Sector Rotation Across the Business Cycle _SSRN-Id1572910

Electronic copy available at: http://ssrn.com/abstract=1572910

Sector Rotation across the Business Cycle

Ben Jacobsen1 Jeffrey Stangl2

Nuttawat Visaltanachoti3

Massey University - Department of Finance and Economics

First draft: July 2006

This draft: December 2009

Abstract Conventional market wisdom posits that sector rotation over various stages of the business cycle generates market outperformance. We introduce a simple way to test the value of sector rotation. In our test, an investor anticipates business cycle stages perfectly and rotates sectors in accordance with conventional practice. Even with perfect foresight and ignoring transactions costs, sector rotation generates, at best, a 2.3 percent annual outperformance from 1948 to 2007. In a more realistic setting, outperformance quickly dissipates. We do find an alternative rotation strategy that historically beats the market by 7 percent. Whether by chance or due to fundamentals time will tell. JEL Classifications: E32, G10, G12 Keywords: market timing, sector rotation, business cycle, investment strategies

1 Massey University, Department of Economics and Finance, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand 0745, E-mail: [email protected] 2 Massey University, Department of Economics and Finance, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand 0745, E-mail: [email protected] 3 Massey University, Department of Economics and Finance, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand 0745, E-mail: [email protected] This paper benefits from presentations at the Australian Banking and Finance Conference (2007), the New Zealand Finance Colloquium (2007), the Financial Services Institute of Australia Conference (2007), the Auckland University of Technology, and the FMA Annual Meeting (2009). We thank Russell Gregory-Allen, Henk Berkman, Utpal Bhattacharya, Ben Marshall, and Phillip Stork for valuable comments and the Institute of Finance Professionals New Zealand for awarding this paper the Best New Zealand Paper in Investments 2007.


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Sector Rotation across the Business Cycle

Abstract Conventional market wisdom posits that sector rotation over various stages of the business cycle generates market outperformance. We introduce a simple way to test the value of sector rotation. In our test, an investor anticipates business cycle stages perfectly and rotates sectors in accordance with conventional practice. Even with perfect foresight and ignoring transactions costs, sector rotation generates, at best, a 2.3 percent annual outperformance from 1948 to 2007. In a more realistic setting, outperformance quickly dissipates. We do find an alternative rotation strategy that historically beats the market by 7 percent. Whether by chance or due to fundamentals time will tell. JEL Classifications: E32, G10, G12 Keywords: market timing, sector rotation, business cycle, investment strategies


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1. Introduction

According to the Fidelity website4, technology stocks outperform the market index after a

trough in the business cycle. Just after a peak, investors are better off putting their money in

Utilities. Other financial websites and advisors share Fidelity’s view on when specific sectors

should perform well over the business cycle. Standard & Poor’s and the website

Marketoracle.co.uk recommend Technology after a recession. With the onset of an economic

slowdown, Goldman Sachs5 and CNN Money6 advised investors to target Utilities.

Conventional wisdom has a perspective on which sectors perform well across the business

cycle and most professional investors seem to agree. Even though, as some suggest, “if you

are in the right sector at the right time, you can make a lot of money very fast,”7 translating

popular beliefs into an exact sector rotation strategy is not straightforward. The problem is to

identify exact turning points and stages of the business cycle contemporaneously. This lack of

clarity may explain why, to date, academic research has not rigorously tested whether

investors can profit from sector rotation based on conventional wisdom.

Please insert Figure I around here.

While we cannot test whether actual sector rotation works, we can test the fundamental

assumptions underlying sector rotation. Do sector returns differ significantly and predictably

across the business cycle? Does rotating sectors in accordance with popular belief outperform

a simple buy-and-hold strategy? We answer these questions using a simple but new approach.

We give sector rotation the benefit of the doubt and assume an investor who perfectly predicts

stages and turning points of the business cycle. As Bodie, Kane and Marcus (2009) comment: 4 http://personal.fidelity.com/products/funds/content/sector/cycle.shtml 5 Reuters (2008) 6 CNN Money (2006) 7 Business Week Online (2002)

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“... sector rotation, like any other form of market timing, will be successful only if one

anticipates the next stage of the business cycle better than other investors,” (pg. 574). If the

business cycle indeed drives sector returns, then a clairvoyant investor who perfectly times

business cycle stages and rotates sectors using conventional wisdom should at least

outperform the market. We then consider how relaxing this perfect foresight assumption and

including transaction costs affects performance. Lastly, to allow for variations in conventional

wisdom on sector rotation, we document whether in general any sector provides systematic

outperformance during any business cycle stage.

In our perfect scenario, the evidence favors sector rotation, but only marginally so. Our

base case covers the 1948–2007 period using phases of economic expansion and recession, as

defined by the National Bureau of Economic Research (NBER). We divide NBER phases into

smaller sub-periods that coincide with business cycle stages where popular belief expects

optimal sector performance. With a few exceptions – attributable to chance – sectors that

should perform well in various stages show no significant outperformance. When we combine

sector returns across stages to implement a sector rotation strategy, we find that investors

guided by conventional market wisdom and foresight of business cycle stages achieve risk

corrected outperformance of 2.3 percent annually, excluding transactions costs. To put this

figure in perspective, we note that for such clairvoyant investors it is easy to design better

market timing strategies.8 When we relax assumptions and add transaction costs, the

outperformance quickly dissipates.

8 For instance, a simple market timing strategy that invests continuously in the market except during early recession generates 2.5 percent outperformance in comparison with 2.3 percent for sector rotation.

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We verify the robustness of our base case and consider a range of alternative tests, data

sets, performance measures, samples, and approaches. We test whether results differ when

investors anticipate changes in turning points earlier or later. However, this worsens

outperformance, which drops from 2.3 percent to 1.9, then 1 percent when investors

implement sector rotation one and two months in advance. Outperformance drops to 2.2 and

1.8 percent when investors delay sector rotation by one and two months, respectively. In

addition to NBER business cycles, we construct business cycle stages from the Chicago

Federal Reserve National Activity Index (CFNAI). The Chicago Federal Reserve Bank builds

the CFNAI from well-known financial and economic variables that, according to the

literature, signal changes in the business cycle. Whether we construct stages from the CFNAI

or use different business cycle proxies suggested in the literature, like term-spread, default-

spread, dividend yield, unemployment, and industrial production, our main result holds. When

we divide the sample period in half and look at the two different sub-periods, we find no

performance improvement. When we divide stages in half, we find no significant differences

between the first and the second half of each stage. Various performance metrics does not

affect results, regardless of whether we use traditional measures such as Sharpe ratios and

Jensen’s alphas or more recent performance measures like the Goetzmann, Ingersoll, Spiegel

and Welch (2007) manipulation-proof performance measure. We verify whether our results

depend on the measure of relative outperformance. For instance, Chordia and Shivakumar

(2002) and Avramov and Chordia (2006) show that size, value, and momentum factors track

business cycles. However, results are similar whether we measure outperformance using the

single index model, the Fama and French three-factor model, or the Carhart four-factor model.

As an alternative to industry returns, we consider more broadly partitioned sector return data

using Standard & Poor’s sector indices, Fama and French sectors, and Fidelity Sector Select

funds; these different data sets and partitions still leave our main result intact.

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We can find no improvement on our base case scenario. Our results suggest that the

popular belief that sector rotation might work is, at best, only marginally correct. Different

sectors do not, significantly and systematically, outperform other sectors across business

cycles, as conventional market wisdom maintains. To be clear, we do not preclude the

possibility that there are practitioners who profit from sector rotation. Our results indicate that

the outperformance of such investors has little to do with what conventional wisdom holds is

the main driver of sector rotation outperformance: systematic variation in sector returns across

the business cycle.

We focus on what one might call mainstream conventional wisdom on sector rotation, as

codified, for instance, by Stovall (1996) and illustrated by the Standard & Poor’s sequence of

cyclical sector performance shown in Figure I. However, as also illustrated in Figure I, other

variations exist. Therefore, as a last robustness check, we test for consistent and significant

outperformance of any sector across any business cycle stage, not just the mainstream

conventional wisdom sectors. This test allows for all possible variations of conventional

wisdom on sector rotation. None of the results suggests that any variation in conventional

wisdom would outperform. We believe, with respect to this general test of sector

performance, that there are two ways to interpret our evidence. If we consider the

outperformance alphas (Jensen, Fama and French, or Carhart), one might argue they are well

in line with the hypothesis of no significant sector outperformance, irrespective of business

cycle stage. We find significance levels only marginally different from those expected to

occur randomly in the absence of any outperformance. However, there appears to be evidence

for an alternative sector rotation strategy, one that is not a variant of any conventional wisdom

strategy with which we are familiar. We are uncomfortable rejecting this alternative strategy

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outright as the result of data mining. In our sample, this strategy generates economically large

outperformance of 7 percent annually. The strategy survives most of our robustness checks,

although sometimes only marginally. Although, with hindsight, justification of any strategy is

possible, one could also argue that there might be underlying fundamental reasons for the

sectors that outperform in various stages. For instance, food and entertainment do well during

recession, which might reflect the idea that consumers indulge in small pleasures during

recessions. Nevertheless, contrary to the conventional wisdom case that dictates when certain

sectors should perform relatively well, we believe it too soon to determine whether these

outperformance results are due to chance or are the result of economic fundamentals.

This study’s contribution to the literature lies in the fact that it is the first to question the

underlying assumption that the business cycle offers opportunities for profitable sector

rotation—at least in the way conventional wisdom suggests. The perfect foresight approach

gives sector rotation the benefit of the doubt and allows us to test its performance. Sector

rotation seems popular among both professionals and individual investors, based on the

number and types of websites dedicated to the topic. “Sector rotation” returns about 95,400

hits on Google compared with 833,000 and 878,000 for more generic terms like “market

timing” and “stock picking.”9 Bodie, Kane and Marcus (2009) state that the notion of sector

rotation is “one way that many analysts think about the relationship between industry analysis

and the business cycle,” (pg. 573).10 Indeed, the CFA curriculum includes sector rotation as

part of the core body of knowledge essential for investment professionals. However, even

9 July 2009. 10 Other textbooks also confirm the important role of sector rotation. For instance Fabozzi (2007) states, “Sector rotation strategies have long played a key role in equity portfolio management.” (p.581). Recent papers that suggest that sector rotation plays an important role in mutual funds include, for instance, Elton, Gruber and Blake (2009) and Avramov and Wermers (2006).

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though there are a number of sector rotation funds,11 it is difficult to obtain exact figures.12

One family of mutual funds alone, Fidelity Select, offers investors a choice of 42 sector

funds.13 The number of sector exchange traded funds has also seen incredible growth from

less than 10 in 1998 to over 180 in 2008 with a total net asset value of over 50 billion USD.14

While this is the first study to consider sector rotation practiced according to conventional

wisdom, interest in sector rotation and industry allocation is growing. Several recent studies

consider sector rotation and other time variations in sector and industry returns. Avramov and

Wermers (2006) suggest a link between mutual fund performance related to industry

allocation and business cycle proxies. Hou (2007) finds a significant lead/lag relation between

the different responses of sectors to new economic information. Commodity or basic material

industries respond more quickly to economic news than consumer goods industries. Hong,

Torous and Valkanov (2007) and Eleswarapu and Tiwari (1996) observe that sectors with

strong business cycle links, such as the metals, services, and petroleum sectors, lead the

general market by as much as two months. Menzly and Ozbas (2004) show how sector

performance relates to its position in the production and consumption supply chain. Conover,

Jensen, Johnson and Mercer (2008) show how sector rotation using monetary conditions may

generate outperformance. Jacobsen and Visaltanachoti (2009) show how sector market timing

based on summer and winter patterns in US sectors outperforms a buy and hold portfolio.

O'Neal (2000) finds that sector momentum is an indicator of future sector performance. A

recent study by Beber, Brandt and Kavajecz (2009) observes sector order flows and finds

evidence that order flows between sectors predicts future economic conditions.

11 Popular funds include the Rydex/SGI All-Cap Opportunity H (RYSRX), Rydex/SGI All-Cap Opportunity A (RYAMX), Claymore/Zacks Sector Rotation (XRO), and PowerShares Value Line Industry Rotation (PYH) 12 Investment Company Institute (2001) 13 http://personal.fidelity.com/products/funds/content/sector/products.shtml 14 Investment Company Institute (2009)

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2. Business Cycles

2.1. NBER business cycle dates

Our base case ‘perfect world’ analysis covers ten business cycles from January 1948 to

December 2007. Two considerations determine the starting point of our sample. First, we

want to eliminate the possibility of business cycle distortions caused by the Great Depression

or World War II.15 For instance, although the US economy was officially in a recession during

1945, industries still operated at full wartime production. Second, studies such as Stock and

Watson (2002) suggest that business cycle duration changed after World War II. Fama (1975)

in part attributes this change to adoption of the 1951 Federal Reserve Accord that allows the

Federal Reserve Bank to moderate business cycles through interest rate adjustments.

The official U.S. government agency responsible for dating business cycles is the NBER.

While NBER cycle reference dates are widely accepted by academics and practitioners, other

measures of business cycle activity are also available.16 The NBER provides dates for cycle

peaks and troughs that define phases of economic expansion and recession (Table I, Panel A).

Panel A also reports business cycle duration from business cycle peak to business cycle peak.

Since 1948, business cycles have lasted on average 71 months, with earlier cycles much

shorter than more recent cycles, particularly during phases of expansion.

Please insert Table I around here.

15 See for example Chatterjee (1999) and Cover and Pecorino (2005) 16 For a survey of business cycle dating methodologies see Chauvet and Hamilton (2005)

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2.2. Business cycle stages

While the NBER defines broad phases of economic expansion and recession, researchers

and investment practitioners commonly divide these phases into smaller sub-periods. A study

by DeStefano (2004) divides business cycles into two stages of expansion (early/late) and two

stages of recession (early/late). Investment professionals and practitioner guides such as

Stovall (1996) commonly divide expansions into three stages (early/middle/late) and

recessions into two stages (early/late) to allow for the much longer duration of economic

expansions. We follow this convention.17

Please insert Figure II around here.

We measure three stages of expansion (of equal length) from the first month following a

cycle trough date to the subsequent cycle peak date and two equal length stages of recession

from the first month following a cycle peak date to the subsequent cycle trough date. We

define our five business cycle stages as early expansion (Stage I), middle expansion (Stage II),

late expansion (Stage III), early recession (Stage IV), and late recession (Stage V). Table I,

Panel B reports the duration of expansions, recessions, and stages over the 10 business cycles

in the post-1948 period along with averages. Expansions last approximately five years on

average and recessions 10 months.

17 For clarification, we adopt the common usage of the term “sectors” as broad segments of the economy with

“industry” sub-units. Sector rotation itself is a top-down strategy based on the expectation of sector performance across business cycles with strategy implementation typically at the industry or firm level. For example, Table II shows that the Utility sector has two industries, Gas & Electric and Telecom.

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3. Sector performance across business cycles

3.1. Data description

For our base case scenario, we use market, industry, and Treasury bill return data from the

Kenneth French website.18 Market returns represent the total value weighted returns for all

NYSE, AMEX, and NASDAQ listed stocks. We use the 49 Fama and French industry

portfolios and omit the “Other” portfolio for a total 48 industries. The one-month Treasury bill

serves as a proxy for the risk-free interest rate. For clarity of interpretation, we report all

results as continuously compounded annualized returns.

Please insert Table II around here.

3.2. Popular guidance on industry performance

Table II shows the particular stage of the business cycle where conventional wisdom

suggests sectors perform best. We follow Stovall (1996) in his popular practitioner guide to

sector investing. Stovall (1996) divides the economy into ten basic sectors, and then maps the

optimal performance of industries within each sector to one of five business cycle stages.19

For example, the Stovall guide suggests that technology and transportation sectors provide the

best early expansion performance, basic materials and capital goods the best middle expansion

performance, and so forth with outperformance shifting from one sector to the next across the

remaining business cycle stages. We map each industry portfolio to its corresponding sector,

then map each sector to the conventionally accepted business cycle stage of expected sector

outperformance, as embodied by the Stovall (1996) classification.

18 See http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html for further detail on the data and the formation of industry portfolios. 19 Lofthouse (2001) traces a similar approach back to Markese (1986). There are other strategies as well. Salsman (1997) describes an alternative strategy that uses not only the dividend yield (as we do) but also short-term interest rates combined with precious metals prices.

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3.3. Nominal industry performance

As an initial test, we simply observe nominal industry performance, with no risk

adjustment, to determine whether there are significant differences over the course of a

business cycle and, if so, whether this performance coincides with conventional wisdom. The

computer software sector, for example, should outperform the market during the first stage of

expansion and the basic materials sector should outperform during the second stage of

expansion. We use equation 1 to estimate nominal industry performance by business cycle

stage and report our results, along with some additional descriptive statistics, in Table III.

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, , ,1

i t i s s t ts

r Dμ ε=

= +∑ (1)

We define ri,t as nominal industry returns and Ds as a dummy variable that indicates one of

five business cycle stages. As an example, D1 takes the value of one during months of early

expansion and zero in all other months. Dummy variables D1, D2, and D3 correspond with the

three stages of economic expansion (early/middle/late) and D4 and D5 with the two stages of

economic recession (early/late). Thus, the μi,s coefficients measure nominal industry returns

for each of the five stages. For brevity, Table III reports industry results only for the stage

where conventional wisdom suggests high performance. We report observations, annualized

returns, standard deviations, betas, and autocorrelation coefficients (all measured during the

indicated business cycle stage) along with average industry and market results beneath each

stage. For comparison, Table III reports annualized industry returns over the full sample

period in the last column. Lastly, Table III contains the p-values of a Wald test that these

returns are significantly different across stages. However, in most cases we reject the null

hypothesis of equal industry returns across the business cycle. This result is encouraging,

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because if we could not reject the null hypothesis of equal returns, the practical usefulness of

sector rotation as a strategy would be questionable from the start.

Please insert Table III around here.

We compare industry returns with market returns during each stage of expected

performance as a simple measure of relative return. As an example, Table III reports

transportation industry returns of 25 percent in comparison with 17 percent market returns

during the months of early expansion. The transportation industry thus provides

outperformance, as expected by conventional wisdom. The realization of expected

outperformance does not occur in all cases. Out of the 48 industries, 33 have raw returns

higher than market returns in the stage of expected outperformance. Thus, two out of three

industries do offer higher nominal returns as expected.

Two stages show surprising results if we look at industry averages for those stages. The

average 14 percent return for industries expected to perform well during early expansion

yields a 3 percent underperformance compared with market return. Similarly, the average

return for those industries that conventional wisdom expects to outperform during middle

expansion is 1 percent less than the market return.

Based on this simple approach, popular belief holds true in the remaining three stages. In

late expansion, early recession, and late recession, industries on average outperform the

market as expected. Overall, it appears that nominal sector performance coincides only

partially with popular belief. Observing the risk measures suggests that these results will

become stronger if we use risk corrected outperformance. In early expansion and middle

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expansion, we observe that on top of lower industry returns, industry risk is actually higher as

measured by both beta and standard deviation. For the other three stages, we observe more

mixed results with mostly lower betas but higher standard deviations.

It seems that, even with this crude approach, results are disappointing for sector rotation

investing. Historically, many sectors would have done better during the early expansion and

middle expansion stages, but these are not included in the popular sector rotation strategy. The

more important question for an investor, and one that we address next, is whether risk

adjusted industry outperformance differs significantly across business cycles.

Please insert Table IV around here.

3.4. Risk adjusted industry performance measures

We next calculate the difference between industry and market Sharpe ratios, excess market

returns, Jensen’s alphas, Fama and French (1992) three-factor alphas, and Carhart (1997)

four-factor alphas for each stage. Table IV reports performance measures as annualized rates

with White (1980) heteroskedasticity consistent t-statistics highlighted for statistical

significance at the 10 percent level. We also test whether industry alpha performance

measures differ significantly over business cycle stages with a Wald test statistic and report p-

values in Table IV under a null hypothesis of equal outperformance. For brevity, Table IV

reports only results for the period of expected optimal industry performance.

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Table IV starts with the difference between industry and market Sharpe ratios.20 If

conventional wisdom holds, we would expect a positive and statistically significant Sharpe

ratio difference. However, only one early recession industry (Gas & Electric) has a Sharpe

ratio significantly higher than the market. All early expansion industries in the technology

sector have statistically significant lower Sharpe ratios than the market. A large majority of

late recession industries also have lower Sharpe ratio performance than the market, although

here none of the differences are significant. The best average performance comes from late

expansion industries, but again none is significantly different. Contrary to conventional

wisdom, industries considered optimal for a particular period mostly underperform the market

on a Sharpe ratio performance basis (28 out of 48 sectors). Sharpe ratios might over penalize

for the idiosyncratic volatility inherent at the industry level. We next use alternative risk

adjustments. Based on equation 2, we estimate excess market industry performance across

business cycles. We run a regression of the difference between industry and market returns

(ri-rmkt) on the cycle dummy variables (Ds) described above. The regression coefficient αmkt is

simply market outperformance for industry i during business cycle stage s.

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, , , , ,1

i t mkt t mkt i s s t ts

r r Dα ε=

− = +∑ (2)

Additionally, we report Jensen’s alphas that we estimate for each stage of the business

cycle with a modified market model using equation 3.

5 5

, , , , 1, , , ,1 1

( )i t t J i s s t i s m kt t t s t ts s

r rf D r rf Dα β ε= =

− = + − +∑ ∑ (3)

20 We estimate Ledoit and Wolf (2008) p-values for industry and market Sharpe ratio differences corrected for potentially non-iid returns and indicate statistically significant differences at the 10 percent level or higher in bold.

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We define ri-rf as excess industry returns above the one-month Treasury bill, Ds as one of

five business cycle timing variables, and rmkt-rf the market risk premium.

To ensure our results do not depend on specific risk factors, we include Fama and French

(1992) three-factor and Carhart (1997) four-factor alphas. We estimate Fama and French

alphas (αF) with an equation similar to (3) where we now control for size and value risk

factors in addition to market risk. We estimate Carhart alphas (αC) with a modified four-factor

model that adds an additional momentum factor to the Fama and French three-factor model.

Regardless of the measure, we find very little evidence of significant industry

outperformance in stages when such industries should outperform as conventional wisdom

maintains. These results strengthen our earlier findings for nominal returns. Based on Jensen’s

alphas, we find six industries with significant outperformance. Based on the Fama and French

three-factor model we find only five industries with significant outperformance in the stage

where they should outperform, and only two using the Carhart four-factor model. At a 10

percent significance level, that is roughly the number of industries out of 48 expected to show

random significant outperformance, even when none is present.21

As an additional step, we test for differences in market outperformance across the five

business cycle stages (αmkt) using a Wald test. We report p-values in Table IV under a null

hypothesis of equal performance. If industry outperformance is unequal across business cycle

stages, we should reject the null hypothesis. We cannot reject the null hypothesis of constant

21 If anything, it seems that Gas & Electric Utilities behave somewhat as popular wisdom suggests showing good relative performance during early recession. While performance is insignificant, it is positive and large, and the limited number of observations might explain the lack of significance.

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excess market industry returns for 30 of the 48 industries. This result differs from the previous

Wald test of constant nominal returns. Sensitivity to general market movements seems largely

to explain differences in industry returns over business cycles. Wald tests of Fama and French

and Carhart alphas also indicate no statistical difference in risk-adjusted industry performance

across business cycles. Our results suggest that after controlling for risk using various

measures, industry outperformance across business cycles does not occur – or occurs only

marginally so – when conventional wisdom tells us it should.

Finally, in unreported results we count the percentage of months in the different stages

where relative industry outperformance actually occurs and verify whether industries

outperform more often in months when they should outperform based on popular belief.

Again, we find no indication that this is the case.

4. Sector rotation performance

Can a strategy of sector rotation still be profitable? We now focus on strategy

implementation to observe the overall joint performance of sector rotation across the entire

business cycle. In our base case scenario, we assume an investor who perfectly times NBER

business cycles and at the start of each stage rotates industries according to conventional

wisdom. We assume equal weights in industries held at each stage. We compare these results

with a simple buy-and-hold strategy in Table V.

Please insert Table V around here.

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The annualized outperformance of sector rotation based on perfect foresight amounts to 2.3

percent.22 This outperformance may appear large enough to be of interest to investors, but it

represents a best-case scenario. Only an investor who followed popular market wisdom in the

last 60 years, who ignored transactions costs, and who has perfectly timed all business cycles

in accordance with the NBER – although the NBER did it ex post – would have realized this

2.3 percent outperformance. To put this number in perspective: an investor who had – based

on the same information — just timed the early recession right and had held cash during that

period and the market during the remainder of the business cycle would already have achieved

a 2.5 percent outperformance. This same investor would also have had a better-diversified

portfolio over time with less industry specific risk. We now consider what happens under

assumptions that are more realistic, where we include transactions costs.

Transaction costs, both explicit and implicit, are difficult to estimate with any precision

and depend on the stock, where it trades, and when it trades.23 We use a range of roundtrip

transaction costs of between 0.5 and 1.5 percent given that estimates vary considerably and

given changes in costs over the sample period.24 Estimated transaction costs include

commissions, bid-ask spread, and market impact. Sector rotation has 50 roundtrip transactions

and the market timing strategy we use for comparison has 20 roundtrip transactions over the

full sample period. Once we include transactions costs, outperformance for the sector rotation

strategy diminishes substantially to between 1.1 and 1.9 percent, statistically indistinguishable

from zero. The alternative strategy based on market timing increases in relative

outperformance owing to fewer transactions.

22 Since we estimate Jensen’s outperformance with a constant beta over the full sample period, outperformance does not equal the weighted average of industry outperformance by business cycle stage reported in Table IV. 23 See for example Goyenko, Holden and Trzcinka (2009) and Hasbrouck (2009). 24 Estimates of total trading costs vary greatly depending on the study. For instance, Lesmond, Schill and Zhou (2004) estimate roundtrip transaction costs of 1 – 2 percent for most large-cap trades while Keim and Madhavan (1998) estimate total round-trip transaction costs as low as 0.2 percent.

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Thus far, our results indicate marginal outperformance, at best, of sector rotation

implemented in accordance with popular wisdom, even if we give investors the benefit of the

doubt and assume that investors correctly time the business cycle. Results for industries

expected to perform well in the early expansion stage and the middle expansion stage are

particularly disappointing. Still, it would be premature to conclude that sector rotation does

not work. Investors may use different industry or sector classifications, different business

cycle indicators, or different business cycle stages. Alternatively, investors may anticipate

business cycles, which could generate outperformance. On the other hand, our results may be

sample specific.

In our robustness tests, we consider all these possible explanations and several others. We

use a range of alternative tests, data sets, performance measures, samples and approaches. We

verify whether results improve if we assume investors anticipate changes in turning points

earlier. In addition to NBER business cycles, we test various business cycle proxies and

business cycle stages constructed from the CFNAI. We separate our sample in two subperiods

and business cycle stages in two halves. We use sector returns from alternative data sources.

We test obvious explanations for our results first, and then progressively relax more

assumptions.

5. Robustness checks

5.1. Other data sets

The Fama and French industries may not adequately represent the investment alternatives

available to sector rotation investors. As such, we test three additional data sets that

incorporate more broadly defined sector partitions: the Standard & Poor’s sector indices, the

Fama and French sectors, and the Fidelity Sector Select funds.

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The Standard & Poor’s indices provide a benchmark of sector performance frequently used

by practitioners. There are a number of Standard & Poor’s indices. We use the 15 Standard &

Poor’s indices available from Global Financial Data for the entire 1948–2007 period.

The Fama and French sectors comprise all NYSE, AMEX, and NASDAQ traded stocks

mapped to one of 17 sector portfolios based on their SIC classification. It is less likely, using

sector mapping, that one or two large firms will dominate portfolio returns.25 We obtain the

Fama and French sector data from the Kenneth French website.

Although available only for a shorter period, the performance of Fidelity Sector Select

funds provides a good proxy for sector rotation strategies implemented by individual

investors. We source Fidelity Sector Select data for 42 funds from Morningstar services. The

earliest start date is August 1981 for the Energy, Health Care, and Technology funds while the

most recent start date is July 2001 for Pharmaceuticals. Due to the shorter Fidelity data series,

and in order to use all available data, we extend the sample period from December 2007 to

August 2008 for the Fidelity fund data. Even so, there are a very limited number of

observations for the more recently added Fidelity Sector Select funds. Total return

observations during recessions are further limited by the infrequency of recessions since 1981.

Please insert Table VI around here.

25 For instance, the Fama and French agriculture industry portfolio includes as few as four firms. Consequently, one can argue that results shown for the agriculture industry might merely measure firm specific developments unrelated to the business cycle.

21

Table VI provides a comparison of average statistics and performance measures for the

different data sets mapped to where popular wisdom, codified by Stovall (1996), expects

outperformance. Here again, there appears no consistency in sector performance regardless of

data set. The Fama and French sectors slightly outperform in early expansion and early

recession. Consistent with earlier results, late expansion and late recession industries perform

best and early expansion industries largely underperform, although results are mostly

insignificant. Only during late recession do the Fidelity sector funds outperform the market

based on all performance measures, although not significantly so. However, this result might

be due to a lack of observations. Alternative data sets do not seem to improve performance.

5.2 Different ways to measure business cycle

We use the CFNAI and Conference Board Leading Indicator as alternatives to NBER cycle

dates. As results for these two indicators differ only marginally, we focus on results for the

CFNAI only. The CFNAI comprises 85 economic and financial variables from four broad

categories: production and income; employment, unemployment, and hours; personal

consumption and housing; and sales, orders, and inventories. CFNAI construction follows the

methodology of Stock and Watson (1989) that uses first principal components of a large

number of economic variables known to track economic activity. By construction, the CFNAI

has a zero mean and unit standard deviation where a positive (negative) index value indicates

above (below) trend economic activity. Publication of the CFNAI began in 2001 with series

data available from 1967.26 In Figure III, we overlay the CFNAI index on NBER delineated

phases of economic expansion and contraction (shaded area). We see that the CFNAI more or

less tracks NBER cycle dates but shows some variation, which may better reflect the

uncertainty investors face when they try to call business cycle stages in real time. Based on

26 More information is available at http://www.chicagofed.org/economic_research_and_data/cfnai.cfm

22

the CFNAI data we try three approaches. We form partitions at values of 0.57, 0.26, -.01, and

-.045 so as to divide the business cycle into five equal stages, then test for outperformance of

the conventional wisdom industries using dummy variables and regressions as above. As an

alternative test, we partition CFNAI values according to the Chicago Federal reserve website,

which defines values above 0.20 as late expansion and values below -0.70 as recession. We

further subdivide these ranges into stages based on values we deem representative: early

recession is the range from 0.0 to -0.70 and early and middle expansion split the 0.0 to 0.20

range.27 Thirdly, observing Figure III, it seems that on average positive CFNAI index levels

and changes characterize an early expansion, and late expansion has positive index levels but

mostly negative changes. In early recession, the CFNAI index has negative levels and

negative changes and in late recession the index levels are still negative but changes are

positive; our last test uses these characterizations. We run a regression for each sector where

we test for sector outperformance based on levels and changes in the CNFAI index. We assign

middle expansion sectors to early or late expansion depending on where they perform best.

Again, this approach gives conventional wisdom the benefit of the doubt and illustrates that

our results are independent of whether we consider four or five stages of the business cycle.

, 0 1 2 ,( )i t t t t i mkt t t tr rf CFNAI CFNAI r rfα α α β ε− = + + Δ + − + (6)

Please insert Figure III and Table VII around here.

Table VII Panel A reports a summary of average statistics and performance measures for

industries grouped according to where they should outperform based on conventional wisdom

27We omit results based on Chicago Federal Reserve cut-off points, as they are materially similar to those from equal CFNAI partitions; we provide them upon request.

23

now using CFNAI delineated stage partitions.28 Industry outperformance is even lower over

CFNAI business cycle stages than previously observed with NBER delineated stages. Only

late expansion industry mean returns are larger than their overall sample mean. Risk adjusted

performance is no better. Average industry Sharpe ratios are lower than the market for all

stages but late recession. All three alpha performance measures are mostly negative and none

are statistically different from zero. There appears no improvement on our base case scenario

if we use CFNAI rather than NBER measured business cycles. Panel B contains the results

where we estimate the sensitivity of sectors to levels and changes of the CFNAI variable. We

report bootstrapped p-values for the likelihood that the level and change coefficients jointly

have the correct sign. We find only four industries at the 10 percent significance level, all in

late recession (Recreation, Printing & Publishing, Apparel, and Textiles), that perform well

when they are so expected. For all other sectors, there is no significant outperformance.29 This

table suggests that only in late recession do some sectors perform significantly better than

others do. Transportation, Electrical Equipment, and Business Services seem to recover faster

than other sectors in late recession.

5.4. Timing the business cycle in advance or with a delay

Investors might profit from consistently timing the business cycle incorrectly. Suppose that

investors consistently assume that turning points occur earlier than the NBER dates or with a

delay. If so, our base case scenario might underestimate actual outperformance of sector

rotation. We advance the implementation of sector rotation by one month, two months, and

three months prior to NBER business cycle turning points. Similarly, we consider delays up to

three months. Table VIII contains our results excluding transactions costs.

28 For brevity, we report industry averages by business cycle stage and provide complete results upon request. 29 For Steel Works (Middle Expansion) the joint probability that significant outperformance occurs in expansion is statistically significant.

24

Please insert Table VIII around here.

Overall performance declines monotonically and becomes insignificant as we rotate sectors

further in advance of NBER business cycle stage turning points. The sector rotation Jensen’s

alpha of 2.3 percent decreases to 1.9 and then 1.0 percent when we rotate sectors one, two,

and three months early, respectively. Similarly, the alphas decrease if we assume investors

respond with a delay. These results suggest the importance of precisely timing business cycle

stages.

5.5. Different business cycle proxies

The literature shows that several economic variables, like term-spread and default-spread,

and dividend yield, proxy business cycles.30 If investors use these variables to predict the

business cycle and rotate sectors accordingly, we can test more directly whether a model that

predicts relative industry or sector outperformance, based on these proxies, aligns itself with

the stages in which conventional wisdom suggest they should outperform.

We create a forecast model using the one-month Treasury bill, term-spread,31 default-

spread,32 and dividend yield as business cycle variables (BCV). Chordia and Shivakumar

(2002) among others show that these variables lagged one period are a good predictor of

momentum profits related to business cycles. Our forecast model uses monthly changes in the

30 See for instance, Campbell (1987), Chen (1991), Chen, Roll and Ross (1986), Fama and French (1989), Jensen, Mercer and Johnson (1996), Keim and Stambaugh (1986), Lewellen (2004), and Petkova (2006). 31 We calculate the term-spread as the difference between the 10-year Treasury constant maturity yield and the three-month Treasury yield. Fama and French (1989) find the term-spread closely tracks short-term business cycles and measures the difference between long-term growth and current short-term business conditions. The term structure is smallest (largest) at NBER defined business cycle peaks (troughs). 32 We calculate the default-spread as the difference between low-grade Baa and high-grade Aaa corporate bonds. The default-spread measures a default premium. Expected returns are greater for risky investments during times of economic uncertainty. As such, the default-spread should increase during periods of recession as investor required rates of return also increase.

25

business cycle variables as a proxy for unexpected shocks, as the literature shows that such

changes provide the best forecast of asset prices.33 We forecast industry outperformance

related to the business cycle with parameter estimates obtained from a regression of excess

industry returns (ri-rf) on a constant, lagged changes in the business cycle variables (ΔBCV),

and excess market returns (rmkt-rf), using equation 7.

4

, 0 , 1 ,1

( )i t t i i t mkt t t ti

r rf c BCV r rfγ β ε−=

− = + Δ + − +∑ (7)

Our model is the single index model with the inclusion of lagged changes in the business

cycle variables to capture the relation between business cycle determinants and industry alpha

performance. We essentially use the gamma parameter estimates (γi) obtained from changes in

the business cycle variables to forecast one period ahead Jensen’s alpha, where we decompose

Jensen’s alpha to allow for the contribution of business cycle determinants to industry

outperformance. Similar to Chordia and Shivakumar (2002), we use a 60-month rolling

window to estimate the (γi) forecast parameters. The rolling window moves forward each

month to obtain γi estimates from the most recent 60-month window. We then use the

parameter estimates to forecast industry outperformance for the following

month , 1ˆ( )J tα + measured with equation 8 as the sum of the gamma estimates times changes in

current business cycle variable values from the proceeding period4

1

ˆ( )i ti

BCVλ=

Δ∑ . Each month

we form a new sector rotation portfolio where we invest equal weights in all industries with

forecast positive outperformance. The following month, we repeat the same process once

again and continue this repetition over the entire sample period.

33 See for example studies by Chen, Roll and Ross (1986) and Keim and Stambaugh (1986), among others.

26

4

, 11

ˆˆJ t i ti

BCVα λ+=

= Δ∑ (8)

To clarify with an example, in month 61 we first estimate the γi parameters with month 1 to

month 60 data. We next multiply the γi parameter estimates by ΔBCVi,61 measured as the

(BCVi,61-BCVi,60) difference, to forecast a Jensen’s alpha attributable to business cycle

determinants. Lastly, we select all industries where 4

1

ˆ 0i ti

BCVλ=

Δ >∑ for inclusion in a sector

rotation portfolio for a one-month holding period. The following month, we move the rolling

window forward one month and repeat the entire process.

Please insert Table IX around here.

Table IX Panel A and Panel B overlays result from the forecast model on sector

performance with NBER delineated business cycle stages. We wish to observe whether

forecast industry outperformance coincides with the popular belief of sector rotation investors

with respect to industry performance.34 Panel A reports the average number of industries the

forecast model selects for inclusion in the sector rotation portfolio during each business cycle

stage. On average, the forecast model selects approximately half of all industries for inclusion

in the sector rotation portfolio during any given business cycle stage.

34 We also overlay the forecast model results on NBER business cycle substages, where we divide each stage into an early and a late stage and additional subperiods where we divide the sample. There is no change in our basic results for both substage and subperiod.

27

Panel B reports the percentage of time a particular industry is included in the sector

rotation portfolio for the full period and for each business cycle stage. We would expect that if

the business cycle variables were able to forecast industry outperformance related to the

business cycle, and if industry performance aligns with popular belief, that the model would

select an industry for inclusion in the portfolio during the period of expected optimal

performance a high percentage of the time. However, the forecast model selects industries for

inclusion evenly across the business cycle and independent of business cycle stage. (Values in

bold indicate percentages that are significantly different from 50 percent at the 10 percent

significance level.) Using this method, there also appears no evidence that sectors perform

well when conventional wisdom suggests they should.

5.6. Description of other robustness tests35

5.6.1. Business cycle proxies: extended analysis

We not only use relative sector outperformance forecasts based on business cycle proxies,

but also seek to establish any correlation between them and sector performance. If

conventional belief claims a sector should outperform during part of an expansion and we

know that an economic variable is relatively high during expansion, we would expect to find a

strong and positive link between outperformance of that sector when that economic variable is

at a high level. We test this relation using the most common business cycle proxies (BCP):

term-spread, default-spread, dividend yield, unemployment, and industrial production.

We first establish how these proxies behave across the business cycle. For instance, the

literature shows that term-spread, default-spread, and dividend yield are smallest near

economic peaks and largest near economic troughs (Fama and French, 1989). Stock and

35 All tables related to these results are available upon request from the authors.

28

Watson (1998) and Hamilton and Lin (1996) show how industrial production growth peaks

and unemployment rates bottom out around business cycle peaks. Boyd, Hu and Jagannathan

(2005) look at the impact on stocks of changes in unemployment across periods of economic

expansion and recession. We confirm findings in the literature with changes in the business

cycle proxies across successive stages that mostly have the expected sign and are statistically

significant. For instance, changes in unemployment rates from one business cycle stage to the

next are all significantly negative across stages of economic expansion and significantly

positive across stages of economic contraction. Similarly, changes in default spread are

negative during early and middle expansion and positive during early and late recession.

Results tend to be less strong and insignificant for dividend yields.

Next, we investigate the connection between industry outperformance and these same

proxies over the business cycle using equation 9.

2

, 0 , , , ,1

( )i t t p BCP p j t mkt p mkt t t tp

r rf D BCP r rfα β β ε=

⎡ ⎤− = + + − +⎣ ⎦∑ (9)

We regress excess industry i returns (ri-rf) during business cycle phase p (where phase is

NBER expansion or recession) at time t on a constant, business cycle proxy j (BCPj), and a

correction for excess market returns (rmkt-rf). Dummy variable Dp indicates the business cycle

phase. The estimate βBCP multiplied by the proxy value captures the contribution of the

business cycle proxy to overall industry outperformance. To make our results independent of

stages, we use full NBER expansion and recession periods rather than stages. For instance,

term-spread becomes smaller across expansions and larger across recessions. Therefore,

industries that should outperform during periods of expansion (recession) should have

29

negative (positive) βterm-spread coefficients. We observe significant coefficients with the correct

sign about 9 percent of the time, more or less what we would expect to observe randomly at a

10 percent significance level. It appears that while the proxies do track business cycles as the

literature suggests, we are unable to establish a link between these same business cycle

proxies and industry outperformance. This general result holds regardless of how we partition

the business cycle or whether we look at levels, one-month lags, or changes in the business

cycle proxies.36

5.6.2. CFNAI forecasts of relative sector performance

Analogous to our forecast model based on business cycle variables, we verify whether

period ahead forecasts based on the CFNAI indicator fare better. There is no difference in our

results when we use changes in the CFNAI indicator rather than changes in the various

business cycle proxies; neither provides guidance for investors on sector rotation nor supports

the view of conventional wisdom on sector performance linked to the business cycle.

5.6.3 Sequencing the industries

As the Standard and Poor’s graph in Figure I shows, the outperformance of Technology

follows outperformance of Utilities, and precedes outperformance of the Financials. The

remaining figures suggest similar sequential patterns. We try a number of tests where we

ignore the business cycle completely and verify whether outperformance of one sector

predicts future performance of other sectors at some lag. We try lags up to 24 months for

nominal returns and Jensen’s alphas. We find no evidence that the conventional wisdom

36 The correspondence between industry outperformance relative to the market and business cycle proxies measured across business cycle stages is materially similar, if not somewhat weaker, than across phases of expansion and recession. Similarly, the results hold regardless of whether we use level, one-month lags, or changes in the business cycle variables. For brevity, we limit our discussion to the link between industry performance across phases of economic expansion and recession using business cycle proxy levels and provide results of the additional tests upon request.

30

sequence of sector performance holds. We do find some one-month lead lag relations between

sectors. However, beyond one-month lags, significant results seem to occur randomly.

5.6.4. Sub-stages

We try a number of variations of the stages that could improve our base case scenario.

Outperformance might only occur at the beginning or end of stages. To account for this

possibility, we divide all stages into early and late halves then run our main tests again. We

find no significant difference between first and second half returns across the stages. Investors

also might anticipate different stages and react in shorter intervals around business cycle

turning points rather than over the full length of a stage. We consider shorter periods where

we test for significant outperformance for two, four and six months around turning points

only. Again, we find no significant outperformance.

5.6.5. Sub-samples

Significant events over a full 60-year sample period, like the 1970’s bear market and the

1990’s dotcom market could overly influence our results. We compare average performance

measures for each stage for the 1948–1977 and 1978–2007 subperiods with the full sample

period measures.37 Industry outperformance appears relatively constant across all periods and

business cycle stages, regardless of the performance metric. Consistent with our previous

analysis, early expansion and middle expansion industries provide inferior outperformance

across both subperiods. Overall, our results do not seem sample specific.

37 The complete results for individual industries are available upon request.

31

5.6.6. Alternative Performance Measures

We use two alternative measures to evaluate the performance of sector rotation, market-

timing, and buy-and-hold strategies. The Goetzmann, Ingersoll, Spiegel and Welch (2007)

performance measure eliminates any bias in Sharpe ratio or Jensen’s alpha measures of

strategy performance attributable to potentially non-normal return distributions. The Barrett

and Donald (2003) stochastic dominance test provides a test of strategy performance

independent of asset pricing benchmarks. Even allowing for such considerations, different

performance measures do not change our results.

6. General sector performance across the business cycle

So far, we find little evidence in favor of sector rotation based on mainstream conventional

wisdom. We acknowledge that variations on conventional wisdom, as Figure I illustrates, do

exist. To allow for all possible variations of conventional wisdom on sector rotation, we take

our results one-step further and test for consistent and significant outperformance of any

sector across any business cycle stage. We also test how well a rotation strategy based on

alternative sectors might perform.

As a first step, we consider the performance measures for all sectors in all stages. Under

the null hypothesis of no significant outperformance, we would expect to find the different

alphas almost normally distributed around zero. In Figure IV, we plot the expected

distribution under the null of no outperformance and the actual distribution of Jensen’s alpha

t-statistics (all other measures show similar patterns). At first sight, both plots seem similar.

However, we find slightly more significant outperforming sectors than we would expect under

the null hypothesis at a 10 percent confidence level (20 versus 12 out of 240 estimations).

This number might be close enough to the null for some. Others might argue that it represents

32

almost double the number of outperforming sectors one would expect under the null. To err

on the side of caution in accounting for any variants of sector rotation, we take a closer look at

whether we can find any group of sectors that otherwise survives all our tests. We do find

sectors with jointly significant Jensen’s, Fama and French, and Carhart alphas during

particular stages of the business cycle. There are no such sectors in early expansion; Candy &

Soda, and Pharmaceuticals in middle expansion; Mining, and Tobacco Products in late

expansion; Shipping Containers, Food products, Utilities, and Entertainment in early

recession; and Personal Services, Food Products and once more Tobacco Products in late

recession.

Please insert Figure IV and Table X around here.

Historically, an alternative sector rotation strategy that holds the market in early expansion

and then rotates sectors across the business cycle as above generates outperformance of 7.3

percent a year (6.1 percent assuming 1.5 percent round trip transactions costs as in Table V).

These alternative sectors perform well in the months of the stages where they are supposed to

perform well about 60–70 percent of the time. If implemented 1, 2, or 3 months in advance,

strategy returns reduce to 6.9, 6.1, and 4.9 percent and if implemented 1, 2, or 3 months late,

to 7.2, 6.5, and 5.6 percent, respectively. All these sectors also outperformed in both the

1948–1977 and 1978–2007 subperiods, although not always significantly so. One could argue

that this lack of significance indicates no outperformance. Alternatively, one might attribute

this result to a lack of observations. Similar sectors and industries in other data sets also show

outperformance, but not significantly so in all cases. Generally, the alternative strategy seems

to survive all our robustness checks, although only marginally. Whether the outperformance

of this alternative strategy is a result of data mining or a result of underlying fundamental

33

reasons we cannot determine. However, based on our results, it seems a more promising

sector rotation strategy, and safer bet, than the traditional rotation strategy based on popular

wisdom, if investors feel the business cycle contains information about sector performance.

7. Conclusion

Despite exhaustive testing, we find little support for the conventional wisdom that sector

rotation across business cycles outperforms the general market. Even if we give sector

rotation the benefit of the doubt, and assume that investors perfectly time business cycles,

returns are only marginally higher than the market. Our study goes one step further and

relaxes any assumption of conventional wisdom to explore whether any sector consistently

and significantly performs better in any business cycle stage. We find only limited evidence

supporting the systematic performance of sectors across the business cycle. An alternative

sector rotation strategy, which is not a variant of conventional wisdom sector performance,

generates economically large outperformance of 7 percent annually. Whether this is due to

chance or fundamentals, only the passage of time will tell. To avoid misunderstanding, our

results do not preclude the possibility that an investor may profit from sector rotation.

Different investments in sector funds, beyond the scope of this study, may indeed outperform

the market. We simply show that sector performance fails to track business cycles, as

conventional wisdom maintains it does or in general. Our results question popular belief in

systematic sector outperformance across the business cycle.

34

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36

Table I. NBER reference business cycle dates and stage partitions Notes: Panel A shows NBER published business cycle peak and trough reference dates from January 1948 to December 2007. We count periods of recession as the first month following a cycle peak to the subsequent trough, and periods of expansion as the first month following a cycle trough to subsequent peak. The last column shows the total months in a business cycle from peak to peak. The last recorded NBER business cycle date is December 2007. Panel B shows the total duration in months for recessions and expansions based on the NBER turning points shown in Panel A. We partition NBER defined periods of expansion into three equal stages (early, middle, and late) and NBER defined periods of recessions into two equal stages (early and late). The bottom of Panel B shows the average duration of each stage. Panel A:

CyclePeak Trough Peak Length11/48 10/49 07/53 5607/53 05/54 08/57 4908/57 04/58 04/60 3204/60 02/61 12/69 11612/69 11/70 11/73 4711/73 03/75 01/80 7401/80 07/80 07/81 1807/81 11/82 07/90 10807/90 03/91 03/01 12803/01 11/01 12/07 81

Panel B:

Early Stage Middle Stage Late Stage Total Early Stage Late Stage Total15 15 15 45 6 5 1113 13 13 39 5 5 108 8 8 24 4 4 835 35 36 106 5 5 1012 12 12 36 6 5 1119 19 20 58 8 8 164 4 4 12 3 3 630 31 31 92 8 8 1640 40 40 120 4 4 825 25 23 73 4 4 8

average: 20 20 20 60 5 5 10

NBER business-cycle dates (Jan 1948 - Dec 2007)

Number of months in NBER delineated business cycle stagesPeriod of RecessionPeriod of Expansion

37

Table II. List of expected best performing industries across business cycle stages Notes: Table reports stages of business cycle where, based on the Stovall (1996) classification and popular investment websites such as those shown in Figure I, sectors/industries provide the best performance. We partition periods of expansion into three equal stages (early, middle, and late) and periods of recession into two equal stages (early and late). We then map each of the 48 Fama and French industries to its appropriate sector and business cycle stage.

Early Expansion - Stage I Middle Expansion - Stage II Late Expansion - Stage III Early Recession - Stage IV Late Recession - Stage VTechnology: Basic Materials: Consumer Staples: Utilities: Consumer Cyclical:Computer Software Precious Metals Agriculture Gas & Electrical Utilities ApparelMeasuring & Control Equip. Chemicals Beer & Liquor Telecom Automobiles & TrucksComputers Steel Works Etc Candy & Soda Business SuppliesElectronic Equipment Non-Metallic & Metal Minin Food Products ConstructionTransportation: Capital Goods: Healthcare Construction MaterialsGeneral Transportation Fabricated Products Medical Equipment Consumer GoodsShipping Containers Defense Pharmaceutical Products Entertainment

Machinery Tobacco Products Printing & PublishingShips & Railroad Equip. Energy: RecreationAircraft Coal Restaraunts, Hotels, MotelsElectrical Equipment Petroleum & Natural Gas RetailServices: Rubber & Plastic ProductsBusiness Services TextilesPersonal Services Wholesale

Financial:BankingInsuranceReal EstateTrading

Period of Expansion Period of Recession

38

Table III. Descriptive industry statistics by NBER delineated business cycle stages Notes: Table reports nominal industry returns and standard deviations for the business cycle stage considered optimal by conventional wisdom as annualized rates. We estimate nominal industry returns for each business cycle stage with equation 1 where we regress industry returns on business cycle dummy variables (Ds) that take a value of 1 or zero depending on the business cycle stage. The beta estimate is from a standard single index model and rho (1) is the first order serial correlation coefficient across stages with statistical significance at 10 percent highlighted. We also report Wald test results for differences in industry returns across the five business cycle stages and report p-values under a null hypothesis of equal industry returns across the business cycle. For comparative purposes, we provide annualized industry returns for the full sample period in the far right column and equally weighted industry averages and market results beneath each business cycle stage. Column 2 also reports the number of industry return observations (obs.) included in a business cycle stage.

5

, , ,1

i t i s s t ts

r Dμ ε=

= +∑ (1)

Sample period: 1948-2007 fullstage Wald sample

Industry obs. mean std. dev. beta rho(1) p-value meanEarly Expansion - Stage I:Computers 201 0.13 0.22 1.38 -0.02 0.00 0.13Computer Software 130 0.00 0.34 1.71 0.05 0.15 0.02Electronic Equipment 201 0.17 0.25 1.50 0.04 0.00 0.11Measuring & Control 201 0.10 0.22 1.36 0.09 0.00 0.12Shipping Containers 201 0.18 0.17 0.96 -0.01 0.00 0.12Transportation 201 0.25 0.17 1.02 0.05 0.00 0.10Industry Averages 0.14 0.23 1.32 0.03 0.03 0.10Market 0.17 0.13 1.00 0.03 0.00 0.12

Middle Expansion - Stage II:Chemicals 202 0.12 0.17 1.12 0.02 0.00 0.11Steel Works 202 0.13 0.22 1.23 -0.03 0.00 0.10Precious Metals 166 0.08 0.32 0.76 -0.05 0.58 0.08Mining 202 0.12 0.23 1.19 -0.05 0.00 0.12Fabricated Products 166 0.12 0.20 1.00 -0.03 0.01 0.05Machinery 202 0.17 0.18 1.22 0.03 0.00 0.11Electrical Equipment 202 0.19 0.19 1.26 -0.03 0.00 0.14Aircraft 202 0.19 0.21 1.15 0.10 0.00 0.14Shipbuilding & Railroad 202 0.08 0.19 1.15 0.00 0.01 0.10Defense 166 0.15 0.21 1.07 -0.01 0.02 0.12Personal Services 202 0.12 0.22 1.17 0.10 0.00 0.09Business Services 202 0.13 0.16 1.04 0.11 0.00 0.10Industry Averages 0.13 0.21 1.11 0.01 0.05 0.10Market 0.14 0.13 1.00 0.03 0.00 0.12

39

Table III. Continued Sample period: 1948-2007 full

stage Wald sampleIndustry obs. mean std. dev. beta rho(1) p-value meanLate Expansion - Stage III:Agriculture 213 0.11 0.22 0.81 -0.06 0.00 0.10Food Products 213 0.07 0.15 0.61 0.03 0.00 0.13Candy & Soda 166 0.05 0.24 0.74 0.01 0.01 0.12Beer & Liquor 213 0.10 0.19 0.81 0.00 0.00 0.13Tobacco Products 213 0.15 0.20 0.40 0.11 0.04 0.15Healthcare 136 0.09 0.33 1.16 0.09 0.02 0.09Medical Equipment 213 0.12 0.17 0.86 -0.02 0.01 0.14Pharmaceutical 213 0.10 0.16 0.70 -0.05 0.01 0.13Coal 213 0.21 0.33 1.02 0.08 0.00 0.14Petroleum & Natural 213 0.11 0.18 0.74 -0.04 0.00 0.14Industry Averages 0.11 0.22 0.79 0.01 0.01 0.13Market 0.07 0.15 1.00 -0.02 0.00 0.12

Early Recession - Stage IV:Utilities 53 0.00 0.16 0.76 0.11 0.05 0.11Communication 53 -0.04 0.14 0.63 0.06 0.07 0.10Industry Averages -0.02 0.15 0.70 0.09 0.06 0.11Market -0.16 0.16 1.00 -0.05 0.00 0.12

Late Recession - Stage V:Recreation 51 0.64 0.31 1.22 -0.13 0.00 0.09Entertainment 51 0.50 0.31 1.28 0.19 0.10 0.14Printing & Publishing 51 0.62 0.23 1.03 0.29 0.00 0.12Consumer Goods 51 0.49 0.21 1.01 0.12 0.00 0.12Apparel 51 0.63 0.27 1.09 0.17 0.00 0.10Rubber & Plastic 51 0.42 0.22 0.90 0.07 0.00 0.12Textiles 51 0.47 0.25 1.09 0.05 0.00 0.10Construction Material 51 0.51 0.23 1.17 0.03 0.00 0.11Construction 51 0.63 0.33 1.51 -0.01 0.00 0.12Automobiles & Truck 51 0.38 0.25 1.06 0.20 0.00 0.11Business Supplies 51 0.44 0.24 1.19 -0.07 0.00 0.11Wholesale 51 0.43 0.23 1.06 0.13 0.00 0.11Retail 51 0.55 0.24 1.11 0.27 0.00 0.12Restaurants & Hotels 51 0.52 0.28 1.27 0.04 0.00 0.12Banking 51 0.48 0.23 1.14 0.11 0.02 0.12Insurance 51 0.44 0.20 0.86 0.14 0.01 0.12Real Estate 51 0.56 0.31 1.21 0.06 0.00 0.07Trading 51 0.53 0.23 1.16 0.12 0.00 0.14Industry Averages 0.51 0.25 1.13 0.10 0.01 0.11Market 0.40 0.18 1.00 0.11 0.00 0.12

40

Table IV. Industry performance measures by NBER delineated business cycle stages Notes: Table reports differences between industry and market Sharpe ratios, excess market returns (αmkt), Jensen’s alphas (αJ), Fama and French (1992) three-factor alphas (αF), and Carhart (1997) four-factor alphas (αC) for the business cycle stage considered optimal by conventional wisdom. We report annualized alpha returns with White (1980) heteroskedasticity consistent t-statistics highlighted for statistical significance at 10 percent. To calculate Sharpe ratios, we divide returns in excess of the one-month Treasury bill by the standard deviation of returns. We estimate Ledoit and Wolf (2008) p-values for industry and market Sharpe ratio differences corrected for potentially non-iid returns and indicate statistically significant differences at the 10 percent level or higher in bold. We estimate excess market returns, Jensen’s alphas, Fama and French alphas, and Carhart alphas by business cycle stage with equations 2–5 respectively using business cycle stage dummy variables (Ds) previously described. We also report Wald test results for differences in performance measures across the five business cycle stages and report p-values under a null hypothesis of constant industry performance. Table also reports equally weighted industry averages beneath each business cycle stage.

5

, , , , ,1

i t mkt t mkt i s s t ts

r r Dα ε=

− = +∑ (2)

5 5

, , , , 1, , , ,1 1

( )i t t J i s s t i s mkt t t s t ts s

r rf D r rf Dα β ε= =

− = + − +∑ ∑ (3)

5 5

, , , , 1, , , 2, , 3, , ,1 1

( )i t t F i s s t i s mkt t t i s t i s t s t ts s

r rf D r rf SMB HML Dα β β β ε= =

⎡ ⎤− = + − + + +⎣ ⎦∑ ∑ (4)

5 5

, , , , 1, , , 2, , 3, , 4, , ,1 1

( )i t t C i s s t i s mkt t t i s t i s t i s t s t ts s

r rf D r rf SMB HML MOM Dα β β β β ε= =

⎡ ⎤− = + − + + + +⎣ ⎦∑ ∑ (5)

Sharpe Ratio Wald Wald Wald WaldIndustries Difference αmkt p-value αJ p-value αF p-value αC p-valueEarly Expansion - Stage I:Computers -0.16 -0.03 0.48 -0.08 0.32 -0.05 0.92 -0.01 0.90Computer Software -0.21 -0.12 0.55 -0.17 0.88 -0.18 0.85 -0.19 0.83Electronic Equip. -0.13 0.00 0.29 -0.06 0.94 -0.04 0.94 -0.01 0.90Measuring & Control -0.19 -0.06 0.06 -0.10 0.05 -0.07 0.22 -0.06 0.22Shipping Containers -0.05 0.01 0.10 0.01 0.12 -0.01 0.15 -0.01 0.15Transportation 0.06 0.07 0.00 0.07 0.00 0.03 0.08 0.02 0.10Industry Average: -0.11 -0.02 -0.05 -0.05 -0.04

Excess Market Jensens alpha Fama-French alpha Carhart alpha

41

Table IV. Continued

Sharpe Ratio Wald Wald Wald WaldIndustries Difference αmkt p-value αJ p-value αF p-value αC p-valueMiddle Expansion - Stage II:Chemicals -0.07 -0.02 0.05 -0.03 0.04 -0.03 0.16 -0.02 0.13Steel Works -0.08 -0.01 0.53 -0.03 0.60 -0.06 0.32 -0.05 0.25Precious Metals -0.14 -0.05 0.97 -0.03 0.97 -0.07 0.97 -0.07 0.96Mining -0.10 -0.01 0.05 -0.03 0.05 -0.06 0.01 -0.06 0.01Fabricated Products -0.07 -0.01 0.16 -0.01 0.24 -0.04 0.16 -0.03 0.16Machinery -0.01 0.03 0.02 0.01 0.19 0.00 0.26 0.00 0.22Electrical Equip. 0.01 0.05 0.36 0.02 0.33 0.02 0.39 0.01 0.41Aircraft 0.00 0.05 0.66 0.03 0.84 0.01 0.96 0.00 0.96Shipbuilding/Railroad -0.14 -0.05 0.62 -0.07 0.62 -0.08 0.58 -0.08 0.59Defense -0.04 0.01 0.67 0.01 0.48 -0.02 0.52 -0.03 0.48Personal Services -0.10 -0.02 0.17 -0.03 0.29 -0.04 0.48 -0.03 0.50Business Services -0.04 0.00 0.09 -0.01 0.13 -0.01 0.16 -0.01 0.17Industry Average: -0.07 0.00 -0.01 -0.03 -0.03Late Expansion - Stage III:Agriculture 0.05 0.04 0.24 0.04 0.20 0.04 0.15 0.04 0.14Food Products 0.00 0.00 0.00 0.01 0.01 0.00 0.01 0.01 0.01Candy & Soda -0.06 -0.03 0.32 -0.03 0.20 -0.04 0.18 -0.03 0.18Beer & Liquor 0.04 0.03 0.37 0.03 0.65 0.03 0.37 0.04 0.37Tobacco Products 0.11 0.08 0.01 0.09 0.09 0.08 0.05 0.10 0.05Healthcare 0.00 0.01 0.23 0.01 0.30 0.01 0.24 0.02 0.24Medical Equipment 0.08 0.05 0.04 0.05 0.05 0.05 0.10 0.03 0.09Pharmaceutical 0.05 0.03 0.00 0.04 0.01 0.04 0.04 0.01 0.04Coal 0.10 0.14 0.06 0.14 0.09 0.13 0.07 0.06 0.06Petroleum & Natural 0.07 0.05 0.50 0.05 0.42 0.04 0.36 0.03 0.35Industry Average: 0.04 0.04 0.04 0.04 0.03Early Recession - Stage IV:Gas & Electric 0.33 0.20 0.01 0.13 0.74 0.12 0.49 0.12 0.50Communication 0.23 0.15 0.02 0.05 0.65 0.04 0.74 0.04 0.64Industry Average: 0.28 0.17 0.09 0.08 0.08Late Recession - Stage V:Recreation -0.04 0.18 0.47 0.10 0.66 0.06 0.56 0.00 0.59Entertainment -0.13 0.07 0.76 -0.01 0.18 -0.05 0.06 -0.04 0.05Printing & Publishing 0.10 0.16 0.06 0.15 0.07 0.12 0.07 0.08 0.07Consumer Goods 0.03 0.07 0.37 0.06 0.28 0.07 0.24 0.00 0.22Apparel 0.02 0.17 0.27 0.14 0.34 0.07 0.27 0.08 0.39Rubber & Plastic -0.07 0.01 0.45 0.04 0.56 0.01 0.47 -0.03 0.47Textiles -0.07 0.05 0.34 0.03 0.34 -0.02 0.81 0.01 0.89Construction Material 0.00 0.08 0.09 0.03 0.33 0.00 0.29 -0.03 0.31Construction -0.07 0.17 0.00 0.01 0.03 -0.01 0.01 0.03 0.01Automobiles & Truck -0.14 -0.01 0.07 -0.03 0.08 -0.07 0.39 -0.05 0.34Business Supplies -0.08 0.03 0.22 -0.03 0.26 -0.04 0.65 -0.04 0.68Wholesale -0.08 0.02 0.56 0.00 0.75 -0.01 0.72 -0.07 0.72Retail 0.02 0.11 0.10 0.08 0.10 0.04 0.09 0.01 0.10Restaraunts & Hotels -0.07 0.09 0.37 0.01 0.57 -0.02 0.60 -0.04 0.66Banking -0.04 0.06 0.43 0.01 0.48 0.00 0.34 -0.05 0.38Insurance -0.01 0.03 0.92 0.07 0.92 0.09 0.82 0.04 0.84Real Estate -0.09 0.11 0.08 0.05 0.14 -0.03 0.10 -0.12 0.11Trading 0.02 0.10 0.02 0.05 0.60 0.03 0.77 0.05 0.82Industry Average: -0.04 0.08 0.04 0.01 -0.01

Excess Market Jensens alpha Fama-French alpha Carhart alpha

42

Table V. Comparison of market, sector rotation, and market timing performance Notes: Table compares Jensen’s alpha and Sharpe Ratio performance measures for the market, sector rotation, and market timing after allowing for a range of transaction costs. The market strategy invests in the market portfolio for the entire period. Sector rotation holds equal weights in sectors/industries based on conventional wisdom during a particular business cycle stage. Market timing holds the market portfolio for all business cycle stages except for cash during early recession. We report Jensen’s alphas as annualized rates with White (1980) heteroskedasticity consistent t-statistics.

Strategy Jensen's alpha t-statistic Sharpe ratioMarket - - 0.13

0% round-trip transaction costsSector rotation 2.3% 1.94 0.15Market-timing 2.5% 3.57 0.17

0.5% round-trip transaction costsSector rotation 1.9% 1.59 0.14Market-timing 2.3% 3.32 0.17

1.0% round-trip transaction costsSector rotation 1.5% 1.24 0.14Market-timing 2.1% 3.06 0.16

1.5% round-trip transaction costSector rotation 1.1% 0.89 0.13Market-timing 1.9% 2.78 0.16*sector rotation and market-timing have respectively 50 and 20 round-trip transactions

Full Period 1948:01 - 2007:12

43

Table VI. Average statistics and performance comparison using different data sets by NBER business cycle stage

Notes: Table reports the average beta, standard deviation, stage mean return, full period mean return, excess market return (αmkt), Jensen’s alpha (αJ), Fama and French three-factor alpha (αF), and Carhart four-factor alpha (αC), and the difference between sector/industry and market Sharpe ratios for the business cycle stage considered optimal by conventional wisdom. We report annualized standard deviations, means, and alpha performance measures.

stage period Sharpe RatioIndustries Period beta std. dev. mean mean αmkt αJ αF αC DifferenceEarly Expansion Industries - Stage I:Fama & French 48 Industries 1948:01-2007:12 1.32 0.23 0.14 0.10 -0.02 -0.05 -0.05 -0.04 -0.11Standard & Poors 15 Sectors 1948:01-2007:12 1.12 0.21 0.15 0.09 0.01 -0.03 -0.03 -0.02 -0.12Fama & French 16 Sectors 1948:01-2007:12 1.00 0.16 0.24 0.11 0.09 0.06 0.03 0.01 0.06Fidelity Select 42 Sectors 1981:08-2008:08 1.45 0.26 0.07 0.07 0.05 0.00 -0.02 -0.02 0.02

Middle Expansion Industries - Stage II:Fama & French 48 Industries 1948:01-2007:12 1.11 0.21 0.13 0.10 0.00 -0.01 -0.03 -0.03 -0.07Standard & Poors 15 Sectors 1948:01-2007:12 1.06 0.25 0.08 0.08 -0.02 -0.05 -0.07 -0.06 -0.14Fama & French 16 Sectors 1948:01-2007:12 1.13 0.19 0.13 0.11 0.00 -0.02 -0.03 -0.02 -0.06Fidelity Select 42 Sectors 1981:08-2008:08 1.10 0.22 0.17 0.11 -0.03 -0.01 0.00 0.00 -0.07

Late Expansion Industries - Stage III:Fama & French 48 Industries 1948:01-2007:12 0.79 0.22 0.11 0.13 0.04 0.04 0.04 0.03 0.04Standard & Poors 15 Sectors 1948:01-2007:12 0.60 0.16 0.07 0.09 0.03 0.01 0.00 0.00 0.00Fama & French 16 Sectors 1948:01-2007:12 0.67 0.16 0.11 0.13 0.03 0.04 0.04 0.03 0.06Fidelity Select 42 Sectors 1981:08-2008:08 0.73 0.21 0.14 0.11 0.03 0.05 0.05 0.03 0.03

Early Recession Industries - Stage IV:Fama & French 48 Industries 1948:01-2007:12 0.70 0.15 -0.02 0.11 0.17 0.09 0.08 0.08 0.28Standard & Poors 15 Sectors 1948:01-2007:12 0.70 0.18 -0.09 0.05 0.16 0.01 -0.01 -0.01 0.18Fama & French 16 Sectors 1948:01-2007:12 0.76 0.16 0.00 0.11 0.22 0.13 0.12 0.12 0.33Fidelity Select 42 Sectors 1981:08-2008:08 1.05 0.21 -0.15 0.07 -0.03 -0.05 -0.02 -0.02 0.00

Late Recession Industries - Stage V:Fama & French 48 Industries 1948:01-2007:12 1.13 0.25 0.51 0.11 0.08 0.04 0.01 -0.01 -0.04Standard & Poors 15 Sectors 1948:01-2007:12 0.90 0.21 0.30 0.07 -0.03 -0.05 -0.07 -0.08 -0.16Fama & French 16 Sectors 1948:01-2007:12 1.13 0.24 0.50 0.11 0.09 0.03 0.00 -0.01 -0.03Fidelity Select 42 Sectors 1981:08-2008:08 1.18 0.26 0.35 0.11 0.14 0.12 0.11 0.09 0.12

Performance Measures

44

Table VII. Industry measures based on the CFNAI over the 1968:01-2007:12 period

Notes: Panel A reports average industry statistics and performance measures by CFNAI delineated business cycle stages. We divide the range of CFNAI values into five equal stages to construct business cycles stages of 96 observations each. We report the average single index model beta, standard deviation, stage mean return, full period mean return, excess market return (αmkt), Jensen’s alpha (αJ), Fama and French three-factor alpha (αF), and Carhart four-factor alpha (αC), and industry-market Sharpe ratio difference for all industries that based on conventional wisdom provide optimal performance during a particular business cycle stage. We report annualized standard deviations, means, and performance measures. Panel B reports regression coefficients from equation (6) and bootstrapped p-values for the likelihood that level and change of CFNAI coefficients jointly have the correct sign.

, 0 1 2 ,( )i t t t t i mkt t t tr rf CFNAI CFNAI r rfα α α β ε− = + + Δ + − + (6)

Panel A:

stage sample Sharpe ratioSector/Industry beta std. dev. mean mean αmkt αJ αF αC Difference

Early Expansion Industries - Stage I: 1.26 0.28 0.06 0.07 -0.02 -0.02 -0.01 0.01 -0.02

Middle Expansion Industries - Stage II: 1.06 0.20 0.04 0.09 -0.01 -0.01 -0.03 -0.03 -0.02

Late Expansion Industries - Stage III: 0.88 0.19 0.17 0.12 0.01 0.02 0.01 0.00 -0.06

Early Recession Industries - Stage IV: 0.89 0.18 0.10 0.11 -0.03 -0.01 -0.03 -0.02 -0.08

Late Recession Industries - Stage V: 1.08 0.27 0.11 0.10 0.02 0.02 0.00 0.01 0.01

Performance Measures

Panel B:

CFNAI ≥ 0 CFNAI ≥ 0 CFNAI < 0 CFNAI < 0 (Mkt-TBL) CFNAI ΔCFNAI and and and and

Stage Industry constant coefficient coefficient coefficient ΔCFNAI ≥ 0 ΔCFNAI < 0 ΔCFNAI < 0 ΔCFNAI ≥ 0 Early Expansion Computers -0.003 1.26 0.004 0.003 0.61 0.32 0.02 0.06

Computer Software -0.009 1.77 -0.007 0.035 0.11 0.00 0.01 0.87Electronic Equipment -0.003 1.48 -0.001 0.012 0.36 0.01 0.01 0.62Measuring & Control -0.003 1.39 -0.001 0.010 0.36 0.03 0.02 0.59Shipping Containers 0.001 0.94 -0.001 0.003 0.21 0.11 0.19 0.49Transportation -0.001 1.08 -0.003 0.012 0.08 0.00 0.01 0.90

joint probability of regression coefficient signs

Industries CFNAI ΔCFNAI Industries CFNAI ΔCFNAIEarly Expansion pos pos Early Recession neg negMiddle Expansion pos - Late Recession neg posLate Expansion pos neg

Expected Sign of CFNAI regression Coefficient

45

Table VII. Continued

CFNAI ≥ 0 CFNAI ≥ 0 CFNAI < 0 CFNAI < 0 (Mkt-TBL) CFNAI ΔCFNAI and and and and

Stage Industry constant coefficient coefficient coefficient ΔCFNAI ≥ 0 ΔCFNAI < 0 ΔCFNAI < 0 ΔCFNAI ≥ 0 Middle Expansion Chemicals 0.000 0.97 -0.002 0.010 0.14 0.01 0.01 0.85

Steel Works -0.003 1.23 0.004 0.006 0.77 0.19 0.00 0.05Precious Metals -0.001 0.71 -0.004 0.014 0.19 0.04 0.10 0.66Mining 0.000 1.02 0.001 0.015 0.64 0.01 0.00 0.35Fabricated Products -0.006 1.09 0.001 0.009 0.60 0.05 0.02 0.33Machinery -0.001 1.18 0.002 0.008 0.88 0.01 0.00 0.11Electrical Equipment 0.002 1.16 -0.002 0.010 0.08 0.00 0.01 0.90Aircraft 0.000 1.14 0.000 0.018 0.43 0.01 0.00 0.56Shipbuilding & Railroad -0.001 1.00 0.002 0.008 0.62 0.10 0.03 0.24Defense 0.003 0.82 -0.002 0.005 0.19 0.08 0.19 0.54Personal Services -0.004 1.15 -0.006 0.010 0.05 0.01 0.09 0.86Business Services -0.001 1.20 -0.003 0.006 0.04 0.01 0.04 0.91

Late Expansion Agriculture 0.001 0.89 0.000 0.002 0.28 0.20 0.19 0.33Food Products 0.003 0.70 -0.005 -0.008 0.00 0.00 0.96 0.03Candy & Soda 0.001 0.84 -0.001 -0.015 0.01 0.41 0.57 0.01Beer & Liquor 0.003 0.80 -0.005 -0.007 0.00 0.04 0.86 0.10Tobacco Products 0.006 0.65 -0.004 -0.025 0.00 0.10 0.90 0.00Healthcare -0.001 1.12 -0.009 0.002 0.01 0.05 0.38 0.57Medical Equipment 0.002 0.89 -0.004 -0.003 0.01 0.03 0.68 0.28Pharmaceutical 0.002 0.82 0.000 -0.013 0.00 0.50 0.49 0.00Coal 0.002 1.10 -0.005 -0.006 0.02 0.16 0.56 0.26Petroleum & Natural 0.003 0.78 0.005 0.000 0.51 0.46 0.01 0.02

Early Recession Utilities 0.002 0.52 -0.002 -0.005 0.01 0.10 0.74 0.14Communication 0.000 0.75 0.002 -0.010 0.03 0.87 0.10 0.00

Late Recession Recreation -0.003 1.18 -0.007 0.017 0.00 0.00 0.01 0.98Entertainment 0.002 1.30 -0.004 -0.005 0.03 0.18 0.56 0.23Printing & Publishing -0.001 1.02 -0.005 0.012 0.02 0.00 0.01 0.97Consumer Goods 0.000 0.83 -0.004 0.003 0.02 0.01 0.22 0.76Apparel 0.000 1.11 -0.010 0.018 0.00 0.00 0.00 1.00Rubber & Plastic 0.000 1.05 -0.002 0.009 0.15 0.01 0.03 0.82Textiles 0.000 0.98 -0.008 0.018 0.00 0.00 0.00 1.00Construction Material 0.000 1.10 -0.003 0.003 0.02 0.01 0.24 0.72Construction -0.001 1.30 -0.004 0.022 0.12 0.00 0.00 0.88Automobiles & Truck -0.002 1.02 -0.004 0.007 0.06 0.01 0.13 0.80Business Supplies 0.000 0.95 -0.001 0.007 0.34 0.06 0.04 0.56Wholesale 0.000 1.09 -0.002 0.012 0.12 0.00 0.00 0.88Retail 0.001 1.03 -0.008 0.004 0.00 0.00 0.20 0.80Restaraunts & Hotels 0.001 1.13 -0.005 0.008 0.06 0.02 0.11 0.81Banking 0.001 1.01 -0.001 -0.010 0.00 0.25 0.72 0.03Insurance 0.002 0.90 -0.002 0.000 0.09 0.14 0.37 0.40Real Estate -0.005 1.09 -0.002 0.014 0.28 0.01 0.02 0.70Trading 0.002 1.23 0.002 -0.002 0.28 0.61 0.05 0.07

joint probability of regression coefficient signs

46

Table VIII. Comparison of strategy performance with changes in timing the business cycle Notes: Table reports the performance of sector rotation and market timing when we advance or delay strategy implementation from the base case by the number of months shown. The table reports Jensen’s alphas (αJ) as annualized rates with White (1980) heteroskedasticity consistent t-statistics and Sharpe ratio performance measures. Table includes market results at the bottom for comparison. The performance results shown are before transaction costs.

Strategy implementation Jensen's alpha t-statistic Sharpe ratioSector Rotation:+ 3 month 1.0% 0.86 0.13+ 2 month 1.0% 0.85 0.13+ 1 month 1.9% 1.63 0.14at turning point 2.3% 1.94 0.15- 1 month 2.2% 1.81 0.15- 2 month 1.8% 1.53 0.14- 3 month 1.5% 1.27 0.14

Market-timing:+ 3 month 1.7% 2.44 0.16+ 2 month 2.6% 3.54 0.18+ 1 month 2.9% 3.75 0.18at turning point 2.5% 3.57 0.17- 1 month 1.2% 3.10 0.15- 2 month 0.9% 2.25 0.15- 3 month 0.3% 0.63 0.13

Market - - 0.13

Full Period 1948:01 - 2007:12

47

Table IX. Construction of sector rotation portfolios based on a one-period-ahead forecast model

Notes: Table reports the composition of sector rotation portfolios constructed with a forecast model using business cycle variables (BCV) that the literature shows forecast stock returns over the course of business cycles. The business cycle variables comprise lagged changes in the one-month Treasury bill, term-structure, default-spread, and dividend yield. We forecast industry with parameters estimated with a regression of excess industry returns (ri,t-rf ) on a constant, lagged change in the business cycle variables (ΔBCVi), and excess market returns (rmkt-rf) using equation 9. We estimate the (γi) forecast parameters with a 60-month rolling window that moves forward each month and use these parameter estimates to obtain period ahead forecasts of industry outperformance calculated as the sum of the gamma estimates times current period changes in business cycle variables from the proceeding period. We include all industries with positive forecast outperformance in the period-ahead sector rotation portfolio. Panel A reports the average number of industries selected for inclusion during each business cycle stage. Panel B reports the percentage of time an industry has positive forecast outperformance and is thus selected for inclusion during a particular business cycle stage. We also test for any difference between the percentage of time the model selects an industry for inclusion in the portfolio and a random 50/50 probability of inclusion, with 10 percent statistical significance indicated in bold. The shaded area in Panel B represents the business cycle stage that conventional wisdom considers optimal.

4

, 0 , 1 ,1

( )i t t i i t mkt t t ti

r rf c BCV r rfγ β ε−=

− = + Δ + − +∑ (7)

Panel A: Average number of industries selected for inclusion by model Full Early Middle Late Early Late

Period Expansion Expansion Expansion Recession Recession23 23 23 23 22 23

Panel B: Percentage of time model forecasts excess industry returns and includes in sector rotation portfolio Full Early Middle Late Early Late

Period Industries Period Expansion Expansion Expansion Recession RecessionEarly Expansion - Stage I Computers 46 48 48 43 40 48

Computer Software 38 38 37 40 38 33Electronic Equipment 47 47 47 47 49 50Measuring & Control 50 50 52 47 43 54Shipping Containers 48 48 42 54 55 46Transportation 49 56 46 44 51 57

Middle Expansion - Stage II Chemicals 50 53 49 46 55 46Steel Works 54 57 56 48 43 67Precious Metals 40 38 42 40 36 43Mining 51 53 52 48 51 52Fabricated Products 40 34 45 44 30 39Machinery 48 56 45 47 45 39Electrical Equipment 47 47 47 45 62 43Aircraft 48 53 48 47 36 50Shipbuilding & Railroad 50 48 50 54 36 54Defense 40 39 41 41 36 39Personal Services 48 46 52 47 53 43Business Services 52 54 55 49 36 57

48

Table IX. Continued Panel B: Continued

Full Early Middle Late Early LatePeriod Industries Period Expansion Expansion Expansion Recession RecessionLate Expansion - Stage III Agriculture 53 53 57 51 53 52

Food Products 49 48 46 52 49 52Candy & Soda 39 33 38 43 53 33Beer & Liquor 49 49 45 50 60 50Tobacco Products 49 47 47 54 49 52Healthcare 32 31 37 34 21 22Medical Equipment 48 40 49 57 53 37Pharmaceutical 51 45 49 57 57 48Coal 49 47 49 49 64 41Petroleum & Natural 52 54 51 51 51 59

Early Recession - Stage IV Utilities 47 39 48 52 55 48Communication 51 45 57 52 55 52

Late Recession - Stage V Recreation 48 55 43 47 36 52Entertainment 46 47 48 42 43 57Printing & Publishing 48 51 48 48 36 43Consumer Goods 48 48 47 45 51 54Apparel 52 55 51 52 45 50Rubber & Plastic 50 60 48 48 40 39Textiles 49 57 47 46 40 43Construction Material 48 49 42 49 47 54Construction 49 51 49 50 40 48Automobiles & Truck 52 56 49 53 43 54Business Supplies 50 55 51 45 49 46Wholesale 49 50 52 45 51 48Retail 48 45 48 48 57 48Restaraunts & Hotels 50 52 53 44 49 57Banking 51 44 52 57 53 46Insurance 50 41 55 56 55 37Real Estate 51 56 52 49 36 54Trading 53 51 58 51 49 54

49

Table X. Alternative sector rotation strategy Notes: Table reports the performance of industries that over the 1948–2007 period provided statistically significant outperformance for the indicated business cycle stage. Column 3 reports the percentage of time (%) that that an industry actually realized statistically significant Jensen’s alpha outperformance. We test the percentage of time an industry actually provides outperformance against a random 50/50 chance with 10 percent statistical significance indicated in bold. Column 4 reports annualized Jensen’s alpha estimates while column 5 reports the Jensen’s alpha White (1980) heteroskedasticity consistent t-statistics highlighted for statistical significance at 10 percent. Period Sector/Industries % αJ t-statisticMiddle Expansion - Stage II Candy & Soda 62 0.10 2.51

Pharmaceutical 55 0.07 2.35Late Expansion - Stage III Mining 53 0.08 2.14

Tobacco Products 59 0.09 1.83Early Recession - Stage IV Shipping Containers 62 0.10 2.42

Food Products 72 0.13 2.12Utilities 66 0.13 2.45Entertainment 66 0.20 2.71

Late Recession - Stage V Personal Services 71 0.15 2.06Food Products 69 0.16 2.78Tobacco Products 61 0.17 1.75

50

Figure I. Conventional Wisdom: Sector Rotation across the Business Cycle

Source: http://personal.fidelity.com/products/funds/content/sector/cycle.shtml

Source: http://www.marketoracle.co.uk/Article3618.html

Source: http://www2.standardandpoors.com/spf/pdf/index/Global_Sector_Investing.pdf

51

Figure II. Stylized business cycles with stage partitions Notes: Figure illustrates a stylized economic business cycle. The official government agency responsible for dating U.S. business cycles is the National Bureau of Economic Research (NBER). The NBER publishes dates for business cycle peaks and troughs. We measure phases of expansion from trough to peak and recession from peak to trough. Similar to Stovall (1996), we divide expansions into three equal stages (early/middle/late) and recessions into two stages (early/late).

NBER trough NBER trough

NBER peak

Stage I Stage II Stage III Stage IV StageV

Expansion Recession

Stages of Expansion Stages of RecessionEarly Expansion - Stage I Early Recession - Stage IVMiddle Expansion - Stage II Late Recession - Stage VLate Expansion - Stage III

52

Figure III. CFNAI business cycle stages Notes: Figure illustrates the CFNAI economic indicator over the period 1968–2007. Shaded areas indicate NBER defined periods of economic contraction. The range of CFNAI values covering the full sample are partitioned into 5 equal periods of economic activity that can be thought of as corresponding to periods of early expansion (SI), middle expansion (SII), late expansion (SIII), early recession (SIV), and late recession (SV). The partitions between adjoining stages are shown with delineations at CFNAI values of 0.57, 0.26, -.01, and -.045 between periods SI|SII, SII|SIII, SIII|SIV, and SIV|SV respectively.

-4.5

-3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5

1968 1974 1979 1985 1990 1996 2001 2007

NBER Recessions S1|S2 S2|S3 S3|S4 S4|S5 CFNAI

53

Figure IV. Distribution of Jensen’s alphas of sectors in different stages Note: Chart illustrates the actual percentage of time that industry Jensen’s alpha t-statistics fall within the indicated range and compares with the expected distribution of t-statistics under a normal distribution. We calculate Jensen’s alphas for each industry during each business cycle for a total of 240 corresponding t-statistics.

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

< ‐3.29

‐3.29 to ‐2

.58

‐2.58 to ‐1

.96

‐1.96 to ‐1

.65

‐1.65 to ‐1

‐1 to

‐0.5

‐0.5 to

0

0 to 0.5

0.5 to 1

1 to 1.65

1.65

to 1.96

1.96

to 2.58

2.58

to 3.29

> 3.29

Freq

uency

T‐Statistic Range

Actual distribution of Jensen's alpha t‐statistics Expected distribution of Jensen's alpha t‐statistics assuming a normal distribution

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Sector Rotation Across the Business Cycle _SSRN-Id1572910

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