Winter Blues: A SAD Stock Market Cycle - Lisa Kramerlisakramer.com/aer-sad.pdf · Winter Blues: A...

Winter Blues A SAD Stock Market Cycle

By MARK J KAMSTRA LISA A KRAMER AND MAURICE D LEVI

And God said Let there be light andthere was light And God saw that thelight was good

Genesis 13

Depression has been linked with seasonalaffective disorder (SAD) a condition that af-fects many people during the seasons of rela-tively fewer hours of daylight Experimentalresearch in psychology has documented a clearlink between depression and lowered risk-taking behavior in a wide range of settingsincluding those of a nancial nature Throughthe links between SAD and depression and be-tween depression and risk aversion seasonalvariation in length of day can translate intoseasonal variation in equity returns Based onsupportive evidence from psychology whichsuggests SAD is linked closely with hours ofdaylight we consider stock market index datafrom countries at various latitudes and on bothsides of the equator We model differences inthe seasonal variation of daylight across coun-

tries to capture the in uence of daylight onhuman sentiment risk tolerance and hencestock returns Our results strongly support aSAD effect in the seasonal cycle of stock re-turns that is both signi cant and substantialeven after controlling for well-known marketseasonals and other environmental factors Pat-terns at different latitudes and in both hemi-spheres provide compelling evidence of a linkbetween seasonal depression and seasonal vari-ation in stock returns higher-latitude marketsshow more pronounced SAD effects and resultsin the Southern Hemisphere are six months outof phase as are the seasons

The remainder of the paper is organized asfollows In Section I we discuss SAD depres-sion and equilibrium market returns In SectionII we introduce the international data sets InSection III we explain the construction of thevariables intended to capture the in uence ofSAD on the stock market We document inSection IV the signi cance of the SAD effectboth statistical and economic and provide anexample of the excess returns that arise fromtrading strategies based on the SAD effect InSection V we explore the robustness of theSAD effect to changes in variable de nitionsand estimation methods Section VI considersSAD in the context of segmented versus inte-grated capital markets Section VII concludes1

I SAD and the Stock Market

As John Keats has written ldquoFour seasons llthe measure of the year There are four seasonsin the mind of manrdquo One important aspect ofthe seasons as they affect the mind is the re-duced daylight hours during the fall and wintermonths According to Norman E Rosenthal(1998) the recurrent problems associated with

Kamstra Atlanta Federal Reserve Bank 1000 PeachtreeStreet NE Atlanta GA 30309 (e-mail markkamstraatlfrborg) Kramer Rotman School of Management Univer-sity of Toronto 105 St George Street Toronto OntarioM5S 3E6 Canada (e-mail lkramerchassutorontoca)Levi Faculty of Commerce and Business AdministrationUniversity of British Columbia 2053 Main Mall VancouverBC V6T 1Z2 Canada (e-mail mauricelevicommerceubcca) We have bene ted from the suggestions of twoanonymous referees of this Review Stanley Coren RickGreen Steven Jones Andrew Karolyi George Kramer TimLoughran Raj Mehra Jacob Sagi Bob Shiller Dick Thalerparticipants at the meetings of the American Finance Asso-ciation the Canadian Econometrics Study Group the Ca-nadian Economics Association the Scottish Institute forResearch in Investment and Finance and seminar partici-pants at the following universities Guelph ManchesterUMIST McMaster Montreal Notre Dame San FranciscoToronto Wilfrid Laurier and York The authors gratefullyacknowledge nancial support of the Social Sciences andHumanities Research Council of Canada and the researchassistance of Andy Bunkanwanicha and Yang Wu Anyremaining errors are solely the responsibility of the authorsThe views expressed here are those of the authors and notnecessarily those of the Atlanta Federal Reserve Bank or theFederal Reserve System

1 An Appendix to this paper is available at wwwmarkkamstracom or from the authors on request The Ap-pendix provides detailed estimation results from Kamstra etal (2000) as well as further robustness and sensitivitychecks described but not provided below

324

diminished daylight take on a particularly se-vere form among the approximately 10 millionAmericans who are af icted with seasonal af-fective disorder where ldquoaffectiverdquo means emo-tional A further 15 million suffer a milder formldquowinter bluesrdquo The problem is also extensivelydocumented outside the United States withsimilar proportions of sufferers in countriesaround the world2 Jeanne Molin et al (1996)and Michael A Young et al (1997) provideevidence that seasonal depression is related tohours of daylight and hence the effects of SADmay be more pronounced in countries at moreextreme latitudes where winter and fall days arerelatively shorter

SAD is clinically de ned as a form of majordepressive disorder3 While usually described interms of prolonged periods of sadness and pro-found chronic fatigue evidence suggests thatSAD is connected to serotonin dysregulation inthe brain Furthermore positron emission to-mography (PET) scans reveal abnormalities inthe prefrontal and parietal cortex areas due todiminished daylight as described in the Na-tional Institute of Mental Health study byRobert M Cohen et al (1992) That is thereappears to be a physiological source to the de-pression related to shorter days SAD symptomsinclude dif culty concentrating loss of interestin sex social withdrawal loss of energy leth-argy sleep disturbance and carbohydrate orsugar craving often accompanied by weightgain4 For those affected the annual onset ofSAD symptoms can occur as early as Septem-ber around the time of autumn equinox SeeSteven C Dilsaver (1990) for example

Experimental research in psychology hasdocumented a direct link between depressionand heightened risk aversion This link is estab-lished by rst providing a measure of risk-

taking tendency in the form of a scale ofldquosensation-seekingrdquo propensity the most widelyused of which was developed by Marvin Zuck-erman (1984) The scale is then correlated withvarious biological and psychological phenom-ena as shown for example by Zuckerman et al(1980) Sensation-seeking measures used tojudge the propensity to take risk have beenextensively documented as reliable measures ofrisk-taking tendency in nancial decision-making settings by Alan Wong and BernardoCarducci (1991) Paula Horvath and Zuckerman(1993) and Howard Tokunaga (1993) amongothers When the willingness to take risk isrelated to measured levels of anxiety and de-pression there is a distinct tendency for greateranxiety or depression to be associated with re-duced sensation seeking and reduced generalwillingness to take risk as shown by Zucker-man (1984 1994) Gregory A Marvel and Bar-bara R Hartman (1986) Solange Carton et al(1992) and Carton et al (1995) In a furtherstudy of depression and risk aversion Amy EEisenberg et al (1998) conducted experimentsin which subjects differing in degree of depres-sion were faced with a series of choices betweenpairs of risky and safe options including someof a nancial nature By setting the choices suchthat in some cases the risky option was thedefault (not requiring action) and in other casesthe safe option was the default the researcherswere able to distinguish risk aversion from pas-sivity depressive symptoms correlated withrisk aversion

The psychological studies cited abovestrongly support the view that the depressionassociated with shorter days translates into agreater degree of risk aversion leading to test-able hypotheses in the context of stock marketreturns Those market participants directly af-fected by SAD can in uence overall marketreturns according to the well-established princi-ple that market equilibrium occurs at priceswhere marginal buyers are willing to exchangewith marginal sellers aggregate demands andsupplies for risky versus riskless assets canthereby affect equilibrium risk premia5 The

2 For example the frequency of SAD in northern Canadais documented by Robert J Williams and G G Schmidt(1993) The incidence of SAD in Italy is discussed byGianni L Faedda et al (1993) There is even evidence fromthe Mayo Clinic (2002) that SAD occurs in countries asclose to the equator as India These and others studiessuggest approximately 10 percent of people suffer fromSAD

3 See for example David H Avery et al (1993) YbeMeesters et al (1993) Georg Leonhardt et al (1994) and RMichael Bagby et al (1996)

4 Mayo Clinic (2002)

5 For further details on the impact of the marginal traderon market equilibria see the classic papers by John R Hicks(1963) and Gerald O Bierwag and M A Grove (1965) as

325VOL 93 NO 1 KAMSTRA ET AL WINTER BLUES A SAD STOCK MARKET CYCLE

implication is a causal relationship between sea-sonal patterns in length of day and market returns

Studies on individuals at extreme latitudesincluding work by Lawrence A Palinkas et al(1996) and Palinkas and Matt Houseal (2000)suggest the depressive effects of SAD andhence risk aversion may be asymmetric aboutwinter solstice Thus two dates symmetric aboutwinter solstice have the same length of night butpossibly different expected returns We antici-pate seeing unusually low returns before wintersolstice and abnormally high returns followingwinter solstice Lower returns should com-mence with autumn as SAD-in uenced indi-viduals begin shunning risk and rebalancingtheir portfolios in favor of relatively safe assetsWe expect this to be followed by abnormallyhigh returns when days begin to lengthen andSAD-affected individuals begin resuming theirrisky holdings As long as there are SAD suf-ferers shunning risk at some times of the yearrelative to other times market returns will con-tain a seasonal According to the medical evi-dence on the incidence of SAD this seasonalrelates to the length of the day not to changes inthe length of the day Therefore against the nullhypothesis that there is no effect of the seasonsrelated to SAD and the winter blues our alter-native hypothesis is that seasonal depressionbrought on by short days lead to relatively lowerreturns in the fall and relatively higher returns inthe winter

A Length of Night and OtherEnvironmental Factors

A related literature in economics investigatesthe in uence of weather on market returns Asargued by Edward M Saunders (1993) andDavid Hirshleifer and Tyler Shumway (2003)the number of hours of sunshine affects peo-plesrsquo moods and hence also possibly marketreturns The amount of sunshine is affected bycloud cover as well as the number of hours ofdaylight and indeed Saunders (1993) uses ameasure of cloudiness by classifying the degreeof cloudiness in New York City into three cat-egories 0 ndash30 percent 40ndash70 percent 80ndash100

percent and nds support for a relation betweensunshine and market returns Hirshleifer andShumway (2003) present further evidence for asunshine effect in a study of 26 internationalstock markets Instead of studying sun or cloudMelanie Cao and Jason Wei (2001) investigatethe in uence of temperature on stock marketreturns and nd evidence of a link in eightinternational markets All of these studies con-sider weather at the level of cities in which themarkets are located

Molin et al (1996) show that among severalenvironmental factors (minutes of sunshinelength of day temperature cloud cover precip-itation global radiation and barometric pres-sure) length of day has the strongest correlationwith seasonal depression They employ step-wise regression to reduce their multiple regres-sion model to include only length of day andtemperature from the set of all the environmen-tal variables considered Young et al (1997)provide further evidence that SAD is related tothe length of day by studying latitude Our studybuilds on the psychology literature linking sea-sonal affective disorder to length of day as wellas the economics literature linking environmen-tal factors to stock market returns Thus we testfor a relationship between length of night andstock returns controlling for other environmen-tal factors which may in uence returns includ-ing cloud cover precipitation and temperature

II Market Returns Data

The daily stock index return data used inthis study are outlined in Table 1 four indicesfrom the United States as well as indices fromeight other countries chosen to represent large-capitalization broad-based economies at differ-ent latitudes in both hemispheres67 We include

well as the Appendix ldquoThe Equilibrium Prices of FinancialAssetsrdquo by James C Van Horne (1984 pp 70 ndash78)

6 Our selection of indices was dictated by several crite-ria including the availability of a suf ciently long timeseries the absence of hyperin ation large capitalizationand representation of a broad range of sectors

7 All of our foreign stock market returns were obtainedfrom Datastream A feature of the Datastream time series isthat they often include nontrading days such as holidaysDatastream typically assigns a value on a nontrading dayequal to the previous dayrsquos price or equivalently a zeroreturn To remove holidays we made use of Datastreamrsquosvacation les (when available) which track various coun-triesrsquo holidays (starting no earlier than 1985) augmented by

326 THE AMERICAN ECONOMIC REVIEW MARCH 2003

the largest exchange among the far northerlymarkets (Stockholm Sweden) and the largestexchange in the Southern Hemisphere (SydneyAustralia) Our longest time series is the USSampP 500 which spans over 70 years The long-est spanning index we could obtain for SouthAfrica is the Datastream Global Index of 70large-cap stocks in that country All of the in-dices we consider are value-weighted returnsexcluding dividend payments For the UnitedStates we also investigated CRSP equal-weighted indices and CRSP indices of returnsincluding dividends and as shown in the Ap-pendix (available from the authors) we foundqualitatively identical results in all cases Therelevance of market segmentationintegrationacross markets at different latitudes is addressedin Section VI

Table 2 displays simple summary statisticsfor the raw data used in this study the dailypercentage returns for the four indices in theUnited States and an index for each of SwedenBritain Germany Canada New Zealand Ja-pan Australia and South Africa Directly be-low the name of each country is the period overwhich the returns were collected The samplesizes range from under 3000 daily observationsfor New Zealand to over 19000 for the US

SampP 500 index The rst column of statistics isthe daily percentage mean return The meandaily return is of the same order of magnitudefor all of the indices ranging from about 001percent to 006 percent Standard deviation ofthe daily returns varies across countries withSouth Africa being the most volatile (uncondi-tionally) at 134 percent and the US NYSE andAMEX the least volatile at 084 percent Thelargest single-day drop a decline exceeding 28percent was experienced in Australia during theOctober 1987 crash The largest single daygains ranged from 760 percent to 1537 per-cent All of the return series are strongly skewedto negative returns as is typical with stockmarket returns All the return series are stronglykurtotic as well Conventional tests of normality(not reported) strongly reject the hypothesis thatany of these return series are normally distributedas is also typical with stock market returns

The returns data are summarized in an aggre-gate form in Figures 1 and 2 Figure 1 plots themonthly means of the daily percentage returnsaveraged across all four of the United Statesindices The graph shows that in September themonth in which the onset of autumn occursreturns are on average at their lowest point ofthe year They gradually recover through thefall and then in winter they become positiveand peak in January the rst month followingwinter solstice Speaking very roughly there isan indication in the data of some sort of cyclethrough fall and winter The raw data suggestthat September and January may be extremepoints on a seasonal cycle

information on foreign holidays gleaned from varioussources including the Worldwide Holiday amp Festival Site(wwwholidayfestivalcom) As shown in the Appendix(available from the authors) we nd qualitatively identicalresults whether controlling for holidays as described aboveor omitting all zero return days

TABLE 1mdashDAILY STOCK INDEX RETURN DATA WITH CORRESPONDING CITIES AND LATITUDES

Country Index City Latitude

United States SampP 500 New York 41degNUnited States NYSE New York 41degNUnited States NASDAQ New York 41degNUnited States AMEX New York 41degNSweden Veckans Affarer Stockholm 59degNBritain FTSE 100 London 51degNGermany DAX 30 Frankfurt 50degNCanada TSE 300 Toronto 43degNNew Zealand Capital 40 Auckland 37degSJapan NIKKEI 225 Tokyo 36degNAustralia All Ordinaries Sydney 34degSSouth Africa Datastream Global Index Johannesburg 26degS

Note Latitudes are rounded to the nearest degree and re ect the location of the citycorresponding to each indexrsquos stock exchange


Figure 2 plots the monthly means of the dailypercentage returns averaged across the eightforeign indices Prior to averaging the returnsthe data for Australia New Zealand and SouthAfrica were shifted six months to adjust for thedifference in seasons across the hemispheresNote that returns are not shifted in this mannerfor any other gure or table in the paper Thehorizontal axis (in Figure 2 only) is labeled withreference to timing in the Northern HemisphereThat is the rst observation is an average ofreturns over the month in which autumn beginsin each country September for the NorthernHemisphere countries and March for the South-ern Hemisphere countries In Figure 2 we ob-serve the lowest average return in the month inwhich the onset of autumn occurs for all coun-tries marked September and the highest aver-age return occurs in the month following wintersolstice marked January Overall the graph ex-hibits what may be interpreted as a seasonalpattern similar to that shown in Figure 1

Figures 3 4 and 5 plot monthly means ofdaily percentage returns for each of the individ-ual indices considered in this paper Panels Athrough D of Figure 3 plot monthly mean re-

turns for the United States indices Panels Athrough D of Figure 4 plot the monthly meansfor Sweden Britain Germany and Canada andPanels A through D of Figure 5 plot monthlymean returns for New Zealand Japan Austra-lia and South Africa (The horizontal axis of theplot for each country starts with the month inwhich autumn equinox actually takes place inthat country March in the Southern Hemisphereand September in the Northern Hemisphere)Each of the US indices shown in Figure 3 dem-onstrate the same approximate pattern lowestannual returns in the early fall months followedby increasing returns peaking in the rst monthof the year Similarly for each of the countriesshown in Figure 4 returns are at their lowest inSeptember and then they peak shortly after win-ter solstice The countries in Figure 5 are thefour closest to the equator among those weconsider and thus we would expect to see lessof a seasonal in these countriesrsquo returns Whilethe pattern for Japanrsquos returns is similar to thosewe have observed for other countries the pat-terns for South Africa Australia and New Zea-land seem more random in nature Regarding allthe individual plots shown in Figures 3 4 and

TABLE 2mdashDAILY PERCENTAGE RETURN SUMMARY STATISTICS FOR EACH INDEX

Country and period Mean Standard deviation Minimum Maximum Skew Kurtosis

United States SampP 50019280104ndash20001229

0024 112 22047 1537 2035 1890

United States NYSE19620705ndash20001229

0035 084 21836 879 2116 2876

United States NASDAQ19721218ndash20001229

0047 110 21135 1057 2048 1208

United States AMEX19620705ndash20001229

0032 084 21275 1056 2086 1641

Sweden19820915ndash20011218

0063 125 28986 978 2025 602

Britain19840104ndash20011206

0037 101 21303 760 2093 1229

Germany19650105ndash20011212

0025 110 21371 887 2050 862

Canada19690103ndash20011218

0023 085 21029 988 2075 1397

New Zealand19910702ndash20011218

0013 097 21331 948 2086 1878

Japan19500405ndash20011206

0037 112 21614 1243 2034 1082

Australia19800103ndash20011218

0033 100 22876 979 2489 13149

South Africa19730103ndash20011206

0054 134 21453 1357 2072 969

Note All indices are value-weighted and do not include dividend distributions


5 although the average annual patterns varysomewhat they typically show weak mean re-turns in early autumn followed by strong returnsshortly after the longest night of the yearBroadly speaking the returns drop thereafterand atten out through the spring and summerThe Southern Hemisphere exchanges uncondi-tionally at least do not follow the same patternin the fall though perhaps it is not a surprise to nd a lack of seasonal patterns in the exchangeslocated closest to the equator where seasonal uctuations in daylight are small

III Measuring the Effect of SAD

In describing the seasonal pattern of lightthrough the course of the year one could equiv-alently consider the number of hours of dayfrom sunrise to sunset or the number of hoursof night which simply equals 24 minus thenumber of hours of day We choose the latter

Figure 6 shows the cycles for the length of thenight for several of the countries included in thisstudy For simplicity the cycles shown in Fig-ure 6 re ect the length of night for the latitudeat which a countryrsquos stock exchange is locatedrounded to the nearest degree The length of thenight during the course of the year peaks in theNorthern Hemisphere on the winter solsticeDecember 21st and reaches a trough on thesummer solstice June 21st8 In the SouthernHemisphere the function is six months out ofphase with its peak on June 21st and trough onDecember 21st The variations in the length ofnight are larger the further away one travels

8 For convenience we assume winter solstice takes placeon December 21 and summer solstice on June 21 In prac-tice the timing can vary by a couple of days

FIGURE 1 COMPOSITE PLOT FOR THE

UNITED STATES INDICES

Notes The Annual Mean represents the daily percentage re-turns averaged over the year across all four US indices TheMonthly Mean represents the daily percentage returns aver-aged over each month across all seven value-weighted indices

FIGURE 2 COMPOSITE PLOT FOR FOREIGN INDICES

Notes The Annual Mean represents the daily percentagereturns averaged over the year across all eight foreignindices The Monthly Mean represents the daily percentagereturns averaged over each month across all eight foreignindices In producing this gure only returns from indicesin the Southern Hemisphere are shifted by six months toalign the seasons and then the horizontal axis is markedwith reference to the timing in the Northern Hemisphere


FIGURE 3 INDIVIDUAL PLOTS OF DATA FOR EACH OF THE UNITED STATES INDICES

Notes The Annual Mean for each index represents the daily percentage returns averaged over the year for that index TheMonthly Mean for each index represents the daily percentage returns averaged over each month for that index


FIGURE 4 INDIVIDUAL PLOTS OF DATA FOR SWEDEN BRITAIN GERMANY AND CANADA



FIGURE 5 INDIVIDUAL PLOTS OF DATA FOR NEW ZEALAND JAPAN AUSTRALIA AND SOUTH AFRICA



from the equator ie the larger is the latitudenorth or south Thus among the countries weconsider Sweden experiences much greatervariability relative to countries closer to theequator like South Africa and Australia

As described above medical evidence indi-cates that variation in the amount of daylightduring the fall and winter has a systematic effecton individualsrsquo moods Thus we use the numberof hours of night during only the fall and winterto capture the effects of SAD on markets InSection V we discuss the similarity of resultsthat arise using alternate speci cations that allowfor SAD-related effects through all four seasons

The length-of-night measure we use to cap-ture the effects of SAD on the stock market hassome desirable features First it allows us to seewhether there are more pronounced stock mar-ket effects due to SAD in countries at moreextreme latitudes where the fall and winter

months have relatively shorter days Secondthe measure varies similarly across entire coun-tries and even hemispheres thus wherever amarginal trader happens to be located within acountry her degree of seasonal depression andhence her in uence on markets would be ex-pected to manifest similarly

A SAD Measure Based on NormalizedHours of Night

De ne Ht as the time from sunset to sunriseat a particular location Then we can de ne ourSAD measure SADt at that location as fol-lows9

(1) SAD t 5 5 H t 2 12 for trading days inthe fall and winter

0 otherwise

Note that SADt varies only over the fall and win-ter the seasons when according to medical evi-dence SAD affects individuals By deducting 12(roughly the average number of hours of nightover the entire year at any location) SADt re ectsthe length of the night in the fall and winterrelative to the mean annual length of 12 hours InSweden for example the SADt variable equals 0at the autumn equinox (September 21) takes onhigher values until it peaks at 16 on winter sol-stice then takes on lower values until it equals 0 atthe spring equinox (March 20) and remains at 0through the spring and summer For countriescloser to the equator the value varies relativelycloser to 0 during the fall and winter

The number of hours of night Ht can bedetermined using standard approximations fromspherical trigonometry as follows To calculatethe number of hours of night at latitude d we rst need the sunrsquos declination angle lt

(2)

l t 5 04102 z sin X 2p

365D ~ julian t 2 8025

9 The fall and winter period is de ned as September 21to March 20 for the Northern Hemisphere and March 21 toSeptember 20 for the Southern Hemisphere We assume thefall and spring equinoxes take place on September 21 andMarch 21 though the actual timing can vary by a couple ofdays

FIGURE 6 HOURS OF NIGHT FOR SEVERAL MARKETS

Notes Actual hours of night are shown for the latitudes atwhich various countriesrsquo stock exchanges are located(rounded to the nearest degree) The latitudes in degreesare as follows 26 South for South Africa 34 South forAustralia 41 North for the United States 50 North forGermany and 59 North for Sweden


where juliant is a variable that ranges from 1 to365 (366 in a leap year) representing the num-ber of the day in the year Juliant equals 1 forJanuary 1 2 for January 2 and so on We canthen calculate the number of hours of night as

(3)

Ht 5

24 2 772 z arccos 2tanX 2pd

360 D tan~lt

in the Northern Hemisphere

772 z arccos 2tanX 2pd

360 D tan~lt

in the Southern Hemisphere

where arccos is the arc cosine

B Asymmetry Around Winter Solstice

There are at least two reasons to expect thelength of night to lead to an asymmetric re-sponse in market returns before winter solsticerelative to after First as mentioned in Section Iresults from Palinkas et al (1996) and Palinkasand Houseal (2000) indicate the depressive ef-fect of SAD may be asymmetric around wintersolstice Second the trading activity of SAD-affected investors may itself cause asymmetricpatterns in equity returns Speci cally if inves-tors become more risk averse at the onset of falland then return to ldquonormalrdquo at the end of winterhigher compensating returns for holding riskyassets between those points in time are gener-ated by an initial price which is lower thanwould otherwise have been observed That iswith the onset of heightened risk aversion asso-ciated with SAD prices rise less quickly thanthey would otherwise After levels of risk aver-sion return to their previous non-SAD in u-enced levels at the end of winter the recoveryof prices from their initial (lower) levels in-creases returns The implication is that returnsare lower in the fall and higher in the winter

In order to allow for an asymmetric effect inthe fall relative to the winter we introduce adummy variable for days of the year which arein the fall season10

(4) D tFall 5 5 1 for trading days in the fall

0 otherwise

Including this dummy variable allows (but doesnot require) the impact of SAD in the fall todiffer from that in the winter If contrary to ourexpectations the effects are symmetric acrossthe two periods this will simply be re ected bya coef cient on Dt

Fall which is insigni cantlydifferent from zero

IV In uence of the SAD Effect

A Estimation

We run a single regression for each countryallowing the impact of SAD to vary freely fromcountry to country Returns are regressed on upto two lagged returns (where necessary to con-trol for residual autocorrelation) a Mondaydummy a dummy variable for a tax-loss sellingeffect the SAD measure a fall dummy cloudcover precipitation and temperature11

(5)

r t 5 m 1 r1 r t 2 1 1 r2 r t 2 2 1 mMonday D tMonday

1 mTax D tTax 1 mSAD SAD t 1 mFall D t

Fall

1 mCloud Cloud t

1 mPrecipitation Precipitation t

1 mTemperature Temperature t 1 laquo t

10 Fall is de ned as September 21 to December 20 in theNorthern Hemisphere and March 21 to June 20 in theSouthern Hemisphere

11 The use of the AR(1) speci cation for stock returns iscommon as is the use of Monday and tax-loss dummyvariables See for instance Vedat Akgiray (1989) AdrianPagan and William Schwert (1990) Raul Susmel and Rob-ert F Engle (1994) and R Glen Donaldson and Kamstra(1997) Seasonality in stock returns is explored in a widerange of papers including Nai-Fu Chen et al (1986) Eric CChang and J Michael Pinegar (1989 1990) and SvenBouman and Ben Jacobsen (2002) There are numerouspapers that study seasonal stock market effects as related totax-loss selling including Philip Brown et al (1983) SehaM Tinic and Richard R West (1984) Kiyoshi Kato andJames S Schallheim (1985) Richard H Thaler (1987) JayR Ritter (1988) Steven L Jones et al (1991) Ravinder KBhardwaj and LeRoy D Brooks (1992) George Athanas-sakos and Jacques A Schnabel (1994) Charles Kramer(1994) and James A Ligon (1997)


Variables are de ned as follows rt is the periodt return for a given countryrsquos index r t2 1 andr t2 2 are lagged dependent variables D t

Monday isa dummy variable which equals one when pe-riod t is the trading day following a weekend(usually a Monday) and equals zero otherwiseD t

Tax is a dummy variable which equals one fora given country when period t is in the lasttrading day or rst ve trading days of the taxyear12 and equals zero otherwise and DFall is adummy variable which equals one for a givencountry when period t is in the fall and equalszero otherwise The environmental factors eachmeasured in the city of the exchange are per-centage cloud cover (Cloud t) millimeters ofprecipitation (Precipitationt) and temperaturein degrees Celsius (Temperaturet)

13

At the end of this subsection we discuss theresults from estimating equation (5) (Most im-portantly the parameter estimates on the SADvariable and fall dummy variable will be shownto be statistically signi cant for almost all theindices we consider) First we present Table3 which provides an analysis of each indexrsquosaverage annual percentage return due to theSAD variable and due to the fall variable Foreach index in our study we present in the rstcolumn of statistics the average annualized re-turn due to our SAD measure In computing thereturn due to SAD for a particular index wecalculate for each trading day the value of theSAD variable (which varies between zero andsix for Sweden for example during the fall andwinter and which equals zero otherwise) mul-tiply by that indexrsquos SAD variable estimate(presented in Tables 4Andash4C) and adjust the

value to obtain an annualized return In the nextcolumn we present for each exchange the aver-age annualized return due to the fall dummyvariable In calculating the return due to the falldummy we calculate for each trading day thatcountryrsquos fall dummy variable estimate (pre-sented in Tables 4Andash4C) multiplied by thevalue of the fall dummy variable (one during thefall zero otherwise) then we adjust the value toobtain an annualized return The nal columnpresents the average annual percentage returnfor each index One two and three asterisks

12 According to Ernst amp Young (1998) the tax yearcommences on January 1 in the United States CanadaGermany Japan and Sweden The tax year starts on April6 in Britain on July 1 in Australia on March 1 in SouthAfrica and on April 1 in New Zealand For Britain sincethe tax year ends on April 5 the tax-year dummy equals onefor the last trading day before April 5 and the rst vetrading days starting on April 5 or immediately thereafterThe tax-year dummy is de ned analogously for the othercountries in the sample

13 All of the climate data (cloud cover precipitation andtemperature) were obtained from the Climate Data Libraryoperated jointly by the International Research Institute forClimate Prediction and the Lamont-Doherty Earth Obser-vatory of Columbia University ingridldeocolumbiaeduWe are grateful to these organizations for making the dataavailable

TABLE 3mdashAVERAGE ANNUAL PERCENTAGE RETURN DUE

TO SAD AND DUE TO FALL DUMMY

Country

Annualreturn

due to SAD

Annualreturn

due to falldummy

Unconditionalannual return

United StatesSampP 500

92 236 63

United StatesNYSE

61 225 92

United StatesNASDAQ

175 281 125

United StatesAMEX

84 251 84

Sweden 135 269 171Britain 103 223 96Germany 82 243 65Canada 132 243 61New Zealand 105 266 33Japan 69 237 97Australia 57 05 88South Africa 175 221 146

Notes In calculating the average annual return due to SADfor a particular country we determine for each trading daythe value of the SAD variable (which varies between zeroand six for Sweden for example during the fall and winterand which equals zero otherwise) multiplied by that coun-tryrsquos SAD variable estimate (from Table 4) then we adjustthe value to obtain an annualized return Similarly in cal-culating the annual average return due to the fall dummy fora particular country we determine for each trading day thatcountryrsquos fall dummy variable estimate (from Table 4) mul-tiplied by the value of the fall dummy variable (one duringthe fall zero otherwise) then we adjust the value to obtainan annualized return In the case of the columns for theannualized returns due to the SAD and fall dummy vari-ables signi cance is based on t-tests on the parameterestimates from Table 4 In the case of the unconditionalreturn column signi cance is based on t-tests for a meandaily return different from zero

Signi cant at the 10-percent level one-sided Signi cant at the 5-percent level one-sided

Signi cant at the 1-percent level one-sided


indicate signi cance at the 10- 5- and 1-percent levels respectively based on one-sidedhypothesis tests For the annualized returns dueto the SAD variable and the fall dummy signi -cance is based on t-tests on the correspondingcoef cient estimates from estimating equation (5)(to be discussed below) upon which the calcula-tions of the annualized returns are based For theunconditional returns signi cance pertains to t-tests on daily returns differing from zero

There are some striking aspects of Table3 First the average annualized return due toSAD is positive in all countries ranging from57 percent to 175 percent For the most partcountries at latitudes closer to the equator tendto have lower less signi cant returns due toSAD than countries further from the equator(In many cases the return due to SAD exceedsthe entire unconditional annual return) Secondthe average annualized return due to the falldummy is negative in all countries except forAustralia Third the positive return due to SADcombined with the negative return due to thefall dummy suggests that on balance the season-ally asymmetric effects of SAD are shiftingreturns from the fall to the winter

Results from estimating equation (5) for eachof our 12 indices appear in Tables 4Andash4CNames of all the parameters from equation (5)are indicated in the rst column and estimatesfor each market appear in the cells under eachmarketrsquos name Below each parameter estimateis a heteroskedasticity-robust t-statistic14 Incases where a particular parameter was not es-timated (r1 andor r2 for some indices) a dash(mdash) appears (We only used as many laggeddepended variables as was required to eliminateresidual autocorrelation up to the 1-percentlevel of signi cance Tests for autocorrelationare discussed below) One two and three as-terisks indicate signi cance at the 10- 5- and1-percent levels respectively based on one-sided hypothesis tests

We see in Tables 4AndashC that the SAD coef- cient estimate is uniformly positive across allcountries and is signi cant in all countries ex-cept one The fall dummy coef cient estimate is

14 The standard errors are calculated using a modi cationof Halbert Whitersquos (1980) standard error estimator sug-gested by James G MacKinnon and White (1985) andrecommended for its sampling distribution properties

TABLE 4AmdashREGRESSION RESULTS FOR EACH

OF THE US INDICES

rt 5 m 1 r1rt2 1 1 r2rt2 2 1 mMondayDtMonday

1 mTaxDtTax 1 mSADSADt 1 mFallDt

Fall

1 mCloudCloudt 1 mPrecipitationPrecipitationt

1 mTemperatureTemperaturet 1 laquot

Panel A Parameter Estimates(Heteroskedasticity-robust t-tests)

ParameterSampP 500

41degNNYSE41degN

NASDAQ41degN

AMEX41degN

m 20049 0015 20017 0051(2045) (013) (2011) (047)

r1 0063 0151 0145 0269(354) (593) (493) (880)

r2 20042 mdash mdash mdash(2240) mdash mdash mdash

mMonday 20209 20124 20256 20280(2950) (2520) (2750) (2120)

mTax 0065 0010 0067 0183(114) (014) (072) (271)

mSAD 0038 0026 0071 0035(243) (161) (296) (234)

mFall 20058 20040 20134 20084(2220) (2140) (2330) (2320)

mCloud 0115 0046 0087 0021(074) (027) (040) (013)

mPrecipitation 20002 20001 20003 20002(2059) (2021) (2061) (2084)

mTemperature 0003 0001 0003 0001(180) (026) (135) (054)

Panel B Diagnostics

R2 0011 0027 0033 0091AR(10)

p-value 0136 0850 0023 0003

Notes This table reports coef cient estimates from runningthe indicated regression for each of the four indices consid-ered Returns (rt) are regressed on a constant (m) laggedreturns where necessary (one lag is required for all indicesexcept the SampP 500 which requires two) a dummy for thetrading day following the weekend (Dt

Monday) a dummy forthe last trading day and rst ve trading days of the tax year(Dt

Tax) the SAD measure (SADt 5 Ht 2 12 during falland winter 0 otherwise where Ht 5 number of hours ofnight) a dummy for trading days in the autumn (Dt

Fall)percentage cloud cover (Cloudt) millimeters of precipita-tion (Precipitationt) and temperature in degrees Celsius(Temperature t) All indices are value-weighted and do notinclude dividend distributions Beneath each indexrsquos namewe indicate the latitude of the city in which the exchange islocated

In Panel A we present parameter estimates with associ-ated t-statistics in parentheses immediately below (calcu-lated using heteroskedasticity-robust standard errors) Forcases where particular parameters were not estimated therelevant cells contain a dash (mdash) In Panel B we present theR2 for each regression as well as the p-value for a x2 test forautocorrelation up to ten lags




TABLE 4BmdashREGRESSION RESULTS FOR EACH OF SWEDENBRITAIN GERMANY AND CANADA



Fall


1 mTemperatureTemperaturet 1 laquo t


ParameterSweden59degN

Britain51degN

Germany50degN

Canada43degN

m 0267 0231 0097 20067(140) (136) (069) (2050)

r1 0110 0061 0057 0153(394) (134) (304) (464)

r2 mdash mdash mdash mdashmdash mdash mdash mdash

mMonday 20036 20117 20149 20131(2076) (2300) (2480) (2550)

mTax 0135 0146 0165 0034(084) (155) (167) (043)

mSAD 0028 0030 0025 0052(197) (203) (158) (324)

mFall 20113 20036 20070 20069(2200) (2080) (2190) (2210)

mCloud 20374 20271 20130 0168(2130) (2100) (2053) (063)

mPrecipitation 0001 20017 0001 20003(009) (2150) (010) (2088)

mTemperature 20001 20001 0001 0002(2017) (2030) (036) (116)

Panel B Diagnostics

R2 0017 0009 0008 0030AR(10)

p-value 0131 0218 0029 0019

Notes This table reports coef cient estimates from runningthe indicated regression for each of the four indices consid-ered Returns (rt) are regressed on a constant (m) laggedreturns where necessary a dummy for the trading day fol-lowing the weekend (Dt

Monday) a dummy for the last trad-ing day and rst ve trading days of the tax year (Dt

Tax) theSAD measure (SADt 5 Ht 2 12 during fall and winter 0otherwise where Ht 5 number of hours of night) a dummyfor trading days in the autumn (Dt

Fall) percentage cloudcover (Cloudt) millimeters of precipitation (Precipita-tiont) and temperature in degrees Celsius (Tempera-ture t) All indices are value-weighted and do not includedividend distributions Beneath each countryrsquos name weindicate the latitude of the city in which the exchange islocated




TABLE 4CmdashREGRESSION RESULTS FOR EACH OF NEW

ZEALAND JAPAN AUSTRALIA AND SOUTH AFRICA



Fall




ParameterNew Zealand

37degSJapan36degN

Australia34degS

SouthAfrica26degS

m 20400 0003 0106 20273(2073) (002) (048) (2140)

r1 mdash mdash 0089 0088mdash mdash (194) (363)


mMonday 20204 20040 20038 20123(2380) (2140) (2110) (2300)

mTax 20218 0009 0125 0012(150) (012) (160) (011)

mSAD 0047 0037 0029 0113(170) (155) (089) (162)

mFall 20108 20060 0007 20033(2220) (2190) (022) (2089)

mCloud 0426 0095 20328 0137(056) (058) (2100) (061)

mPrecipitation 0001 20004 20005 20001(043) (2110) (2220) (2026)

mTemperature 0011 20001 0005 0015(148) (2047) (080) (156)

Panel B Diagnostics

R2 0010 0002 0010 0010AR(10)

p-value 0972 0011 0203 0071

Notes This table reports coef cient estimates from runningthe indicated regression for each of the four indices consid-ered Returns (rt) are regressed on a constant (m) laggedreturns where necessary (New Zealand and Japan do notrequire lagged returns) a dummy for the trading day fol-lowing the weekend (Dt








negative in all countries except one and is sig-ni cantly negative in all cases except threeOverall this is consistent with a SAD-inducedseasonal pattern in returns as depressed andrisk-averse investors shun risky assets in the falland resume their risky holdings in the winterleading to returns in the fall which are lowerthan average and returns following the longestnight of the year which are higher than averageRecall from Table 3 that the magnitude andsigni cance of the SAD effect is broadly relatedto latitude countries at higher latitudes (wherethe seasonal variation in daylight is more ex-treme) tend to experience larger more signi -cant returns due to the SAD effect relative tothose closer to the equator

Regarding other aspects of the estimation we nd the Monday dummy and tax-loss dummy aresigni cant for many countries The parameter es-timates associated with cloud cover precipitationand temperature are typically insigni cant InPanel B of each table we present the R2 for eachregression as well as the p-value for a x2 testfor autocorrelation up to ten lags In all cases wefail to reject the null hypothesis of no residualautocorrelation at the 1-percent level with the ex-ception of the AMEX An expanded model con-trolling for autocorrelation in the AMEX indexproduces qualitatively identical results

B Trading Strategies

The results in Tables 3 and 4Andash4C suggestpotential gains to employing a trading strategybased on the SAD effect To explore this pos-sibility we provide an illustration of the returnsearned by an investor from various trading strat-egies for a sample pair of countries one fromeach hemisphere We select for our exampleSweden and Australia each being one of themost extremely located countries in its hemi-sphere and each having available roughly thesame length of returns data (starting in the early1980rsquos) Consider rst the benchmark ldquoneutralrdquoportfolio allocation strategy in which an inves-tor in the early 1980rsquos placed 50 percent of herportfolio in the Swedish index and 50 percent inthe Australian index Twenty years later theaverage annual return to this neutral strategywould have been 132 percent (using annualizedreturns based on the daily returns shown inTable 2) Next had the investor adopted a pro-

SAD portfolio allocation strategy in which shereallocated 100 percent of her portfolio twice ayear at fall and spring equinox placing hermoney in the Swedish market during the North-ern Hemispherersquos fall and winter then movingit into the Australian market for the SouthernHemispherersquos fall and winter her average an-nual return would have been 211 percent(which is 79 percent more than under the neu-tral strategy)15 By comparison had she in-stead allocated her portfolio across countries inorder to act against the SAD effect moving hermoney into the Swedish market for the NorthernHemispherersquos spring and summer and then intothe Australian market for the Southern Hemi-spherersquos spring and summer her average annualreturn would have been 52 percent (which is80 percent less than she would have earnedunder the neutral strategy)

Had the investor been willing and able toassume short positions she might have at-tempted to pro t from the SAD effect by short-ing the Swedish market during the NorthernHemispherersquos spring and summer and goinglong in the Australian market during the sametime (when it is fall and winter in the SouthernHemisphere) then going long in the Swedishmarket during the Northern Hemispherersquos falland winter while shorting the Australian mar-ket The average annual return per dollar in-vested in this strategy would have been 159percent Of course had she taken long and shortpositions in the two markets in a reverse patternacting against the SAD effect her average an-nual return would have been 2159 percentOverall we nd that by adopting a pro-SADstrategy the investor in our example wouldhave realized relatively substantial excess re-turns while trading against the SAD effectwould have been costly16 Interestingly for all

15 The returns for all the trading strategies other than theneutral strategy are based on the six-month returns corre-sponding to the fall and winter or the spring and summer asappropriate for the index in question For simplicity weneglect transaction costs

16 In considering pro-SAD trading strategies across othercountries we found the following Applying the pro-SADportfolio allocation strategy an investor would have en-joyed positive excess returns reallocating her funds betweenAustralia and all Northern Hemisphere indices as well asbetween New Zealand and all Northern Hemisphere mar-kets except the United States Pro-SAD trading strategies


the countries we consider the volatility of re-turns does not vary appreciably across thespringsummer and fallwinter periods suggest-ing that there is little difference in risk acrossthe trading strategies we consider

V Robustness Checks

All of the detailed estimation results de-scribed in this section are provided in the Ap-pendix (available from the authors)

A Maximum-Likelihood Model

In the previous section we addressed theissue of autocorrelation by introducing lags ofthe dependent variable and we addressed thepossibility of heteroskedasticity by usingWhite (1980) standard errors We have alsoestimated a maximum-likelihood modelwhich jointly models the mean and varianceof returns We controlled for heteroskedasticityusing the Sign-GARCH model of Lawrence RGlosten et al (1993) and produced robust t-testsusing the robust (to heteroskedasticity and non-normality) standard errors of Tim Bollerslev andJeffrey M Wooldridge (1992)17 With the excep-tion of some minor quantitative changes overallthe maximum-likelihood results are very similarto the results reported above Though we typically nd coef cients on the SAD variable and thetax-loss and fall dummies are slightly reduced inmagnitude we do still see large economicallymeaningful effects due to SAD

B Other Measures for SAD

As previously discussed theory does notspecify the exact form that the SAD measure

must take Therefore we considered some al-ternate measures including using the number ofhours of night normalized to lie between 0 and1 the number of hours of night normalized tolie between 21 and 11 and allowing the SADmeasure to take on nonzero values through allfour seasons Broad qualitative statements thatcan be made about the economically signi cantmagnitude sign and statistical signi cance ofthe SAD effect through the fall and winter areroughly the same across all measures weexplored

C SAD and Asymmetry AroundWinter Solstice

All of the results reported above were basedon allowing for asymmetry around winter sol-stice by using a dummy variable set to equal oneduring trading days in the fall We also exploredan alternative parameterization allowing thefall to differ from the winter by splitting theSAD measure into two separate regressors(One regressor was set to equal the value of theSAD measure during the fall and zero other-wise The other regressor was set to equal thevalue of the SAD measure during the winter andzero otherwise) There was no need for a falldummy variable in this case We found no qual-itative difference in results to those presented inthis paper With both types of parameteriza-tions we nd evidence of the same asymmetricSAD effects

We additionally explored the timing ofbreakpoints (around which point in time thefallwinter asymmetry would revolve) as wellas whether we should allow for any asymmetryat all Allowing for a breakpoint at winter sol-stice seemed best able to capture the asymmetryof the SAD effect Results using differentbreakpoints or using no breakpoint producebroadly supportive results

D Rede ning the Tax-Loss Variable

In the results presented above the tax-lossdummy variable equals one for a given countrywhen period t is in the last trading day or rst ve trading days of the tax year and equals zerootherwise consistent with what other studies inthe tax-loss literature have documented An-other possible speci cation is to de ne the

would have yielded a mix of positive and negative returnsfor reallocations between South Africa and Northern Hemi-sphere markets perhaps due to the fact that many largeSouth African companies are gold-producing companieswhich are cross-listed in London and New York Detailedresults on strategies based on all combinations of themarkets we consider are available on the Web at wwwmarkkamstracom or from the authors on request

17 The Sign-GARCH model was selected because amongcommonly applied methods it tends to work most reliablySee for example Robert F Engle and Victor K Ng (1993)and Donaldson and Kamstra (1997)


tax-loss dummy to equal one for all the tradingdays in the rst month of the tax year Whenthis alternate speci cation is employed theSAD effect is somewhat stronger and the tax-loss effect is somewhat weaker in signi cance

VI Market Segmentation and SAD Effects

To the extent that there is cross listing ofstocks from for example Australia that alsotrade in New York as American DepositaryReceipts (ADRs) or in other forms arbitragewould tend to dampen any potential SAD ef-fects in the much smaller Southern Hemispheremarkets Nevertheless we still nd evidence ofa SAD effect in the Southern Hemisphere de-spite any dampening that might be occurringAlso if the international capital markets werefully integrated there would be dampening ofthe SAD effect across the hemispheres inves-tors from the Northern Hemisphere would buyin the Southern Hemisphere at the very time thatthose in that hemisphere were selling and viceversa However the evidence as described byMaurice D Levi (1997) Karen K Lewis(1999) and others suggests that markets are notfully integrated there is a strong home-equitybias Market segmentation is also supported bycorrelations between national savings and in-vestment rates as shown by Martin Feldsteinand Charles Horioka (1980) these correlationsare higher than one would expect in an inte-grated international capital market Further-more even if international capital markets wereintegrated the dominant size of the NorthernHemisphere markets would mean that we wouldstill expect to see a SAD effect (albeit that of theNorthern Hemisphere)

VII Conclusion

The preponderance of the evidence in thispaper supports the existence of an importanteffect of seasonal affective disorder on stockmarket returns around the world Speci callyeven when controlling for the in uence of otherenvironmental factors and well-known marketseasonals we still nd a large and signi cantSAD effect in every northern country we con-sider In general the effect is greater the higherthe latitude Furthermore evidence suggests theimpact of SAD in the Southern Hemisphere is

out of phase by six months relative to the northas expected Overall results are robust to dif-ferent measures to capture the effect of SADand do not appear to be an artifact of heteroske-dastic patterns in stock returns

Supporting our argument is the fact that day-light has been shown in numerous clinical stud-ies to have a profound effect on peoplersquosmoods and in turn peoplersquos moods have beenfound to be related to risk aversion SAD is arecognized clinical diagnosis with recom-mended treatments including light therapymedication and behavior modi cation suffer-ers are urged to spend time outdoors or takevacations where daylight and sunlight are moreplentiful Of course we are not suggesting thesetreatments be applied to inuence market re-turns Rather we believe that we have identi edanother behavioral factor that should not beignored in explaining returns

REFERENCES

Akgiray Vedat ldquoConditional Heteroscedasticityin Time Series of Stock Returns Evidenceand Forecastsrdquo Journal of Business January1989 62(1) pp 55ndash80

Athanassakos George and Schnabel Jacques AldquoProfessional Portfolio Managers and theJanuary Effect Theory and Evidencerdquo Re-view of Financial Economics Fall 1994 4(1)pp 79ndash91

Avery David H Bolte Mary A Dager StephenR Wilson Laurence G Weyer MatthewCox Gary B and Dunner David L ldquoDawnSimulation Treatment of Winter DepressionA Controlled Studyrdquo American Journal ofPsychiatry January 1993 150(1) pp 113ndash17

Bagby R Michael Schuller Debra R LevittAnthony J Joffe Russel T and HarknessKate L ldquoSeasonal and Non-Seasonal Depres-sion and the Five-Factor Model of Personal-ityrdquo Journal of Affective Disorders June1996 38(2ndash3) pp 89ndash95

Bhardwaj Ravinder K and Brooks LeRoy DldquoThe January Anomaly Effects of Low SharePrices Transactions Costs and Bid-AskBiasrdquo Journal of Finance June 1992 47(2)pp 553ndash75

Bierwag Gerald O and Grove M A ldquoOnCapital Asset Prices Commentrdquo Journal


of Finance March 1965 20(1) pp 89ndash93

Bollerslev Tim and Wooldridge Jeffrey MldquoQuasi-maximum Likelihood Estimation andInference in Dynamic Models with Time-Varying Covariancesrdquo Econometric Re-views 1992 11(2) pp 143ndash72

Bouman Sven and Jacobsen Ben ldquoThe Hallow-een Indicator lsquoSell in May and Go AwayrsquoAnother Puzzlerdquo American Economic Re-view December 2002 92(5) pp 1618ndash35

Brown Philip Keim Donald B Kleidon AllanW and Marsh Terry A ldquoStock Return Sea-sonalities and the Tax-Loss Selling Hypoth-esis Analysis of the Arguments andAustralian Evidencerdquo Journal of FinancialEconomics June 1983 12(1) pp 105ndash27

Cao Melanie and Wei Jason ldquoStock MarketReturns A Temperature Anomalyrdquo Workingpaper University of Toronto November2001

Carton Solange Jouvent Roland BungenerCatherine and Widlocher D ldquoSensation Seek-ing and Depressive Moodrdquo Personality andIndividual Differences July 1992 13(7) pp843ndash49

Carton Solange Morand Pauline BungenerCatherine and Jouvent Roland ldquoSensation-Seeking and Emotional Disturbances in De-pression Relationships and EvolutionrdquoJournal of Affective Disorders June 199534(3) pp 219ndash25

Chang Eric C and Pinegar J Michael ldquoSea-sonal Fluctuations in Industrial Productionand Stock Market Seasonalsrdquo Journal of Fi-nancial and Quantitative Analysis March1989 24(1) pp 59ndash74

ldquoStock Market Seasonals and Pre-speci ed Multifactor Pricing RelationsrdquoJournal of Financial and Quantitative Anal-ysis December 1990 25(4) pp 517ndash33

Chen Nai-Fu Roll Richard and Ross Stephen AldquoEconomic Forces and the Stock MarketrdquoJournal of Business July 1986 59(3) pp383ndash403

Cohen Robert M Gross M Nordahl ThomasE Semple W E Oren D A and RosenthalNorman E ldquoPreliminary Data on the Meta-bolic Brain Pattern of Patients with WinterSeasonal Affective Disorderrdquo Archives ofGeneral Psychiatry July 1992 49(7) pp545ndash52

Dilsaver Steven C ldquoOnset of Winter DepressionEarlier than Generally Thoughtrdquo Journal ofClinical Psychiatry June 1990 51(6) p 258

Donaldson R Glen and Kamstra Mark J ldquoAnArti cial Neural NetworkmdashGARCH Modelfor International Stock Return VolatilityrdquoJournal of Empirical Finance January 19974(1) pp 17ndash46

Eisenberg Amy E Baron Jonathan and Selig-man Martin E P ldquoIndividual Differences inRisk Aversion and Anxietyrdquo Working paperDepartment of Psychology University ofPennsylvania 1998

Engle Robert F and Ng Victor K ldquoMeasuringand Testing the Impact of News on Volatil-ityrdquo Journal of Finance December 199348(5) pp 1749ndash78

Ernst amp Young International Ltd 1999 world-wide executive tax guide New York Ernst ampYoung International Ltd September 1998

Faedda Gianni L Tondo Leonardo TeicherM H Baldessarini Ross J Gelbard H Aand Floris G F ldquoSeasonal Mood DisordersPatterns in Mania and Depressionrdquo Archivesof General Psychiatry January 1993 50(1)pp 17ndash23

Feldstein Martin and Horioka Charles ldquoDomes-tic Saving and International Capital FlowsrdquoEconomic Journal June 1980 90(358) pp314ndash29

Glosten Lawrence R Jagannathan Ravi andRunkle David E ldquoThe Relationship BetweenExpected Value and the Volatility of theNominal Excess Return on Stocksrdquo Journalof Finance December 1993 48(5) pp1779ndash801

Hicks John R ldquoLiquidityrdquo Economic JournalDecember 1963 72(288) pp 789ndash802

Hirshleifer David and Shumway Tyler ldquoGoodDay Sunshine Stock Returns and theWeatherrdquo Journal of Finance 2003

Horvath Paula and Zuckerman Marvin ldquoSensa-tion Seeking Risk Appraisal and Risky Behav-iorrdquo Personality and Individual DifferencesJanuary 1993 14(1) pp 41ndash52

Jones Steven L Lee Winston and ApenbrinkRudolf ldquoNew Evidence on the January Effectbefore Income Taxesrdquo Journal of FinanceDecember 1991 46(5) pp 1909ndash24

Kamstra Mark J Kramer Lisa A and LeviMaurice D ldquoWinter Blues Seasonal Affec-tive Disorder (SAD) and Stock Market


Returnsrdquo Working paper University of Brit-ish Columbia January 2000

Kato Kiyoshi and Schallheim James S ldquoSeasonaland Size Anomalies in the Japanese StockMarketrdquo Journal of Financial and Quantita-tive Analysis June 1985 20(2) pp 243ndash60

Kramer Charles ldquoMacroeconomic Seasonalityand the January Effectrdquo Journal of FinanceDecember 1994 49(5) pp 1883ndash91

Leonhardt Georg Wirz-Justice Anna KrauchiKurt Graw Peter Wunder Dorothea andHaug Hans-Joachim ldquoLong-Term Follow-upof Depression in Seasonal Affective Disor-derrdquo Comparative Psychiatry NovemberndashDecember 1994 35(6) pp 457ndash64

Levi Maurice D ldquoAre Capital Markets Interna-tionally Integratedrdquo in Thomas J Courcheneand Edwin H Neave Reforming the Cana-dian nancial sector Kingston OntarioQueens University Press 1997 pp 63ndash84

Lewis Karen K ldquoTrying to Explain Home Biasin Equities and Consumptionrdquo Journal ofEconomic Literature June 1999 37(2) pp571ndash608

Ligon James A ldquoA Simultaneous Test of Com-peting Theories Regarding the January Ef-fectrdquo Journal of Financial Research Spring1997 20(1) pp 13ndash32

MacKinnon James G and White HalbertldquoSome Heteroskedasticity-Consistent Co-variance Matrix Estimators with ImprovedFinite Sample Propertiesrdquo Journal of Econo-metrics September 1985 29(3) pp 305ndash25

Marvel Gregory A and Hartmann Barbara RldquoAn lsquoEconomicrsquo Theory of Addiction Hypo-mania and Sensation Seekingrdquo InternationalJournal of the Addictions 1986 21(4 ndash5) pp495ndash508

Mayo Clinic Seasonal affective disorder June2002 online at wwwmayocliniccom

Meesters Ybe Jansen Jaap H Beersma Dom-ien G Bouhuys A L Netty and van denHoofdakker Rudi H ldquoEarly Light TreatmentCan Prevent an Emerging Winter Depressionfrom Developing into a Full-Blown Depres-sionrdquo Journal of Affective Disorders Sep-tember 1993 29(1) pp 41ndash47

Molin Jeanne Mellerup Erling Bolwig TomScheike Thomas and Dam Henrik ldquoThe In- uence of Climate on Development of Win-ter Depressionrdquo Journal of AffectiveDisorders April 1996 37(2ndash3) pp 151ndash55

Pagan Adrian and Schwert William ldquoAlterna-tive Models for Conditional Stock Volatil-ityrdquo Journal of Econometrics July 199045(1ndash2) pp 267ndash90

Palinkas Lawrence A and Houseal Matt ldquoStagesof Change in Mood and Behavior During aWinter in Antarcticardquo Environment and Be-havior January 2000 32(1) pp 128ndash41

Palinkas Lawrence A Houseal Matt andRosenthal Norman E ldquoSubsyndromal Sea-sonal Affective Disorder in AntarcticardquoJournal of Nervous and Mental Disease Sep-tember 1996 184(9) pp 530ndash34

Ritter Jay R ldquoThe Buying and Selling Behaviorof Individual Investors at the Turn of theYearrdquo Journal of Finance July 1988 43(3)pp 701ndash17

Rosenthal Norman E Winter blues Seasonalaffective disorder What it is and how toovercome it 2nd Ed New York GuilfordPress 1998

Saunders Edward M ldquoStock Prices and WallStreet Weatherrdquo American Economic Re-view December 1993 83(5) pp 1337ndash45

Susmel Raul and Engle Robert F ldquoHourly Vol-atility Spillovers between International Eq-uity Marketsrdquo Journal of InternationalMoney and Finance February 1994 13(1)pp 3ndash25

Thaler Richard H ldquoAnomalies The JanuaryEffectrdquo Journal of Economic PerspectivesSummer 1987 1(1) pp 197ndash201

Tinic Seha M and West Richard R ldquoRisk andReturn January vs the Rest of the YearrdquoJournal of Financial Economics December1984 13(4) pp 561ndash74

Tokunaga Howard ldquoThe Use and Abuse ofConsumer Credit Application of Psycholog-ical Theory and Researchrdquo Journal of Eco-nomic Psychology June 1993 14(2) pp285ndash316

Van Horne James C Financial market rates and ows (2nd edition) Englewood Cliffs NJPrentice Hall 1984

White Halbert ldquoA Heteroskedasticity-Consis-tent Covariance Matrix Estimator and a DirectTest for Heteroskedasticityrdquo EconometricaMay 1980 48(4) pp 817ndash38

Williams Robert J and Schmidt G G ldquoFre-quency of Seasonal Affective DisorderAmong Individuals Seeking Treatment at aNorthern Canadian Medical Health Centerrdquo


Psychiatry Research January 1993 46(1)pp 41ndash45

Wong Alan and Carducci Bernardo ldquoSensationSeeking and Financial Risk Taking in Every-day Money Mattersrdquo Journal of Business andPsychology Summer 1991 5(4) pp 525ndash30

Young Michael A Meaden Patricia M FoggLouis F Cherin Eva A and Eastman Char-mane I ldquoWhich Environmental Variables AreRelated to the Onset of Seasonal AffectiveDisorderrdquo Journal of Abnormal PsychologyNovember 1997 106(4) pp 554ndash62

Zuckerman Marvin ldquoSensation Seeking AComparative Approach to a Human TraitrdquoBehavioral and Brain Sciences 1984 7(3)pp 413ndash71

Behavioral expression and biosocialbases of sensation seeking Cambridge Cam-bridge University Press 1994

Zuckerman Marvin Buchsbaum Monte S andMurphy Dennis L ldquoSensation Seekingand Its Biological Correlatesrdquo Psycholog-ical Bulletin January 1980 88(1) pp 187ndash214


diminished daylight take on a particularly se-vere form among the approximately 10 millionAmericans who are af icted with seasonal af-fective disorder where ldquoaffectiverdquo means emo-tional A further 15 million suffer a milder formldquowinter bluesrdquo The problem is also extensivelydocumented outside the United States withsimilar proportions of sufferers in countriesaround the world2 Jeanne Molin et al (1996)and Michael A Young et al (1997) provideevidence that seasonal depression is related tohours of daylight and hence the effects of SADmay be more pronounced in countries at moreextreme latitudes where winter and fall days arerelatively shorter

SAD is clinically de ned as a form of majordepressive disorder3 While usually described interms of prolonged periods of sadness and pro-found chronic fatigue evidence suggests thatSAD is connected to serotonin dysregulation inthe brain Furthermore positron emission to-mography (PET) scans reveal abnormalities inthe prefrontal and parietal cortex areas due todiminished daylight as described in the Na-tional Institute of Mental Health study byRobert M Cohen et al (1992) That is thereappears to be a physiological source to the de-pression related to shorter days SAD symptomsinclude dif culty concentrating loss of interestin sex social withdrawal loss of energy leth-argy sleep disturbance and carbohydrate orsugar craving often accompanied by weightgain4 For those affected the annual onset ofSAD symptoms can occur as early as Septem-ber around the time of autumn equinox SeeSteven C Dilsaver (1990) for example

Experimental research in psychology hasdocumented a direct link between depressionand heightened risk aversion This link is estab-lished by rst providing a measure of risk-

taking tendency in the form of a scale ofldquosensation-seekingrdquo propensity the most widelyused of which was developed by Marvin Zuck-erman (1984) The scale is then correlated withvarious biological and psychological phenom-ena as shown for example by Zuckerman et al(1980) Sensation-seeking measures used tojudge the propensity to take risk have beenextensively documented as reliable measures ofrisk-taking tendency in nancial decision-making settings by Alan Wong and BernardoCarducci (1991) Paula Horvath and Zuckerman(1993) and Howard Tokunaga (1993) amongothers When the willingness to take risk isrelated to measured levels of anxiety and de-pression there is a distinct tendency for greateranxiety or depression to be associated with re-duced sensation seeking and reduced generalwillingness to take risk as shown by Zucker-man (1984 1994) Gregory A Marvel and Bar-bara R Hartman (1986) Solange Carton et al(1992) and Carton et al (1995) In a furtherstudy of depression and risk aversion Amy EEisenberg et al (1998) conducted experimentsin which subjects differing in degree of depres-sion were faced with a series of choices betweenpairs of risky and safe options including someof a nancial nature By setting the choices suchthat in some cases the risky option was thedefault (not requiring action) and in other casesthe safe option was the default the researcherswere able to distinguish risk aversion from pas-sivity depressive symptoms correlated withrisk aversion

The psychological studies cited abovestrongly support the view that the depressionassociated with shorter days translates into agreater degree of risk aversion leading to test-able hypotheses in the context of stock marketreturns Those market participants directly af-fected by SAD can in uence overall marketreturns according to the well-established princi-ple that market equilibrium occurs at priceswhere marginal buyers are willing to exchangewith marginal sellers aggregate demands andsupplies for risky versus riskless assets canthereby affect equilibrium risk premia5 The

2 For example the frequency of SAD in northern Canadais documented by Robert J Williams and G G Schmidt(1993) The incidence of SAD in Italy is discussed byGianni L Faedda et al (1993) There is even evidence fromthe Mayo Clinic (2002) that SAD occurs in countries asclose to the equator as India These and others studiessuggest approximately 10 percent of people suffer fromSAD

3 See for example David H Avery et al (1993) YbeMeesters et al (1993) Georg Leonhardt et al (1994) and RMichael Bagby et al (1996)

4 Mayo Clinic (2002)

5 For further details on the impact of the marginal traderon market equilibria see the classic papers by John R Hicks(1963) and Gerald O Bierwag and M A Grove (1965) as






























0024 112 22047 1537 2035 1890


0035 084 21836 879 2116 2876


0047 110 21135 1057 2048 1208


0032 084 21275 1056 2086 1641


0063 125 28986 978 2025 602


0037 101 21303 760 2093 1229


0025 110 21371 887 2050 862


0023 085 21029 988 2075 1397


0013 097 21331 948 2086 1878

Japan19500405ndash20011206

0037 112 21614 1243 2034 1082


0033 100 22876 979 2489 13149


0054 134 21453 1357 2072 969






























0 otherwise



(2)

l t 5 04102 z sin X 2p

365D ~ julian t 2 8025






(3)

Ht 5


360 D tan~lt



360 D tan~lt







0 otherwise




A Estimation


(5)



Fall

1 mCloud Cloud t









13







Country

Annualreturn

due to SAD

Annualreturn

due to falldummy



92 236 63

United StatesNYSE

61 225 92

United StatesNASDAQ

175 281 125

United StatesAMEX

84 251 84












OF THE US INDICES



Fall




ParameterSampP 500

41degNNYSE41degN

NASDAQ41degN

AMEX41degN

m 20049 0015 20017 0051(2045) (013) (2011) (047)

r1 0063 0151 0145 0269(354) (593) (493) (880)


mMonday 20209 20124 20256 20280(2950) (2520) (2750) (2120)

mTax 0065 0010 0067 0183(114) (014) (072) (271)

mSAD 0038 0026 0071 0035(243) (161) (296) (234)

mFall 20058 20040 20134 20084(2220) (2140) (2330) (2320)

mCloud 0115 0046 0087 0021(074) (027) (040) (013)

mPrecipitation 20002 20001 20003 20002(2059) (2021) (2061) (2084)

mTemperature 0003 0001 0003 0001(180) (026) (135) (054)

Panel B Diagnostics

R2 0011 0027 0033 0091AR(10)

p-value 0136 0850 0023 0003












Fall





Britain51degN

Germany50degN

Canada43degN

m 0267 0231 0097 20067(140) (136) (069) (2050)

r1 0110 0061 0057 0153(394) (134) (304) (464)


mMonday 20036 20117 20149 20131(2076) (2300) (2480) (2550)

mTax 0135 0146 0165 0034(084) (155) (167) (043)

mSAD 0028 0030 0025 0052(197) (203) (158) (324)

mFall 20113 20036 20070 20069(2200) (2080) (2190) (2210)

mCloud 20374 20271 20130 0168(2130) (2100) (2053) (063)

mPrecipitation 0001 20017 0001 20003(009) (2150) (010) (2088)

mTemperature 20001 20001 0001 0002(2017) (2030) (036) (116)

Panel B Diagnostics

R2 0017 0009 0008 0030AR(10)

p-value 0131 0218 0029 0019












Fall





37degSJapan36degN

Australia34degS

SouthAfrica26degS

m 20400 0003 0106 20273(2073) (002) (048) (2140)



mMonday 20204 20040 20038 20123(2380) (2140) (2110) (2300)

mTax 20218 0009 0125 0012(150) (012) (160) (011)

mSAD 0047 0037 0029 0113(170) (155) (089) (162)

mFall 20108 20060 0007 20033(2220) (2190) (022) (2089)

mCloud 0426 0095 20328 0137(056) (058) (2100) (061)

mPrecipitation 0001 20004 20005 20001(043) (2110) (2220) (2026)

mTemperature 0011 20001 0005 0015(148) (2047) (080) (156)

Panel B Diagnostics

R2 0010 0002 0010 0010AR(10)

p-value 0972 0011 0203 0071



















V Robustness Checks


















VII Conclusion




REFERENCES






























































































0024 112 22047 1537 2035 1890


0035 084 21836 879 2116 2876


0047 110 21135 1057 2048 1208


0032 084 21275 1056 2086 1641


0063 125 28986 978 2025 602


0037 101 21303 760 2093 1229


0025 110 21371 887 2050 862


0023 085 21029 988 2075 1397


0013 097 21331 948 2086 1878

Japan19500405ndash20011206

0037 112 21614 1243 2034 1082


0033 100 22876 979 2489 13149


0054 134 21453 1357 2072 969






























0 otherwise



(2)

l t 5 04102 z sin X 2p

365D ~ julian t 2 8025






(3)

Ht 5


360 D tan~lt



360 D tan~lt







0 otherwise




A Estimation


(5)



Fall

1 mCloud Cloud t









13







Country

Annualreturn

due to SAD

Annualreturn

due to falldummy



92 236 63

United StatesNYSE

61 225 92

United StatesNASDAQ

175 281 125

United StatesAMEX

84 251 84












OF THE US INDICES



Fall




ParameterSampP 500

41degNNYSE41degN

NASDAQ41degN

AMEX41degN

m 20049 0015 20017 0051(2045) (013) (2011) (047)

r1 0063 0151 0145 0269(354) (593) (493) (880)


mMonday 20209 20124 20256 20280(2950) (2520) (2750) (2120)

mTax 0065 0010 0067 0183(114) (014) (072) (271)

mSAD 0038 0026 0071 0035(243) (161) (296) (234)

mFall 20058 20040 20134 20084(2220) (2140) (2330) (2320)

mCloud 0115 0046 0087 0021(074) (027) (040) (013)

mPrecipitation 20002 20001 20003 20002(2059) (2021) (2061) (2084)

mTemperature 0003 0001 0003 0001(180) (026) (135) (054)

Panel B Diagnostics

R2 0011 0027 0033 0091AR(10)

p-value 0136 0850 0023 0003












Fall





Britain51degN

Germany50degN

Canada43degN

m 0267 0231 0097 20067(140) (136) (069) (2050)

r1 0110 0061 0057 0153(394) (134) (304) (464)


mMonday 20036 20117 20149 20131(2076) (2300) (2480) (2550)

mTax 0135 0146 0165 0034(084) (155) (167) (043)

mSAD 0028 0030 0025 0052(197) (203) (158) (324)

mFall 20113 20036 20070 20069(2200) (2080) (2190) (2210)

mCloud 20374 20271 20130 0168(2130) (2100) (2053) (063)

mPrecipitation 0001 20017 0001 20003(009) (2150) (010) (2088)

mTemperature 20001 20001 0001 0002(2017) (2030) (036) (116)

Panel B Diagnostics

R2 0017 0009 0008 0030AR(10)

p-value 0131 0218 0029 0019












Fall





37degSJapan36degN

Australia34degS

SouthAfrica26degS

m 20400 0003 0106 20273(2073) (002) (048) (2140)



mMonday 20204 20040 20038 20123(2380) (2140) (2110) (2300)

mTax 20218 0009 0125 0012(150) (012) (160) (011)

mSAD 0047 0037 0029 0113(170) (155) (089) (162)

mFall 20108 20060 0007 20033(2220) (2190) (022) (2089)

mCloud 0426 0095 20328 0137(056) (058) (2100) (061)

mPrecipitation 0001 20004 20005 20001(043) (2110) (2220) (2026)

mTemperature 0011 20001 0005 0015(148) (2047) (080) (156)

Panel B Diagnostics

R2 0010 0002 0010 0010AR(10)

p-value 0972 0011 0203 0071



















V Robustness Checks


















VII Conclusion




REFERENCES





























































































0 otherwise



(2)

l t 5 04102 z sin X 2p

365D ~ julian t 2 8025






(3)

Ht 5


360 D tan~lt



360 D tan~lt







0 otherwise




A Estimation


(5)



Fall

1 mCloud Cloud t









13







Country

Annualreturn

due to SAD

Annualreturn

due to falldummy



92 236 63

United StatesNYSE

61 225 92

United StatesNASDAQ

175 281 125

United StatesAMEX

84 251 84












OF THE US INDICES



Fall




ParameterSampP 500

41degNNYSE41degN

NASDAQ41degN

AMEX41degN

m 20049 0015 20017 0051(2045) (013) (2011) (047)

r1 0063 0151 0145 0269(354) (593) (493) (880)


mMonday 20209 20124 20256 20280(2950) (2520) (2750) (2120)

mTax 0065 0010 0067 0183(114) (014) (072) (271)

mSAD 0038 0026 0071 0035(243) (161) (296) (234)

mFall 20058 20040 20134 20084(2220) (2140) (2330) (2320)

mCloud 0115 0046 0087 0021(074) (027) (040) (013)

mPrecipitation 20002 20001 20003 20002(2059) (2021) (2061) (2084)

mTemperature 0003 0001 0003 0001(180) (026) (135) (054)

Panel B Diagnostics

R2 0011 0027 0033 0091AR(10)

p-value 0136 0850 0023 0003












Fall





Britain51degN

Germany50degN

Canada43degN

m 0267 0231 0097 20067(140) (136) (069) (2050)

r1 0110 0061 0057 0153(394) (134) (304) (464)


mMonday 20036 20117 20149 20131(2076) (2300) (2480) (2550)

mTax 0135 0146 0165 0034(084) (155) (167) (043)

mSAD 0028 0030 0025 0052(197) (203) (158) (324)

mFall 20113 20036 20070 20069(2200) (2080) (2190) (2210)

mCloud 20374 20271 20130 0168(2130) (2100) (2053) (063)

mPrecipitation 0001 20017 0001 20003(009) (2150) (010) (2088)

mTemperature 20001 20001 0001 0002(2017) (2030) (036) (116)

Panel B Diagnostics

R2 0017 0009 0008 0030AR(10)

p-value 0131 0218 0029 0019












Fall





37degSJapan36degN

Australia34degS

SouthAfrica26degS

m 20400 0003 0106 20273(2073) (002) (048) (2140)



mMonday 20204 20040 20038 20123(2380) (2140) (2110) (2300)

mTax 20218 0009 0125 0012(150) (012) (160) (011)

mSAD 0047 0037 0029 0113(170) (155) (089) (162)

mFall 20108 20060 0007 20033(2220) (2190) (022) (2089)

mCloud 0426 0095 20328 0137(056) (058) (2100) (061)

mPrecipitation 0001 20004 20005 20001(043) (2110) (2220) (2026)

mTemperature 0011 20001 0005 0015(148) (2047) (080) (156)

Panel B Diagnostics

R2 0010 0002 0010 0010AR(10)

p-value 0972 0011 0203 0071



















V Robustness Checks


















VII Conclusion




REFERENCES



































































(3)

Ht 5


360 D tan~lt



360 D tan~lt







0 otherwise




A Estimation


(5)



Fall

1 mCloud Cloud t









13







Country

Annualreturn

due to SAD

Annualreturn

due to falldummy



92 236 63

United StatesNYSE

61 225 92

United StatesNASDAQ

175 281 125

United StatesAMEX

84 251 84












OF THE US INDICES



Fall




ParameterSampP 500

41degNNYSE41degN

NASDAQ41degN

AMEX41degN

m 20049 0015 20017 0051(2045) (013) (2011) (047)

r1 0063 0151 0145 0269(354) (593) (493) (880)


mMonday 20209 20124 20256 20280(2950) (2520) (2750) (2120)

mTax 0065 0010 0067 0183(114) (014) (072) (271)

mSAD 0038 0026 0071 0035(243) (161) (296) (234)

mFall 20058 20040 20134 20084(2220) (2140) (2330) (2320)

mCloud 0115 0046 0087 0021(074) (027) (040) (013)

mPrecipitation 20002 20001 20003 20002(2059) (2021) (2061) (2084)

mTemperature 0003 0001 0003 0001(180) (026) (135) (054)

Panel B Diagnostics

R2 0011 0027 0033 0091AR(10)

p-value 0136 0850 0023 0003












Fall





Britain51degN

Germany50degN

Canada43degN

m 0267 0231 0097 20067(140) (136) (069) (2050)

r1 0110 0061 0057 0153(394) (134) (304) (464)


mMonday 20036 20117 20149 20131(2076) (2300) (2480) (2550)

mTax 0135 0146 0165 0034(084) (155) (167) (043)

mSAD 0028 0030 0025 0052(197) (203) (158) (324)

mFall 20113 20036 20070 20069(2200) (2080) (2190) (2210)

mCloud 20374 20271 20130 0168(2130) (2100) (2053) (063)

mPrecipitation 0001 20017 0001 20003(009) (2150) (010) (2088)

mTemperature 20001 20001 0001 0002(2017) (2030) (036) (116)

Panel B Diagnostics

R2 0017 0009 0008 0030AR(10)

p-value 0131 0218 0029 0019












Fall





37degSJapan36degN

Australia34degS

SouthAfrica26degS

m 20400 0003 0106 20273(2073) (002) (048) (2140)



mMonday 20204 20040 20038 20123(2380) (2140) (2110) (2300)

mTax 20218 0009 0125 0012(150) (012) (160) (011)

mSAD 0047 0037 0029 0113(170) (155) (089) (162)

mFall 20108 20060 0007 20033(2220) (2190) (022) (2089)

mCloud 0426 0095 20328 0137(056) (058) (2100) (061)

mPrecipitation 0001 20004 20005 20001(043) (2110) (2220) (2026)

mTemperature 0011 20001 0005 0015(148) (2047) (080) (156)

Panel B Diagnostics

R2 0010 0002 0010 0010AR(10)

p-value 0972 0011 0203 0071



















V Robustness Checks


















VII Conclusion




REFERENCES





































































13







Country

Annualreturn

due to SAD

Annualreturn

due to falldummy



92 236 63

United StatesNYSE

61 225 92

United StatesNASDAQ

175 281 125

United StatesAMEX

84 251 84












OF THE US INDICES



Fall




ParameterSampP 500

41degNNYSE41degN

NASDAQ41degN

AMEX41degN

m 20049 0015 20017 0051(2045) (013) (2011) (047)

r1 0063 0151 0145 0269(354) (593) (493) (880)


mMonday 20209 20124 20256 20280(2950) (2520) (2750) (2120)

mTax 0065 0010 0067 0183(114) (014) (072) (271)

mSAD 0038 0026 0071 0035(243) (161) (296) (234)

mFall 20058 20040 20134 20084(2220) (2140) (2330) (2320)

mCloud 0115 0046 0087 0021(074) (027) (040) (013)

mPrecipitation 20002 20001 20003 20002(2059) (2021) (2061) (2084)

mTemperature 0003 0001 0003 0001(180) (026) (135) (054)

Panel B Diagnostics

R2 0011 0027 0033 0091AR(10)

p-value 0136 0850 0023 0003












Fall





Britain51degN

Germany50degN

Canada43degN

m 0267 0231 0097 20067(140) (136) (069) (2050)

r1 0110 0061 0057 0153(394) (134) (304) (464)


mMonday 20036 20117 20149 20131(2076) (2300) (2480) (2550)

mTax 0135 0146 0165 0034(084) (155) (167) (043)

mSAD 0028 0030 0025 0052(197) (203) (158) (324)

mFall 20113 20036 20070 20069(2200) (2080) (2190) (2210)

mCloud 20374 20271 20130 0168(2130) (2100) (2053) (063)

mPrecipitation 0001 20017 0001 20003(009) (2150) (010) (2088)

mTemperature 20001 20001 0001 0002(2017) (2030) (036) (116)

Panel B Diagnostics

R2 0017 0009 0008 0030AR(10)

p-value 0131 0218 0029 0019












Fall





37degSJapan36degN

Australia34degS

SouthAfrica26degS

m 20400 0003 0106 20273(2073) (002) (048) (2140)



mMonday 20204 20040 20038 20123(2380) (2140) (2110) (2300)

mTax 20218 0009 0125 0012(150) (012) (160) (011)

mSAD 0047 0037 0029 0113(170) (155) (089) (162)

mFall 20108 20060 0007 20033(2220) (2190) (022) (2089)

mCloud 0426 0095 20328 0137(056) (058) (2100) (061)

mPrecipitation 0001 20004 20005 20001(043) (2110) (2220) (2026)

mTemperature 0011 20001 0005 0015(148) (2047) (080) (156)

Panel B Diagnostics

R2 0010 0002 0010 0010AR(10)

p-value 0972 0011 0203 0071



















V Robustness Checks


















VII Conclusion




REFERENCES








































































OF THE US INDICES



Fall




ParameterSampP 500

41degNNYSE41degN

NASDAQ41degN

AMEX41degN

m 20049 0015 20017 0051(2045) (013) (2011) (047)

r1 0063 0151 0145 0269(354) (593) (493) (880)


mMonday 20209 20124 20256 20280(2950) (2520) (2750) (2120)

mTax 0065 0010 0067 0183(114) (014) (072) (271)

mSAD 0038 0026 0071 0035(243) (161) (296) (234)

mFall 20058 20040 20134 20084(2220) (2140) (2330) (2320)

mCloud 0115 0046 0087 0021(074) (027) (040) (013)

mPrecipitation 20002 20001 20003 20002(2059) (2021) (2061) (2084)

mTemperature 0003 0001 0003 0001(180) (026) (135) (054)

Panel B Diagnostics

R2 0011 0027 0033 0091AR(10)

p-value 0136 0850 0023 0003












Fall





Britain51degN

Germany50degN

Canada43degN

m 0267 0231 0097 20067(140) (136) (069) (2050)

r1 0110 0061 0057 0153(394) (134) (304) (464)


mMonday 20036 20117 20149 20131(2076) (2300) (2480) (2550)

mTax 0135 0146 0165 0034(084) (155) (167) (043)

mSAD 0028 0030 0025 0052(197) (203) (158) (324)

mFall 20113 20036 20070 20069(2200) (2080) (2190) (2210)

mCloud 20374 20271 20130 0168(2130) (2100) (2053) (063)

mPrecipitation 0001 20017 0001 20003(009) (2150) (010) (2088)

mTemperature 20001 20001 0001 0002(2017) (2030) (036) (116)

Panel B Diagnostics

R2 0017 0009 0008 0030AR(10)

p-value 0131 0218 0029 0019












Fall





37degSJapan36degN

Australia34degS

SouthAfrica26degS

m 20400 0003 0106 20273(2073) (002) (048) (2140)



mMonday 20204 20040 20038 20123(2380) (2140) (2110) (2300)

mTax 20218 0009 0125 0012(150) (012) (160) (011)

mSAD 0047 0037 0029 0113(170) (155) (089) (162)

mFall 20108 20060 0007 20033(2220) (2190) (022) (2089)

mCloud 0426 0095 20328 0137(056) (058) (2100) (061)

mPrecipitation 0001 20004 20005 20001(043) (2110) (2220) (2026)

mTemperature 0011 20001 0005 0015(148) (2047) (080) (156)

Panel B Diagnostics

R2 0010 0002 0010 0010AR(10)

p-value 0972 0011 0203 0071



















V Robustness Checks


















VII Conclusion




REFERENCES





































































Fall





Britain51degN

Germany50degN

Canada43degN

m 0267 0231 0097 20067(140) (136) (069) (2050)

r1 0110 0061 0057 0153(394) (134) (304) (464)


mMonday 20036 20117 20149 20131(2076) (2300) (2480) (2550)

mTax 0135 0146 0165 0034(084) (155) (167) (043)

mSAD 0028 0030 0025 0052(197) (203) (158) (324)

mFall 20113 20036 20070 20069(2200) (2080) (2190) (2210)

mCloud 20374 20271 20130 0168(2130) (2100) (2053) (063)

mPrecipitation 0001 20017 0001 20003(009) (2150) (010) (2088)

mTemperature 20001 20001 0001 0002(2017) (2030) (036) (116)

Panel B Diagnostics

R2 0017 0009 0008 0030AR(10)

p-value 0131 0218 0029 0019












Fall





37degSJapan36degN

Australia34degS

SouthAfrica26degS

m 20400 0003 0106 20273(2073) (002) (048) (2140)



mMonday 20204 20040 20038 20123(2380) (2140) (2110) (2300)

mTax 20218 0009 0125 0012(150) (012) (160) (011)

mSAD 0047 0037 0029 0113(170) (155) (089) (162)

mFall 20108 20060 0007 20033(2220) (2190) (022) (2089)

mCloud 0426 0095 20328 0137(056) (058) (2100) (061)

mPrecipitation 0001 20004 20005 20001(043) (2110) (2220) (2026)

mTemperature 0011 20001 0005 0015(148) (2047) (080) (156)

Panel B Diagnostics

R2 0010 0002 0010 0010AR(10)

p-value 0972 0011 0203 0071



















V Robustness Checks


















VII Conclusion




REFERENCES












































































V Robustness Checks


















VII Conclusion




REFERENCES





































































VII Conclusion




REFERENCES


































































Winter Blues: A SAD Stock Market Cycle - Lisa Kramerlisakramer.com/aer-sad.pdf · Winter Blues: A...

Documents

Transcript of Winter Blues: A SAD Stock Market Cycle - Lisa Kramerlisakramer.com/aer-sad.pdf · Winter Blues: A...