a time-series portfolio formation setting.
我們研究商品期貨市場(chǎng)中特異波動(dòng)率定價(jià)問題時(shí)遇到的第一個(gè)棘手的問題，是如何選擇一個(gè)合適的資產(chǎn)定價(jià)模型或者參照基準(zhǔn)來衡量特異波動(dòng)率。傳統(tǒng)的權(quán)益類市場(chǎng)或固定收益市場(chǎng)中的風(fēng)險(xiǎn)因子，或者由APT定價(jià)模型產(chǎn)生的風(fēng)險(xiǎn)因子被證明對(duì)商品期貨的定價(jià)是不成功的 (Dusak, 1973; Bodie and Rosansky, 1980; Kolb, 1996; Erb and Harvey, 2006; or,more recently Daskalaki et al., 2012)。由于考慮了Kaldor(1939) 和 Working(1948,1949)在貯藏理論，以及Cootner (1960) 和 Hirshleifer (1988)在套保壓力假設(shè)理論中提出的升水和貼水的基礎(chǔ)概念，一些商品期貨獨(dú)有的風(fēng)險(xiǎn)因子(Carter et al., 1983; Chang,1985; Bessembinder, 1992; De Roon et al., 2000; Basu and Miffre, 2012; Daskalaki et al., 2012; Gorton et al., 2012) 受到更好一些的評(píng)價(jià)，但并非毫無異議。盡管學(xué)術(shù)界對(duì)于商品期貨定價(jià)的模型或參照基準(zhǔn)缺少一致性，本文的第一個(gè)目標(biāo)是證明多樣化的風(fēng)險(xiǎn)因子能夠解釋不同商品期貨在一個(gè)時(shí)間截面上的收益率的差異。本文的第二個(gè)目的，是為了用我們考慮的多樣化資產(chǎn)定價(jià)模型來測(cè)試商品期貨的特異波動(dòng)率和平均收益率之間的關(guān)系，我們既基于時(shí)間截面框架來考慮這個(gè)問題，也基于組合信息的時(shí)間序列來研究這個(gè)問題。
The main contribution of our study is to demonstrate empirically that inferences on the relation
between lagged idiosyncratic volatility and expected returns in commodity futures markets hinge
on the choice of asset pricing model. When the pricing model fails to recognize the fundamentals
of backwardation and contango it is shown that: a) idiosyncratic volatility is negatively priced
cross-sectionally, and b) a mimicking portfolio that over time buys low idiosyncratic volatility
commodities and shorts high idiosyncratic volatility commodities offers sizeable alpha. These
results are aligned with those reported by Ang et al. (2006, 2009) in international equity markets.
In sharp contrast, if the natural propensity of commodity markets to be in backwardation/
contango is explicitly factored in the benchmark, idiosyncratic volatility is no longer priced crosssectionally
and the alpha of a portfolio that buys low idiosyncratic volatility commodities and
shorts high idiosyncratic volatility commodities becomes insignificant. This outcome agrees with the fundamental tenet of finance theory that idiosyncratic volatility can be diversified away and
hence, it is not priced. Further, we show that the seemingly negative premium associated with
idiosyncratic volatility when inappropriate asset pricing models are used reflects the pricing of
contangoed (rather than backwardated) portfolios, suggesting that idiosyncratic volatility acts,
in fact, as a proxy for the systematic risk associated with contangoed assets.
本文主要的貢獻(xiàn)在于經(jīng)驗(yàn)性地展示了商品期貨市場(chǎng)延遲的特異波動(dòng)率和預(yù)期的回報(bào)率會(huì)隨著定價(jià)模型的選擇而變化。如果定價(jià)模型沒能識(shí)別期貨貼水和升水的基礎(chǔ)，那么 a) 特異波動(dòng)率的定價(jià)是負(fù)的。b）一個(gè)反復(fù)地購買低波動(dòng)率的商品期貨并做空高波動(dòng)率的商品期貨的組合，將能夠提供可觀的alpha。 這些結(jié)論和Ang et al.（2006,2009）在全球股票市場(chǎng)得出的結(jié)論一致。與之形成鮮明對(duì)比的是，如果商品期貨貼水或升水的自然傾向被明顯地包含在基準(zhǔn)中，特異波動(dòng)率在時(shí)間截面上的將定價(jià)為0，買入低波動(dòng)率的商品期貨組合并賣空高波動(dòng)率的商品期貨組合所獲得的alpha將不顯著。這個(gè)結(jié)論和基礎(chǔ)的金融學(xué)原則一致，特異波動(dòng)率由于可以通過持有多樣化組合的方法消除掉，所以其定價(jià)應(yīng)當(dāng)為0。進(jìn)一步地，我們的研究顯示，當(dāng)采用不合適的資產(chǎn)定價(jià)模型來反映升水的（而非貼水）組合時(shí)，與特異波動(dòng)率相關(guān)的看似為負(fù)的超額收益率實(shí)際上暗示我們，特異波動(dòng)率其實(shí)代表著和溢價(jià)資產(chǎn)相關(guān)聯(lián)的系統(tǒng)風(fēng)險(xiǎn)。
The paper is structured as follows. Section 2 introduces the commodity futures data. Section
3 motivates the pricing models considered both theoretically and empirically. Sections 4 and
5 provide cross-sectional and time-series evidence on the relationship between idiosyncratic
volatility and commodity futures returns. Section 6 concludes.
本文結(jié)構(gòu)如下。第2部分介紹了商品期貨的數(shù)據(jù)。第3部分闡述了從理論上和經(jīng)驗(yàn)上考慮的定價(jià)模型。
第4部分和第5部分提供了時(shí)間截面和時(shí)間序列上的證據(jù)，展示特異波動(dòng)率和商品期貨收益率之間的關(guān)系。第6部分總結(jié)。
2，商品期貨數(shù)據(jù) Commodity Futures Data
The research is based on daily settlement prices and volume data for 27 commodity futures from
January 2, 1979 to August 31, 2011, from Datastream. The 27 commodities are: 12 agricultural
(cocoa, coffee C, corn, cotton n°2, frozen concentrated orange juice, rough rice, oats, soybean
meal, soybean oil, soybeans, sugar n° 11, wheat), 5 energy (electricity, gasoline, heating oil n° 2,
light sweet crude oil, natural gas), 4 livestock (feeder cattle, frozen pork bellies, lean hogs, live
cattle), 5 metal (copper, gold, palladium, platinum, silver), and random length lumber. We track
the futures prices on all nearest and second-nearest contracts in order to work with the most
traded contracts; the nearest contract is held up to one month before maturity when the position
is rolled over to the second-nearest contract. Excess returns (referred to as "returns" afterwards
for expositional ease) are measured as logarithmic price differences.
我們的研究基于27種商品期貨從 1979年1月2日至2011年 8月31日每日的結(jié)算價(jià)格和交易量數(shù)據(jù)，數(shù)據(jù)來源是Datastream。這27種商品包括：12種農(nóng)產(chǎn)品（cocoa, coffee C, corn, cotton n°2, frozen concentrated orange juice, rough rice, oats, soybean meal, soybean oil, soybeans, sugar n° 11, wheat），5種能源商品 (electricity, gasoline, heating oil n° 2,light sweet crude oil, natural gas)，4種牲畜（feeder cattle, frozen pork bellies, lean hogs, live cattle)，5種金屬（copper, gold, palladium, platinum, silver）和 任意長(zhǎng)度的木材。我們跟蹤了這些商品期貨中時(shí)間最鄰近和第二鄰近的合約的價(jià)格，以便找到主力合約：最鄰近的合約在到期一個(gè)月之前被停止，并讓位于第二鄰近的合約。超額收益率（為敘述方便，下文將簡(jiǎn)稱為"收益率"）通過使用對(duì)數(shù)價(jià)差方法來衡量。
Our empirical analysis also requires observations on the positions of large traders in commodity
futures markets, which are provided weekly by the Commodity Futures Trading Commission
(CFTC), from January 1986 to August 2011. Large traders have to report weekly to the CFTC
whether they are commercial (hedgers) or non commercial (speculators) and whether they are
long or short. Their declarations compiled in the Aggregated Commitment of Traders report
serve as inputs to calculate two hedging pressure measures. Speculators’ hedging pressure is
calculated as the number of their long positions (i.e., open interests or the amount of outstanding
contracts) divided by the total number of positions taken by non-commercial traders over the
week. Hedgers’ hedging pressure is defined in terms of their long positions as a fraction of the
total open interests associated with commercial traders over the week. For example, a hedging
pressure of 0.2 for hedgers means that 20% of hedgers were long and thus 80% were short
over the week, which is (as argued in detail in Section 3.1) a sign of backwardation. A hedging
pressure of 0.2 for speculators means that 20% of speculators were long and thus 80% were
short over the week, which is (as explained next) an indication of contango. The cross-section size
(N=27 commodities) of our sample is, in fact, dictated by data availability from the Aggregated
Commitment of Traders report.
我們的研究同時(shí)也需要對(duì)商品期貨市場(chǎng)中大單交易的觀察，這由商品期貨交易委員會(huì)(CFTC)每周公布，時(shí)間從1986年1月至2011年8月。 大單交易必須每周向CFTC匯報(bào)交易情況：是套保交易還是投機(jī)交易，是多單還是空單。這些聲明將被收集到交易商承諾匯總報(bào)告中，我們把它作為一個(gè)輸入來計(jì)算兩種對(duì)沖壓力量。投機(jī)的對(duì)沖壓力量用投機(jī)商一周內(nèi)總的多頭持倉（亦即未平倉合約）除以投資商一周內(nèi)的總持倉來計(jì)算。套期保值的對(duì)沖壓力量用一周內(nèi)的多頭套保持倉除以一周內(nèi)的全部套保持倉來計(jì)算。例如，0.2 的套期保值對(duì)沖壓力量意味著一周內(nèi)有20%的套期保值持倉為多頭，而另外的80%的套期保值持倉為空頭，這是一種貼水的征兆（我們將在 Section 3.1詳細(xì)討論這一點(diǎn)）。0.2的投機(jī)壓力量意味著一周內(nèi)20%的投機(jī)倉位是多頭而80%的投機(jī)倉位是空頭，這是一種升水的征兆（我們將在后面解釋這一點(diǎn)）。實(shí)際上，我們?cè)谝粋€(gè)時(shí)間截面上的合約數(shù)量（N = 27 種商品期貨）正是由CFTC每周的交易商承諾匯總報(bào)告有效的數(shù)據(jù)量決定的。
3，時(shí)間截面上商品期貨收益率的解釋
Explaining the Cross-Section of Commodity Futures Returns
This section begins by presenting the theoretical motivation behind the pricing models employed
and continues by offering empirical evidence on their plausibility.
這個(gè)部分我們將首先展示我們應(yīng)用的定價(jià)模型的理論動(dòng)機(jī)然后為其合理性提供經(jīng)驗(yàn)證據(jù)。
3.1 Theoretical Underpinning of Systematic Risk Factors
As there is no consensus on the systematic risk factors that should be adopted to model expected
commodity futures returns, we measure idiosyncratic volatility relative to several pricing models.
This section theoretically motivates the various risk factors. Some of them are borrowed from
the literature on the pricing of traditional assets (equities and bonds) under the Law of One Price
theory which contends that financial markets are fully integrated (Cochrane, 2005). All other
factors we consider are commodity-specific and are intended to account for the fundamental
backwardation/contango cycle of commodity futures.
3.1 系統(tǒng)性風(fēng)險(xiǎn)因素的理論基礎(chǔ)
由于學(xué)術(shù)界對(duì)商品期貨預(yù)期收益率的系統(tǒng)性風(fēng)險(xiǎn)因素定價(jià)應(yīng)當(dāng)采用的模型沒有達(dá)成一致性，我們將用多個(gè)定價(jià)模型來衡量商品期貨的特異波動(dòng)率。這個(gè)部分我們將從理論上研究多種風(fēng)險(xiǎn)因子。它們中的一些借用自一些傳統(tǒng)資產(chǎn)（股票和債券）的定價(jià)模型的一些文獻(xiàn)，因?yàn)楦鶕?jù)一價(jià)定律，各個(gè)不同的金融市場(chǎng)實(shí)際上是相連相通的一個(gè)集成體(Cochrane, 2005)。我們考慮的一些其它的因子是商品特有的，它們被用來將商品期貨基本的貼水和升水周期納入我們的理論體系。
We use as traditional risk factors: i) the three equity factors of Fama and French (1993), namely,
the equity market premium, the size premium (SMB), and the value premium (HML), obtained
from Kenneth French’s website, and ii) the excess returns of the Barclays US aggregate bond
index obtained from Bloomberg. The equity market excess return is used as substitute for the
true market portfolio assumed by the CAPM. SMB and HML are included as proxies for shifts in
the investment opportunity set of agents over time (Petkova, 2006); as such, they could be priced
in commodity futures markets too. The inclusion of a fixed income benchmark is motivated by
the theory of storage that explains the shape of the commodity futures curve via the cost of
borrowing.
The commodity-specific risk factors attempt mainly to capture the fundamentals of backwardation
and contango. Broadly speaking, backwardation means that the futures price of a commodity
is expected to appreciate as maturity approaches. Contango means the opposite. Figure 1
depicts the theoretical price evolution of two contangoed contracts (continuous lines) and two
backwardated contracts (dashed lines) with maturities n for the nearby contract and d for the
distant contract.
我們使用了以下一些傳統(tǒng)的風(fēng)險(xiǎn)因子：i）Fama和French(1993)提出的三個(gè)股票因子，也就是股票市場(chǎng)超額收益率，市值超額收益率(SMB)，以及估值超額收益率(HML)，這些數(shù)據(jù)可以從 Kenneth French 的網(wǎng)站上獲得。2）巴克萊美國綜合債券指數(shù)的超額收益率，這個(gè)數(shù)據(jù)可以從Bloomberg獲得。股票市場(chǎng)的超額收益率被用來代替CAPM模型中所假設(shè)的真實(shí)市場(chǎng)組合。SMB 和 HML 被包括進(jìn)來作為客戶投資機(jī)會(huì)隨著時(shí)間變化的代表(Petkova, 2006);因此，在期貨市場(chǎng)中，它們也是可以被定價(jià)的。 將固定收益基準(zhǔn)包括進(jìn)來是受到貯藏理論的啟發(fā)，這個(gè)理論解釋了商品期貨曲線形狀與借貸成本之間的關(guān)系。
我們采用商品期貨特有的風(fēng)險(xiǎn)因子主要用來捕獲貼水和升水的基礎(chǔ)原理。一般來說，貼水意味著商品期貨的價(jià)格預(yù)期將要上漲，隨著交割日臨近。升水則意味著相反。Figure 1 描述了兩個(gè)升水合約(實(shí)線)和兩個(gè)貼水合約(虛線)的理論上的價(jià)格演化走勢(shì)，其中近期合約離交割日n天，遠(yuǎn)期合約離交割日d天。
Figure 1. Theoretical price evolution of commodity futures. The figure represents the evolution in the futures prices of two contracts
with maturity n and d (n < d) for a hypothetical commodity when the market is in backwardation (dashed lines) and when it is in
contango (continuous lines). Backwardated (contangoed) contracts are characterized by positive roll yield (negative roll yield), low (high)
hedgers' hedging pressure (HP), high (low) speculators' hedging pressure and are winners (losers) in a momentum portfolio. St denotes the
commodity spot price.
Figure 1. 理論上商品期貨的價(jià)格演化。這個(gè)圖片代表了兩個(gè)期貨合約價(jià)格的演化，它們的到期日分別是n和d天，我們假設(shè)市場(chǎng)是分別貼水的（虛線）和升水（實(shí)線）的。貼水(升水)合約的特征是有一個(gè)正的滾動(dòng)收益（負(fù)的滾動(dòng)收益），套期保值的對(duì)沖壓力量較低（高），投機(jī)的對(duì)沖壓力量較高（低），并且在一個(gè)動(dòng)量組合 [momentum portfolio] 中為盈利方（虧損方）。St 表示商品現(xiàn)貨價(jià)格。
We summon two theoretical rationales to motivate the price evolutions depicted in Figure 1. The
first relies on Kaldor’s (1939) and Working’s (1948, 1949) theory of storage which is empirically
supported by Gorton et al. (2012). This theory explains the shape of the commodity futures curve
by means of the incentive that inventory holders have in owning the commodity spot. Given
the difficulty of collecting reliable inventory data, we rely on the slope of the term structure
(hereafter TS) of commodity futures prices ? instead of standardized inventory levels ? as signal
for backwardation and contango (Erb and Harvey, 2006; Gorton and Rouwenhorst, 2006; Fuertes
et al., 2010; Daskalaki et al., 2012; Gorton et al., 2012). According to the storage theory, as
implicitly suggested in Figure 1, we extract the commodity futures risk premium by systematically
buying the backwardated contracts with the highest roll yields (or roll returns) and shorting the
contangoed contracts with the lowest roll yields.
我們總結(jié)了兩個(gè)理論上的依據(jù)來解釋 Figure 1中價(jià)格的演化。 第一個(gè)依據(jù)依賴于 Kaldor’s (1939) 和 Working’s (1948, 1949) 的貯藏理論，這個(gè)理論被 Gorton et al. (2012)從經(jīng)驗(yàn)數(shù)據(jù)上給予了支持。這個(gè)理論用庫存持有者持有現(xiàn)貨的動(dòng)機(jī)的方法來解釋商品期貨曲線的形狀?？紤]到收集可靠的存貨數(shù)據(jù)是非常困難的，我們使用商品期貨期限結(jié)構(gòu)（此后用 TS 表示期限結(jié)構(gòu)：term structure）的斜率，而不是標(biāo)準(zhǔn)得存貨水平，來作為貼水和升水的征兆 (Erb and Harvey, 2006; Gorton and Rouwenhorst, 2006; Fuertes et al., 2010; Daskalaki et al., 2012; Gorton et al., 2012)。根據(jù)貯藏理論，如同 Figure 1所建議的那樣，我們用如下方法提取商品期貨的風(fēng)險(xiǎn)超額收益率，即系統(tǒng)性地買入擁有最高滾動(dòng)收益的貼水合約，并做空擁有最低滾動(dòng)回報(bào)的升水合約。
The second theoretical rationale for the backwardation/contango price evolution depicted in
Figure 1 comes from the hedging pressure (hereafter HP) hypothesis of Cootner (1960) which is
generalized in Hirshleifer (1988) and validated empirically in Bessembinder (1992) and Basu and
Miffre (2012). This theory relates backwardation and contango to the propensity of hedgers to
be net short or net long. As illustrated in Figure 1, the idea is to capture the risk premium of
commodity futures contracts by buying backwardated commodities for which hedgers are the
shortest and speculators the longest and by shorting contangoed commodities for which hedgers
are the longest and speculators the shortest. To put this differently, the HP mimicking portfolio
buys (sells) the commodities for which hedgers' hedging pressure is the lowest (highest) and
speculators' hedging pressure is the highest (lowest) following the double-sorting methodology
developed in Basu and Miffre (2012)
第二個(gè)針對(duì)Figure 1中 貼水和升水期貨的價(jià)格演化的理論根據(jù)來自于 Cootner （1960）的對(duì)沖壓力假設(shè)(此后用HP表示對(duì)沖壓力因子，hedging pressure)，這個(gè)理論被 Hirshleifer（1988）所推廣，并被 Bessembinder (1992) 和 Basu、Miffre (2012) 從經(jīng)驗(yàn)證據(jù)上所證實(shí)。這個(gè)理論用套期保值交易者傾向于純多頭或純空頭來解釋貼水和升水。如同 Figure 1所展示的那樣，這個(gè)理論通過如下方法來捕獲商品期貨合約的風(fēng)險(xiǎn)超額收益，即買入套期保值交易商做空最多而投機(jī)商做多最多的貼水商品，同時(shí)賣空套期保值者做多最多而投機(jī)商做空最多的升水商品期貨。換句話說，HP理論的模擬組合買入(賣空)套保對(duì)沖壓力最低 (高) 而投機(jī)的對(duì)沖壓力最高（低）的商品，這可以依據(jù) Basu 和 Miffre（2012）年發(fā)展的雙排序方法。
Our third risk factor is the commodity momentum portfolio (hereafter Mom) advocated by Erb
and Harvey (2006) and Miffre and Rallis (2007) that systematically longs commodities with the
best past performance and shorts commodities with the worst past performance. While it is
not directly intended to do so, this momentum portfolio can also capture to some extent the
backwardation/contango cycle. Indeed, Miffre and Rallis (2007) show that the winners (losers)
tend to have positive (negative) roll yields making them backwardated (contangoed). However,
as illustrated empirically in Fuertes et al. (2010), there is no full overlapping of Mom and TS
portfolio returns and therefore they can be used in conjunction to model commodity futures risk
premia.
我們的第三個(gè)風(fēng)險(xiǎn)因子來自于Erb、Harvey (2006) 和 Miffre、Rallis (2007) 所倡導(dǎo)的商品動(dòng)量（此后用 Mom 表示動(dòng)量組合因子，Momentum）組合，這種組合系統(tǒng)性地買入過去表現(xiàn)最好的商品并做空過去表現(xiàn)最差的商品。雖然并非出自本意，這種動(dòng)量組合在某種程度上也能捕獲貼水和升水的循環(huán)。實(shí)際上， Miffre 和 Rallis (2007) 顯示 具有盈利（虧損）傾向的合約常常使得他們貼水（升水）。但是，就如同 Fuertes et al.(2010) 用經(jīng)驗(yàn)數(shù)據(jù)論證的那樣，Mom 和 TS 組合回報(bào)之間并沒有完全重疊，因此它們可以聯(lián)合起來使用，以便對(duì)商品期貨的風(fēng)險(xiǎn)溢價(jià)建立模型。
Building on the Keynesian hypothesis that commodity futures markets are normally backwardated
(Keynes, 1930), we also include as potential risk factor the S&P-GSCI (Standard & Poor's Goldman
Sachs Commodity Index) as a long-only commodity market portfolio. Daily data for S&P-GSCI are
obtained from Bloomberg.
Finally, given that investors demand a premium for holding less liquid assets and in line with the
work of Han and Lesmond (2011) that relates the pricing of idiosyncratic volatility to liquidity
risk, all our benchmarks include as risk factor the liquidity risk premium (LRP) of Pastor and
Stambaugh (2003) that we apply to commodities.
In the remainder of the paper, we adopt the terminology fundamental commodity benchmarks
to refer to commodity pricing models that account for the fundamentals of backwardation
and contango (i.e., those including the TS, HP and/or Mom factors) and traditional benchmarks
to refer to models that fail to do so (i.e., those based on the Fama-French factors, bond risk
premium and S&P-GSCI). The liquidity risk premium is included consistently in all benchmarks of
either type.
根據(jù)凱恩斯假設(shè)，商品期貨市場(chǎng)一般情況下是貼水的(Keynes, 1930)。作為一個(gè)僅可單向做多的商品市場(chǎng)組合的S&P-GCSI指數(shù) (Standard & Poor's Goldman Sachs Commodity Index) 被我們作為一個(gè)潛在的風(fēng)險(xiǎn)因子包括進(jìn)來了。S&P-GSCI 的每日數(shù)據(jù)從 Bloomberg獲取。
最后，考慮到對(duì)于缺乏流動(dòng)性的資產(chǎn)，投資者將要求額外的回報(bào)。與 Han 和 Lesmond (2011) 建立的特異波動(dòng)率和流動(dòng)性風(fēng)險(xiǎn)關(guān)聯(lián)的工作一致，我們研究的所有商品期貨的基準(zhǔn)都包含了 Pastor 和 Stambaugh (2003) 提出的流動(dòng)性風(fēng)險(xiǎn)溢價(jià)作為風(fēng)險(xiǎn)因子。
在我們論文的剩余部分，我們采用專有的商品期貨基準(zhǔn)來指代將貼水和升水原理考慮進(jìn)來的商品定價(jià)模型（例如，那些包括了TS，HP 和/或 Mom 因子的模型）而用傳統(tǒng)的基準(zhǔn)來指代那些沒能包括貼水和升水原理的模型（例如，那些建立在 Fama-French 因子，債券風(fēng)險(xiǎn)溢價(jià)，以及 S&P-GSCI上的模型）。無論對(duì)于哪種類型的基準(zhǔn)，流動(dòng)性風(fēng)險(xiǎn)溢價(jià)都被包括進(jìn)來了。
3.2 Empirical Motivation for Fundamental Commodity Benchmarks
This section complements the preceding one by empirically providing some intuition for the
TS, HP and Mom factors as drivers of a systematic risk premium in commodity futures markets.
Figure 2 plots the evolution from January 1986 to August 2011 of end-of-month futures prices
for crude oil. Shaded areas signify backwardated months according to each of three different
signals: when the roll yield is positive (TS signal; Panel A), when speculators are net long at the
beginning and end of month (HP signal; Panel B), and when 12-month past returns are positive
(Mom signal; Panel C). Thus non-shaded areas indicate non-backwardated months when the
roll yield is negative (Panel A), speculators are net short at the beginning and end of the month
or changed positions within the month (Panel B), and when 12-month past performance was
negative (Panel C). Given that the shaded areas do not strictly coincide in the three panels, we
use the TS, HP and Mom factors conjunctly (in pairs or all three) in the benchmarks used to
extract and subsequently price idiosyncratic volatility.
3.2 基礎(chǔ)性商品基準(zhǔn)的經(jīng)驗(yàn)性動(dòng)機(jī)
在這個(gè)部分我們將用一些經(jīng)驗(yàn)性的直觀數(shù)據(jù)補(bǔ)充論證之前所說的 TS，HP，和 Mom 因子作為商品期貨市場(chǎng)中系統(tǒng)性風(fēng)險(xiǎn)超額收益補(bǔ)償?shù)尿?qū)動(dòng)的觀點(diǎn)。Figure 2 畫的是 1986年1月 至2011年 8月 原油商品期貨月底價(jià)格的走勢(shì)。陰影區(qū)域表示貼水月份，依據(jù)于以下三個(gè)不同的信號(hào)：當(dāng)滾動(dòng)收益率為正時(shí)（TS 信號(hào)； Panel A），當(dāng)投機(jī)持倉在月初和月末為純多頭時(shí)（HP 信號(hào)； Panel B），當(dāng)過去的12個(gè)月的收益為正時(shí)（Mom 信號(hào)；Panel C）?？紤]到在這三個(gè)子圖（Panel）里這些陰影區(qū)域不嚴(yán)格一致，我們?cè)诨鶞?zhǔn)中使用TS，HP和Mom 因子聯(lián)合起來（成對(duì)或三個(gè)一起）提取特異波動(dòng)率并隨后為之定價(jià)。
Figure 2. Historical crude oil futures prices. The figure plots monthly futures prices of crude oil alongside shaded areas which indicate
backwardated months when roll-returns are positive (Panel A), when speculators are net long at the beginning and end of month (Panel B)
and when 12-month past returns are positive (Panel C).
Figure 2. 原油期貨的歷史價(jià)格走勢(shì)。這個(gè)圖片畫的是原油商品期貨每月的價(jià)格，圖片中的陰影區(qū)域表示貼水的月份，即當(dāng)滾動(dòng)收益率為正的時(shí)候(Panel A)，當(dāng)投機(jī)持倉在月初和月末為純多頭的時(shí)候（Panel B）以及當(dāng)過去12個(gè)月份收益率為正的時(shí)候（Panel C）.
Figure 2 中的三個(gè)子圖支持了貼水（陰影區(qū)域）和商品期貨價(jià)格上漲趨勢(shì)是緊密相連的。與之相反，商品期貨升水（非陰影區(qū)域）與價(jià)格下跌趨勢(shì)緊密相連。為了量化在 Figure 2中的證據(jù)，我們創(chuàng)造了四個(gè)虛設(shè)的變量。一個(gè)是 D_R(t)，當(dāng)商品期貨每月回報(bào)為正時(shí)它取值為1，為負(fù)時(shí)它取值為0. 另外三個(gè)虛設(shè)變量是為了標(biāo)注原油處于貼水狀態(tài)：如果每月滾動(dòng)收益為正，D_TS(t)取1否則取0；當(dāng)投機(jī)持倉在月初和月末都為純多頭時(shí)D_HP(t)取1，否則取0；而 如果過去的12個(gè)月收益率平均值為正D_Mom(t)取1否則取0. D_R(t) 和其它三個(gè)虛設(shè)的貼水變量D_TS(t)，D_HP(t)，D_Mom(t)之間的相關(guān)系數(shù)(p-values) 分別是 30.18%（0.00）,13.68%(0.00) 和 11.17% （0.05）。這些顯著為正的相關(guān)系數(shù)支持 TS，HP 和Mom 確實(shí)是非常合適的 捕獲基礎(chǔ)的 貼水和升水周期的信號(hào)，因此可以對(duì)商品期貨市場(chǎng)內(nèi)在的系統(tǒng)性風(fēng)險(xiǎn)溢價(jià)進(jìn)行建模。
3.3 Pricing of Systematic Risk Factors
The following four principles are maintained in constructing the TS, HP and Mom mimicking
portfolios that act as proxies for a fundamental commodity risk factor related to the backwardation/
contango cycle. First, the long-short portfolios are formed by taking long positions in the 20%
most backwardated commodity contracts whose prices are expected to appreciate and short
positions in the 20% most contangoed commodity contracts whose prices are expected to
decline. Second, the ranking period over which the TS, HP or Mom signals are averaged out is
set to 12 months, and the holding period over which the long-short portfolios are being held
is set to 1 month.8 Third, in line with Erb and Harvey (2006) among others, the constituents of
the long and short portfolios are equally-weighted. Fourth, the long-short portfolios are fully
collateralized, meaning that 1/2 of the trading capital is invested in risk-free interest bearing
accounts for the longs and likewise for the shorts. Thus the return of the long-short portfolios
equals half the return of the long portfolios minus half the return of the short portfolios.
3.3 系統(tǒng)性風(fēng)險(xiǎn)因子的定價(jià)
在構(gòu)建 TS，HP 和 Mom 模擬組合作為與貼水和升水周期相關(guān)聯(lián)的基礎(chǔ)性商品風(fēng)險(xiǎn)因子的代表時(shí)，我們始終遵循著下面四個(gè)原則。第一，我們構(gòu)建的多空組合中，多頭持倉選擇 前20%貼水最多的商品合約，它們的價(jià)格預(yù)期將要上漲，空頭持倉選擇前20%升水最多的商品合約，它們的價(jià)格預(yù)期將要下跌。第二，計(jì)算TS，HP 和Mom信號(hào)平均數(shù)的排序期為12個(gè)月，持有多空組合的時(shí)間長(zhǎng)度為1個(gè)月。第三，與 Erb 和 Harvey (2006) 以及其它研究者相一致，多空組合的各個(gè)組成成分是等權(quán)重分配的。第四，多空組合是完全對(duì)沖的，即有一半的資產(chǎn)被投資在與無風(fēng)險(xiǎn)收益率相關(guān)的多頭頭寸，另外一半類似地投資在空頭頭寸。因此，多空組合的收益一半取決于多頭組合的收益，一半取決于空頭組合的收益。
Our sample comprises daily observations on the three Fama-French risk factors, the commodity
futures returns and the (backfilled) S&P-GSCI returns for the period from January 2, 1979 to
August 31, 2011. Because the ranking window to construct the long-short TS and Mom mimicking
portfolios is set to 12 months, the first set of returns available for them corresponds to January
2, 1980. Since the ranking window for the liquidity risk mimicking portfolio is 60 months, as in
Pastor and Stambaugh (2003), the first set of returns for the liquidity risk factor corresponds to
January 2, 1985. On the other hand, the availability of hedging pressure data in the Aggregated
Commitment of Traders report forces us to start our analysis of the HP risk premium on January
2, 1987. Finally, as the returns on the Barclays bond index are available at a daily frequency from
January, 3 1989 onwards, the sample period that is common to all series runs from January 3,
1989 to August 31, 2011.
我們的樣本包含了對(duì)1979年1月2日至2011年8月31日三個(gè) Fama-French風(fēng)險(xiǎn)因子，商品期貨回報(bào)以及S&P-GSCI 的每日觀察。因?yàn)闃?gòu)建多空 TS和Mom模擬組合呢的排序時(shí)間窗口是12個(gè)月，因此，有效的第一個(gè)回報(bào)率數(shù)據(jù)是 1980年1月2日的。由于流動(dòng)性風(fēng)險(xiǎn)的模擬組合的排序期是60 個(gè)月，如同 Pastor 和Stambaugh （2003）所提出的那樣，第一個(gè)有效的流動(dòng)性風(fēng)險(xiǎn)回報(bào)率數(shù)據(jù)在 1985年1月2日。
Table 1 presents pairwise correlations between the daily returns for all risk factors considered
over the longest period possible from January 3, 1989 to August 31, 2011. The average absolute
correlation is low at 0.08. Unsurprisingly, the highest pairwise correlation of 0.44 corresponds
to the two long-short commodity portfolios (Mom and TS), followed by a significant correlation
of 0.34 between Mom and HP. Relatively high pairwise correlations among TS, HP and Mom are
expected because, arguably, the three factors capture the fundamentals of backwardation and
contango. But the fact that these correlations statistically differ from 1 (according to t-tests
for Pearson correlation) motivates our decision to include two or three of these risk factors
simultaneously in the benchmarks; this was also borne out earlier by Figure 2. At the other
extreme, the correlation between the equity market factor and HML factor is small at -0.17, and
is followed closely by that between HML and SMB also very small at -0.12, as well as between
Barclays’ bond index and SMB at -0.12 too.
Table 1 展示了從1989年1月3日至2011年8月31日最長(zhǎng)時(shí)期中每日收益率和所考慮的風(fēng)險(xiǎn)因子之間的相關(guān)系數(shù)。相關(guān)系數(shù)絕對(duì)值最低為 0.08。并不讓人感到驚奇的是，最高的相關(guān)系數(shù)為0.44，這是兩個(gè)多空商品組合之間的相關(guān)系數(shù)（Mom 和 TS），緊隨其后的 Mom 和 HP之間0.34的相關(guān)系數(shù)。 TS，HP和Mom 之間相對(duì)較高的相關(guān)系數(shù)是預(yù)料之中的，因?yàn)榘蠢碚f，這三個(gè)因子都可以捕獲貼水和升水的基礎(chǔ)原理。但是這些相關(guān)系數(shù)統(tǒng)計(jì)上地與1存在較大差別（根據(jù) Pearson 相關(guān)系數(shù)的 t-檢驗(yàn)）的事實(shí)，激發(fā)我們考慮將這些風(fēng)險(xiǎn)因子中的兩個(gè)或者三個(gè)同時(shí)包括在我們的基準(zhǔn)中，這一點(diǎn)在之前的 Figure 2 中已經(jīng)得到了證實(shí)。在另一個(gè)極端，股票市場(chǎng)因子和 HML因子之間的相關(guān)系數(shù) 小至 -0.17，緊隨其后的是 HML和 SMB之間 -0.12 的相關(guān)系數(shù)，同樣地，巴克萊債券指數(shù)和 SMB 之間的相關(guān)系數(shù)也是 - 0.12.
Table 2 reports summary statistics for the daily (annualized or per annum, p.a.) excess returns
of the aforementioned risk factors over the period January 3, 1989 to August 31, 2011. Panel
A presents the results for the equity and fixed income motivated risk factors whereas Panel B
pertains to the commodity-specific risk factors.
Table 2 展示了前述風(fēng)險(xiǎn)因子在1989年1月3日至2011年8月31日期間的每日（年化）超額收益率的統(tǒng)計(jì)情況。Panel A 展示了股票和固定收益資產(chǎn)相關(guān)的傳統(tǒng)風(fēng)險(xiǎn)因子，而 Panel B 是關(guān)于商品特有的風(fēng)險(xiǎn)因子。
In line with the theoretical argument that the fundamentals of backwardation and contango
matter to the pricing of commodity futures contracts, the statistics reported in Panel B provide
evidence that the Mom and HP factors, followed by the TS factor, offer the highest Sharpe ratios
and thus are more mean-variance efficient than the backwardated-only S&P-GSCI portfolio.
Aligned with the notion that long backwardated (contangoed) positions make (lose) money, more
detailed analysis reveals that the long TS, HP and Mom portfolios earn positive mean returns
of 4.69%, 4.09% and 7.32% p.a., respectively, while the short TS, HP and Mom portfolios earn
negative mean returns of -5.34%, -7.17% and -8.00% p.a., respectively.
與理論上貼水和升水將對(duì)商品期貨合約的定價(jià)產(chǎn)生重要影響的觀點(diǎn)一致，Panel B 的統(tǒng)計(jì)數(shù)據(jù)提供證據(jù)表明 Mom 和 HP因子，以及 TS因子將提供最高的Sharpe 比率。因此按照均值方差模型它們比 單純貼水的 S&P-GSCI 組合更為有效。與上述觀點(diǎn)一致，對(duì)貼水（升水）商品的多頭持倉在盈利（虧損），更多的細(xì)節(jié)分析顯示 多頭的 TS，HP 和Mom組合平均每年分別賺得4.69%，4.09%，和7.32%的收益，而空頭的 TS，HP 和Mom 組合平均每年分別賺得 -5.32%，-7.17%和 -8.00% 的收益。
An appropriate common risk factor should be able to explain the cross-sectional variation in
realized commodity futures returns. To gauge this, we follow the two-step approach of Fama
and MacBeth (1973) as deployed by Ang et al. (2009) to analyze the pricing of idiosyncratic
volatility for equities. First, we run time-series regressions for each of the 27 commodity futures,
to explain daily returns on the basis of M risk factors
一個(gè)恰當(dāng)?shù)墓餐L(fēng)險(xiǎn)因子應(yīng)當(dāng)能夠解釋真實(shí)商品期貨在時(shí)間截面上收益的差別。為了評(píng)估這一點(diǎn)，我們仿照了 Fama 和 MacBeth (1973) 采用的量?jī)刹椒椒?，這種方法被 Ang et al.(2009）擴(kuò)展用來分析股票特異波動(dòng)率的定價(jià)。首先，我們對(duì)27種商品期貨跑一個(gè)時(shí)間序列回歸，用以解釋 M種風(fēng)險(xiǎn)因子的每日匯報(bào)。
其中 r_i,d 是第 i 個(gè)商品期貨合約在給定月份中第d = 1,...,D 天的回報(bào)，其中D是那個(gè)月份的天數(shù)； f_ j,d 是第j個(gè)風(fēng)險(xiǎn)因子，j = 1,...,M; epsilon_i,d 是殘差項(xiàng)，（beta_1,i,...,beta_M,i）'是我們關(guān)注的beta系數(shù)。因子的數(shù)量，M，取決于我們手上的基準(zhǔn)。例如，我們的第一個(gè)傳統(tǒng)的基準(zhǔn)使用3個(gè) Fama-French 因子，巴克萊債券指數(shù)，S&P-GSCI 和 LRP，因此一共 M= 6 個(gè)因子被使用。
第二步，我們用第一步得到的每月 beta系數(shù)跑一個(gè)時(shí)間截面上每月商品期貨收益率的回歸，可以表示成如下形式。
regression 2.jpg
其中 r_i,t+1 是第 i 個(gè)商品期貨合約在 第 t+1月份的收益率； beta_ j, i, t+1是 equation (1) 中以t+1月份的每日收益率為基礎(chǔ)使用 OLS方法估計(jì)出來的每月的beta （也就是說，估計(jì)beta依賴的變量和beta 是同一時(shí)期的）；（lambda_1,t+1,……，lambda_M,t+1）是 用equation(2) 用OLS方法估計(jì)出來的 第 t+1月份的 lambda 系數(shù) 或 風(fēng)險(xiǎn)因子定價(jià)。然后對(duì) equation(1)的回歸估計(jì)時(shí)間區(qū)間向前滾動(dòng)一個(gè)月，然后得到的 beta 再帶入到 equation (2) 來重新估計(jì)出一組新的 lambdas，如此滾動(dòng)向前。 Shanken （1992）的修正的 t-檢驗(yàn)方法被用于lambdas 的時(shí)間序列，并決定哪些因子對(duì)于時(shí)間截面上不同的商品期貨具有定價(jià)功能。
Table 3 展示了平均的 lambdas , 顯著性 t-檢驗(yàn) 和調(diào)整的 R^2統(tǒng)計(jì)
Table 3 reports the averaged lambdas, significance t-tests and adjusted-R2 statistics.
Table 3.jpg
Notwithstanding the similar explanatory power for the cross-sectional variation in commodity
futures returns of all models, the analysis reveals that the HP factor stands out by being able to
price the cross-section of commodity futures returns. The largest lambdas in magnitude, strongly
significant at the 1% level, are those corresponding to the HP factor in the fundamental commodity
benchmarks. This evidence challenges the often-held view that commodities do not constitute
another asset class because they do not seem to have a common risk factor (Erb and Harvey,
2006; Daskalaki et al., 2012). The fact that there is at least one commodity-specific risk factor
that prices commodity futures cross-sectionally indicates that commodities instead constitute
a homogeneous alternative asset class. Finding that the sources of risk that explain the cross
sectional variations in stocks and bonds returns fail to command a risk premium in commodity
futures markets supports, however, the contention that financial markets are segmented.
盡管所有的模型對(duì)于時(shí)間截面上不同商品期貨的收益率都具有類似的解釋能力，但是我們的分析顯示 HP 因子對(duì)于時(shí)間截面上不同商品期貨的定價(jià)能力尤其突出。~~量級(jí)上最大的lambda, 在 1%的水平上具有非常強(qiáng)的顯著性，是那些在基礎(chǔ)商品期貨基準(zhǔn)中與HP因子對(duì)應(yīng)的 lambda ~~。這個(gè)證據(jù)挑戰(zhàn)了人們通常持有的觀點(diǎn)——商品期貨不構(gòu)成另外一種類型的資產(chǎn)，因?yàn)樗鼈儾]有一個(gè)共同的風(fēng)險(xiǎn)因子（Erb 和 Harvey, 2006; Daskalaki et al., 2012）. 至少存在一個(gè)商品期貨獨(dú)有的風(fēng)險(xiǎn)因子可以對(duì)不同的商品期貨在時(shí)間截面上定價(jià)的事實(shí)，標(biāo)示著商品期貨實(shí)際上構(gòu)成了另外一種可供選擇的資產(chǎn)類別。我們同時(shí)發(fā)現(xiàn)，用以解釋股票和債券收益率在時(shí)間截面上差別根源的那些風(fēng)險(xiǎn)因子，并不能驅(qū)動(dòng)商品期貨市場(chǎng)的風(fēng)險(xiǎn)超額收益率。這個(gè)發(fā)現(xiàn)支持了金融市場(chǎng)實(shí)際上是隔離的觀點(diǎn)。
